MARC2 Puzzle Inspector

▶ Task 1: "A narcissistic painting reproduces itself wherever it sees i ... [18 chars truncated]" k=1 alts: 0/0 007bbfb7

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Example 5

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Literal Description

See: The input is a 3×3 grid containing some colored cells and some black (empty) cells. The colored cells all share one color.

Do: Create a 9×9 output grid initialized to all black. Divide it into a 3×3 arrangement of 3×3 blocks (block at row i, column j occupies output rows 3i to 3i+2 and columns 3j to 3j+2). For each cell (i, j) in the input: if the cell is colored, paste a complete copy of the entire 3×3 input grid into the corresponding 3×3 block of the output. If the cell is black, leave that block entirely black.

Grid: The input grid is always 3×3. The output grid is always 9×9, consisting of a 3×3 tiling of 3×3 blocks. The background color is black (.).

Figurative Descriptions (1 variants)

"A narcissistic painting reproduces itself wherever it sees its own reflection."

qwen3.6-35b: k=1

See: A tiny 3×3 canvas holds a scattered portrait painted in a single color against darkness. Each colored cell is a mirror; each black cell is a curtain drawn shut.

Do: The painting gazes into a 3×3 hall of mirrors. Wherever a mirror hangs, the painting sees its own full reflection staring back — a faithful copy of itself. Where a curtain is drawn, only darkness remains. The hall assembles these reflections and shadows into one grand mosaic.

Grid: The intimate canvas is 3×3. The hall of mirrors expands to 9×9 — three reflections wide, three reflections tall. Darkness is the default behind every curtain.

qwen3.6-35b — MARC valid, solved with 1 example

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Reasoning (29941 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **Input:** A 3x3 grid containing colored cells (O=orange) and black cells (.=black).
*   **Output:** A 9x9 grid.
*   **Metaphor:**
    *   Input grid is a "tiny 3x3 canvas" with a "portrait" (colored cells) against "darkness" (black cells).
    *   Colored cells are "mirrors".
    *   Black cells are "curtains drawn shut".
    *   The output is a "3x3 hall of mirrors" (9x9 grid).
    *   "Wherever a mirror hangs, the painting sees its own full reflection staring back — a faithful copy of itself."
    *   "Where a curtain is drawn, only darkness remains."
    *   "The hall assembles these reflections and shadows into one grand mosaic."

**2. Identifying the CAST**

*   **Input Grid (3x3):**
    *   Cells with color (O): Mirrors.
    *   Cells with black (.): Curtains.
*   **Output Grid (9x9):**
    *   Divided into 3x3 blocks, each block being 3x3 in size.
    *   Let's denote the input grid as $I$ and the output grid as $O$.
    *   $I$ has dimensions $3 \times 3$.
    *   $O$ has dimensions $9 \times 9$.
    *   The output grid can be viewed as a $3 \times 3$ arrangement of $3 \times 3$ sub-grids. Let's call the sub-grid at position $(r, c)$ in the macro grid $S_{r,c}$, where $r, c \in \{0, 1, 2\}$.

**3. Identifying the AFFORDANCES**

*   **Mirror (Colored cell in Input):** If $I[r][c]$ is a color (not black), it acts as a mirror.
    *   The description says: "Wherever a mirror hangs, the painting sees its own full reflection staring back — a faithful copy of itself."
    *   This implies that if the input cell at $(r, c)$ is a mirror, the corresponding sub-grid $S_{r,c}$ in the output should be a copy of the *entire* input grid $I$.
    *   Wait, let's re-read carefully. "The painting sees its own full reflection". The painting is the input grid. So the reflection is the input grid.
    *   So, if $I[r][c]$ is a mirror, $S_{r,c} = I$.
*   **Curtain (Black cell in Input):** If $I[r][c]$ is black, it acts as a curtain.
    *   The description says: "Where a curtain is drawn, only darkness remains."
    *   This implies that if the input cell at $(r, c)$ is black, the corresponding sub-grid $S_{r,c}$ in the output should be a $3 \times 3$ grid of black cells (darkness).
    *   So, if $I[r][c]$ is black, $S_{r,c} = \text{BlackGrid}$ (where BlackGrid is a 3x3 grid of '.').

**4. Identifying the TRANSFORMATION RULE**

Let's verify this hypothesis with Example 1.

**Example 1 Analysis:**
Input:
```
M M .
M . .
. M M
```
Let's label the input cells $(r, c)$ for $r, c \in \{0, 1, 2\}$.
(0,0): M (Mirror) -> Output block (0,0) should be copy of Input.
(0,1): M (Mirror) -> Output block (0,1) should be copy of Input.
(0,2): . (Curtain) -> Output block (0,2) should be Black.
(1,0): M (Mirror) -> Output block (1,0) should be copy of Input.
(1,1): . (Curtain) -> Output block (1,1) should be Black.
(1,2): . (Curtain) -> Output block (1,2) 

... [27277 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.11)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 25: "A stone skipping across a dark lake leaves ripples where it ... [88 chars truncated]" k=2 alts: 0/0 0b17323b

Training Examples

Example 1

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Example 2

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Literal Description

See: The input grid contains a small number of blue (B) dots placed on a black (.) background. These blue dots form a diagonal line with a constant step size: each consecutive blue dot is offset from the previous one by the same number of rows down and the same number of columns to the right.

Do: 1. Identify all blue (B) cells and sort them by row (or equivalently by column, since they lie on a diagonal). 2. Compute the constant step between consecutive blue dots: Δrow = row difference, Δcol = column difference. 3. Starting from the last blue dot, repeatedly add (Δrow, Δcol) to generate new positions. 4. For each new position that falls within the grid boundaries, place a red (R) dot. Continue until the next position would fall outside the grid. 5. Leave all existing blue dots and the black background unchanged.

Grid: The grid is 15 rows by 15 columns with a black (.) background. Blue dots appear at regular diagonal intervals. The grid uses a 0-indexed coordinate system with (0,0) at the top-left corner.

Figurative Descriptions (1 variants)

"A stone skipping across a dark lake leaves ripples where it bounces, then sinks beneath the surface and continues its path as a red glow underwater."

qwen3.6-35b: k=2

See: A handful of blue stones have been skipped across the surface of a still, dark lake. Each stone's bounce mark is perfectly spaced — the thrower had a steady hand, and the stones hop in a clean diagonal rhythm across the water.

Do: The last stone finally loses its energy and sinks beneath the surface, but its momentum carries it forward through the deep water. Trace the phantom path it follows underwater — same rhythm, same angle, same stride between bounces — but now each mark glows red instead of blue, the color of something submerged. The stone keeps drifting until it would pass beyond the lake's edge.

Grid: The lake is a 15-by-15 stretch of dark water. Blue marks sit on the surface where the stone kissed the water. Red marks glow beneath the surface where the stone continued its ghostly journey after sinking.

qwen3.6-35b — MARC valid, solved with 2 examples

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Reasoning (27389 chars)

The user wants me to solve a grid transformation puzzle.

**1. Analyze the Input and Output:**
- **Input Grid:** 15x15 grid.
- **Colors:**
    - `.` = black (background)
    - `B` = blue (input stones)
    - `R` = red (output stones)
- **Metaphorical Description:**
    - "A handful of blue stones have been skipped across the surface of a still, dark lake." -> Blue stones are present.
    - "Each stone's bounce mark is perfectly spaced — the thrower had a steady hand, and the stones hop in a clean diagonal rhythm across the water." -> The blue stones form a diagonal line.
    - "The last stone finally loses its energy and sinks beneath the surface, but its momentum carries it forward through the deep water." -> The sequence of blue stones stops, but continues.
    - "Trace the phantom path it follows underwater — same rhythm, same angle, same stride between bounces — but now each mark glows red instead of blue, the color of something submerged." -> The path continues diagonally from the last blue stone, but the new marks are red.
    - "The stone keeps drifting until it would pass beyond the lake's edge." -> The red path continues until it hits the boundary of the grid.

**2. Analyze Training Examples:**

*   **Example 1:**
    *   Input Blue stones at: (0,0), (4,4), (8,8). (Using 0-indexed row, col).
    *   Wait, let's look closer.
    *   Row 0: `B` at col 0.
    *   Row 4: `B` at col 4.
    *   Row 8: `B` at col 8.
    *   Pattern: Diagonal line with slope 1 (down-right). Step size is 4 rows and 4 cols.
    *   Output:
        *   Blue stones remain at (0,0), (4,4), (8,8).
        *   Red stones appear at (12,12).
        *   Wait, let's check the output grid provided.
        *   Row 12: `... R ...` at col 12.
        *   Is that it?
        *   Let's check the description again. "The last stone finally loses its energy and sinks... Trace the phantom path... same rhythm... same stride".
        *   The stride is 4.
        *   Last blue stone is at (8,8).
        *   Next position in sequence: (8+4, 8+4) = (12, 12).
        *   Next would be (16, 16) which is out of bounds.
        *   So, a single red stone at (12, 12).
        *   Wait, looking at the output grid for Example 1:
            Row 12: `. . . . . . . . . . . . R . .` -> Yes, R is at index 12.
            Wait, let me double check the indices.
            Row 0: B at 0.
            Row 4: B at 4.
            Row 8: B at 8.
            Row 12: R at 12.
            This matches the stride of 4.

*   **Example 2:**
    *   Input Blue stones at:
        *   Row 1: `B` at col 1.
        *   Row 3: `B` at col 3.
        *   Row 5: `B` at col 5.
    *   Pattern: Diagonal line with slope 1. Step size is 2 rows and 2 cols.
    *   Output:
        *   Blue stones remain.
        *   Red stones appear.
        *   Last blue stone at (5,5).
        *   Stride is 2.
        *   Next position: (5+2, 5+2) = (7, 7).
        *   Next: (9, 9).
        *   Next: 

... [24458 chars truncated]

Test

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.99)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 27: "A costume party where everyone swaps disguises according to ... [25 chars truncated]" k=2 alts: 0/0 0becf7df

Training Examples

Example 1

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Example 2

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Example 3

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Literal Description

See: The grid contains two distinct elements: (1) a 2x2 color key located in the top-left corner (rows 0-1, columns 0-1), containing four colored cells arranged as a square, and (2) a collection of colored cells scattered across the rest of the grid, forming various shapes. The four colors in the 2x2 key define two swap pairs: the two colors in the top row are paired together, and the two colors in the bottom row are paired together. All colored cells outside the key use only these same four colors.

Do: 1. Read the 2x2 color key in the top-left corner. Label the cells as: top-left=C1, top-right=C2, bottom-left=C3, bottom-right=C4. 2. Define two swap pairs: C1 swaps with C2, and C3 swaps with C4. 3. Leave the 2x2 key unchanged. 4. For every other cell in the grid: if it contains C1, replace it with C2; if it contains C2, replace it with C1; if it contains C3, replace it with C4; if it contains C4, replace it with C3. Black (empty) cells remain unchanged.

Grid: The grid is 10x10 with a black (.) background. The 2x2 key always occupies the top-left corner (rows 0-1, columns 0-1). The remaining colored cells appear elsewhere in the grid, never overlapping the key. Grid dimensions and the position of the key are fixed.

Figurative Descriptions (1 variants)

"A costume party where everyone swaps disguises according to the host's seating chart."

qwen3.6-35b: k=2

See: In the top-left corner sits a tiny 2×2 table — the host's seating chart for a masquerade ball. Each row of the chart pairs two dance partners: the couple seated across the top row, and the couple seated across the bottom row. Scattered across the rest of the dark ballroom floor, guests mingle in costumes matching exactly these four colors.

Do: When the music starts, every guest on the ballroom floor finds their dance partner from the seating chart and swaps costumes with them. Top-row partners trade outfits with each other; bottom-row partners do the same. The seating chart itself remains untouched on its little table — only the guests on the floor change their appearances. The empty darkness between them stays still.

Grid: The ballroom is a 10×10 floor of darkness. The host's seating chart is always pinned in the top-left 2×2 corner and never moves. The costumed guests are scattered elsewhere across the floor, never standing on the chart itself.

qwen3.6-35b — MARC valid, solved with 2 examples

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Reasoning (27889 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **The Seating Chart (Host):** Located in the top-left 2x2 corner. It defines the transformation rules. It contains 4 specific colors.
    *   **The Guests:** Colored pixels scattered elsewhere in the 10x10 grid. They are the ones being transformed.
    *   **The Floor:** The background, represented by '.' (black).

*   **AFFORDANCES (Properties/Actions):**
    *   **Seating Chart:**
        *   Top-left cell (0,0): Color $C_{TL}$
        *   Top-right cell (0,1): Color $C_{TR}$
        *   Bottom-left cell (1,0): Color $C_{BL}$
        *   Bottom-right cell (1,1): Color $C_{BR}$
        *   The description says: "Each row of the chart pairs two dance partners: the couple seated across the top row, and the couple seated across the bottom row."
        *   "Top-row partners trade outfits with each other" -> $C_{TL}$ swaps with $C_{TR}$.
        *   "Bottom-row partners do the same" -> $C_{BL}$ swaps with $C_{BR}$.
        *   Wait, let's re-read carefully. "Top-row partners trade outfits with each other; bottom-row partners do the same."
        *   Does this mean the colors *in the chart* swap? No, "The seating chart itself remains untouched on its little table".
        *   So the chart acts as a *key* or *legend* for swapping colors in the rest of the grid.
        *   Let's check the wording again: "When the music starts, every guest on the ballroom floor finds their dance partner from the seating chart and swaps costumes with them."
        *   "Top-row partners trade outfits with each other" -> This likely refers to the colors defined in the top row of the chart. If the chart has colors $C_1, C_2$ in the top row, then any guest with color $C_1$ swaps to $C_2$, and any guest with color $C_2$ swaps to $C_1$.
        *   "Bottom-row partners do the same" -> If the chart has colors $C_3, C_4$ in the bottom row, then any guest with color $C_3$ swaps to $C_4$, and any guest with color $C_4$ swaps to $C_3$.
    *   **Guests:** They change color based on the mapping defined by the chart.
    *   **Floor:** Unchanged.

*   **TRANSFORMATION RULE:**
    1.  Read the 2x2 grid at (0,0) to (1,1). Let's call the colors $T_1, T_2$ (top row) and $B_1, B_2$ (bottom row).
    2.  Identify all occurrences of $T_1$ and $T_2$ in the grid (excluding the chart itself, though the chart is at 0,0-1,1, so guests are elsewhere).
    3.  Swap all $T_1$ with $T_2$.
    4.  Identify all occurrences of $B_1$ and $B_2$ in the grid.
    5.  Swap all $B_1$ with $B_2$.
    6.  All other colors remain unchanged.

    *Self-Correction/Refinement:*
    Let's verify this interpretation with the Training Examples.

    **Example 1 Analysis:**
    Input Chart (Top-Left 2x2):
    Row 0: B G
    Row 1: R A
    So, Top pair: B <-> G.
    Bottom pair: R <-> A.

    Input Grid (Guests):
    Row 1: R A . . . . B . . . -> R is at (1,0), A is at (1,1

... [25644 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.74)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 35: "Seeds dropped in soil grow into sedimentary rock layers, eac ... [44 chars truncated]" k=1 alts: 10/15 0f63c0b9

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Literal Description

See: The input is a 15x15 grid with a black background containing several single colored pixels (dots) scattered at various positions. Each dot is a different color. The dots' row positions determine how the output grid is partitioned into horizontal bands.

Do: 1. Identify all colored dots in the input grid and record each dot's color and row index. Ignore column positions. 2. Sort the dots by row index from top to bottom. 3. Partition the 15 rows into consecutive bands by computing midpoints between adjacent dots' row indices. The boundary between two adjacent dots at rows r1 and r2 is floor((r1 + r2) / 2) + 1, meaning the first band ends at row floor((r1+r2)/2) and the next band starts at floor((r1+r2)/2)+1. The topmost band starts at row 0 and the bottommost band ends at row 14. 4. For each band, fill it with its dot's color as follows: a. The row where the dot originally sat becomes a full solid horizontal line (all 15 cells filled with the dot's color). b. The first and last rows of the entire grid (row 0 and row 14), if they fall within this band, also become full solid horizontal lines of the dot's color. c. All other rows in the band become border rows: only the leftmost cell (column 0) and rightmost cell (column 14) are filled with the dot's color; the interior cells (columns 1-13) remain black.

Grid: Both input and output grids are 15x15. The background color is black (.). The input contains exactly N single-colored pixels (N varies per puzzle instance) placed at distinct positions. The output uses the full 15x15 grid, partitioned into N horizontal bands with no gaps or overlaps, each rendered as a rectangular frame segment in the corresponding dot's color.

Figurative Descriptions (16 variants)

"Seeds dropped in soil grow into sedimentary rock layers, each mineral claiming its stratum of the earth."

qwen3.6-35b: k=1

See: A column of dark earth stretches before you. Scattered at different depths, tiny mineral seeds sit buried — each a different color, each waiting to crystallize. Their depth is everything; their left-right position is forgotten the moment they begin to grow.

Do: Each seed awakens and claims a horizontal stratum of the earth proportional to the space between its neighbors above and below. Where the seed was planted, a solid vein of ore runs the full width of the earth — the densest concentration. At the very surface and the very bottom of the world, exposed strata also harden into solid bands. Everywhere else within a stratum, the mineral only lines the walls — crystallizing along the left and right edges while the interior remains hollow dark rock, like a geode split open.

Grid: The earth is a 15-layer-deep cross-section. Each mineral seed is a single colored speck in the dark. Once they crystallize, the entire cross-section is claimed — no dark void is left unowned. Each stratum is a hollow corridor: solid colored ceiling where the seed sat, colored walls on left and right edges, and darkness filling the interior between them.

qwen3.6-35b — MARC valid, solved with 1 example

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Reasoning (36486 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Input and Output Grids:**

*   **Grid Size:** The input grids are 15x15.
*   **Input Content:** Mostly dots (`.`) representing black/empty space. There are specific colored characters (`R`, `O`, `A`, `B`, `G`, etc.) scattered at specific coordinates.
*   **Output Content:** The grid is filled with colored characters and dots. The structure looks like horizontal bands or layers.

**2. Analyze the Metaphorical Description:**

*   **"A column of dark earth stretches before you."** -> The grid is a vertical column (15 layers deep).
*   **"Scattered at different depths, tiny mineral seeds sit buried"** -> The colored characters in the input are "seeds".
*   **"Their depth is everything; their left-right position is forgotten the moment they begin to grow."** -> The horizontal position (column index) of the seed doesn't matter for the final shape, only the vertical position (row index) matters.
*   **"Each seed awakens and claims a horizontal stratum of the earth proportional to the space between its neighbors above and below."** -> This is the crucial part. It suggests that the space between seeds is divided.
*   **"Where the seed was planted, a solid vein of ore runs the full width of the earth — the densest concentration."** -> The row containing the seed becomes a solid line of that color.
*   **"At the very surface and the very bottom of the world, exposed strata also harden into solid bands."** -> The top row (index 0) and bottom row (index 14) become solid bands.
*   **"Everywhere else within a stratum, the mineral only lines the walls — crystallizing along the left and right edges while the interior remains hollow dark rock, like a geode split open."** -> Rows that are *not* the seed row, but are part of a stratum, have the color on the left and right edges (columns 0 and 14) and are empty (`.`) in between.
*   **"Each stratum is a hollow corridor: solid colored ceiling where the seed sat, colored walls on left and right edges, and darkness filling the interior between them."** -> This confirms the structure.

**3. Analyze the Training Examples to Deduce the Rule:**

*   **Example 1 Input:**
    *   Grid size: 15x15.
    *   Seeds:
        *   `R` at row 3, col 6.
        *   `O` at row 7, col 7.
        *   `A` at row 12, col 2.
    *   Wait, let's look closer at the input grid provided in the prompt.
    *   Row 3: `... R ...` (index 3)
    *   Row 7: `... O ...` (index 7)
    *   Row 12: `... A ...` (index 12)
    *   Wait, looking at the output for Example 1:
        *   Row 0: `R R R ...` (Solid Red)
        *   Row 1: `R . . ... R` (Red walls)
        *   Row 2: `R . . ... R` (Red walls)
        *   Row 3: `R R R ...` (Solid Red) -> This is where the seed `R` was.
        *   Row 4: `R . . ... R` (Red walls)
        *   Row 5: `R . . ... R` (Red walls)
        *   Row 6

... [33765 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 45: "Small tribes without enough members to survive are absorbed ... [20 chars truncated]" k=2 alts: 3/15 12eac192

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Literal Description

See: The input grid contains black (.) background cells and non-black colored cells (which may include any combination of B, O, A, X, and possibly other colors). The non-black cells form connected components of same-colored cells using 4-connectivity (up, down, left, right — not diagonal). These components vary in size from single isolated cells to larger groups of 3 or more connected same-colored cells.

Do: 1. Identify every non-black cell in the grid and determine its color. 2. For each non-black cell, find the entire connected component it belongs to, where a connected component is defined as all cells of the same color reachable via 4-directional adjacency (up, down, left, right). 3. Count the number of cells in each connected component. 4. If a connected component has 3 or more cells, leave all its cells unchanged (they keep their original color). 5. If a connected component has fewer than 3 cells (i.e., size 1 or 2), replace every cell in that component with green (G). 6. All black (.) cells remain black.

Grid: The output grid has the same dimensions as the input grid. The background is black (.). The coordinate system is row-column with the origin at the top-left. There are no fixed size constraints — the grid can be any rectangular dimensions.

Figurative Descriptions (16 variants)

"Small tribes without enough members to survive are absorbed by the green forest."

qwen3.6-35b: k=2

See: A dark landscape dotted with settlements of various colored tribes — blue villages, orange encampments, azure outposts, grey hermitages. Some tribes have gathered in strength, their people clustered tightly together along roads running north-south and east-west. Others are lonely — a single wanderer here, a pair of companions there, cut off from their kin.

Do: The green forest is always growing, always hungry. It respects strength in numbers — any tribe that has gathered at least three of its people together in an unbroken chain stands firm, their settlement walls holding back the encroaching woods. But the stragglers, the isolated outcasts and small pairs who couldn't find enough of their own kind to form a viable community, are swallowed by the forest. Their colors fade beneath the canopy, replaced by green. The darkness between settlements is too barren even for the forest — it remains untouched.

Grid: The landscape is a rectangular territory viewed from above, dark ground forming the empty wilderness between settlements. Tribe members touch only along the four cardinal roads — diagonal neighbors are strangers. The forest's green conquest replaces the lost, while the dark ground and the strong tribes remain exactly as they were.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

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Reasoning (23449 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   `.` (black): Empty wilderness / background.
    *   `B` (blue), `O` (orange), `A` (azure), `X` (grey): "Tribes" or settlements. These are the colored pixels.
    *   `G` (green): The "forest". This is the result color for specific conditions.
    *   Connectivity: "Cardinal roads" means 4-connectivity (up, down, left, right). Diagonals don't count.

*   **AFFORDANCES (Properties/Actions):**
    *   Tribes (colored pixels) form clusters or connected components.
    *   "Strength in numbers": A cluster needs to be "unbroken" (connected) and have a size of at least 3.
    *   "Stragglers/Isolated": Clusters with size < 3 (size 1 or 2).
    *   "Swallowed by the forest": Stragglers turn into `G` (green).
    *   "Strong tribes": Clusters with size >= 3 remain unchanged.
    *   "Darkness": `.` (black) remains `.` (black).

*   **TRANSFORMATION RULE:**
    1.  Identify all connected components of non-black pixels (colors other than `.`).
    2.  For each connected component, count the number of pixels (size).
    3.  If size >= 3, keep the original colors.
    4.  If size < 3, change all pixels in that component to `G` (green).
    5.  Black pixels (`.`) remain `.`.

Let's double-check the examples to confirm this hypothesis.

**Example 1 Analysis:**
Input:
```
B O O B . A . X
B O O B B . B .
A A . . O O O O
. B . . . . B B
X . A . B . B B
```
Output:
```
G O O B . G . G
G O O B B . G .
G G . . O O O O
. G . . . . B B
G . G . G . B B
```

Let's trace components.
Row 0: `B` at (0,0). Neighbors: `B` at (1,0). `O` at (0,1).
Wait, let's look at the colors.
(0,0) is B. (1,0) is B. They are connected.
(0,1) is O. (0,2) is O. (1,1) is O. (1,2) is O.
Let's list connected components by color.

**Color B (Blue):**
- (0,0) B. Connected to (1,0) B.
- (0,3) B. Connected to (1,3) B, (1,4) B.
- (1,4) B. Connected to (0,3) B, (1,3) B.
- (1,3) B. Connected to (0,3) B, (1,4) B.
- (2,4) O... wait, (2,4) is O.
- (3,1) B.
- (4,4) B.
- (4,6) B. (4,7) B. (3,6) B. (3,7) B.
Let's look at the output for B's.
(0,0) became G. (1,0) became G.
(0,3) stayed B. (1,3) stayed B. (1,4) stayed B.
(3,1) became G.
(4,4) became G.
(4,6) stayed B. (4,7) stayed B. (3,6) stayed B. (3,7) stayed B.

Let's check connectivity for B's.
Component 1: (0,0) and (1,0). Size = 2. Output: G, G. Correct.
Component 2: (0,3), (1,3), (1,4).
(0,3) is B. (1,3) is B. (1,4) is B.
(0,3) connects to (1,3). (1,3) connects to (1,4).
Size = 3. Output: B, B, B. Correct.
Component 3: (3,1) is B. Neighbors: (2,1) is A, (4,1) is ., (3,0) is ., (3,2) is ..
Wait, (3,1) is B. Is it connected to anything?
(2,1) is A. (4,1) is .. (3,0) is .. (3,2) is ..
So (3,1) is isolated. Size = 1. Output: G. Correct.
Component 4: (4,4) is B. Neighbors: (3,4) is ., (5,4) is ., (4,3) is ., (4,5) is ..
Isolated. Size = 1. Output: G. Correct.
Component 5: (3,6), (3,7), (4,6), (4,7).
(3,6) B, (3,7) B. (4,6) B, (4,7)

... [20908 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.25)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 52: "Three stars form a constellation; the night sky traces their ... [25 chars truncated]" k=1 alts: 0/0 1478ab18

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input is an 8x8 grid with an orange (O) background containing exactly four grey (X) cells. Two of these X cells form a diagonal pair whose axis-aligned bounding rectangle has exactly one of its other two corners occupied by a third X cell. The fourth X cell is elsewhere and irrelevant to the construction.

Do: 1. Identify all four X cells. Find the pair of X cells that are diagonally positioned such that their bounding rectangle's two non-occupied corners include exactly one other X cell. These two X cells are the endpoints of the triangle's hypotenuse. 2. Of the bounding rectangle's two remaining corners (not the hypotenuse endpoints), one is occupied by an X cell and one is empty. The empty corner is the right-angle vertex of the triangle. 3. Draw a right triangle connecting the two hypotenuse-endpoint X cells with the right angle at the empty corner: (a) draw the horizontal leg from the right-angle corner along its row to the X endpoint that shares that row, filling all intermediate cells with azure (A); (b) draw the vertical leg from the right-angle corner along its column to the X endpoint that shares that column, filling all intermediate cells with azure (A); (c) draw the diagonal hypotenuse connecting the two X endpoints, filling all intermediate cells with azure (A). 4. Do not overwrite any X cells. All other cells remain unchanged.

Grid: The grid is 8x8. The background color is orange (O). Grey (X) cells are fixed landmarks and are never moved or recolored. Azure (A) cells are added to form the triangle edges. The coordinate system is row-column with (0,0) at the top-left corner.

Figurative Descriptions (1 variants)

"Three stars form a constellation; the night sky traces their triangle in azure light."

qwen3.6-35b: k=1

See: An orange desert stretches 8×8 under a blank sky. Four grey standing stones are scattered across the sand. Three of them whisper to each other — two share a diagonal sightline, and a third lurks at a corner of their invisible rectangle, forming a secret triangle. The fourth stone is a hermit and takes no part in the ritual.

Do: The three conspiring stones awaken a constellation between them. Azure light races along the two straight edges of their right triangle — one beam horizontal, one vertical — meeting at the empty corner where no stone stands but where the angle bends. A third beam of azure streaks diagonally between the two stones that anchor the longest side. The light fills every cell it crosses but dares not cover the stones themselves; they remain grey and immovable, the anchors around which the luminous triangle is woven.

Grid: The desert is 8×8 orange (O) sand. The four standing stones are grey (X) and eternal — never moved, never painted over. The constellation lines are azure (A), drawn only along the three edges of the triangle. All sand not touched by the light stays orange.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (37503 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and a training example.

**1. Analyze the Input and Output Grids:**

*   **Grid Size:** 8x8.
*   **Colors:**
    *   `O` = Orange (Background/Sand)
    *   `X` = Grey (Standing stones)
    *   `A` = Azure (Light/Constellation lines)

**2. Analyze the Metaphorical Description:**

*   **Scene:** 8x8 grid of Orange (`O`) sand.
*   **Objects:** Four Grey (`X`) standing stones.
*   **The "Conspiracy":** Three stones form a right triangle.
    *   Two share a diagonal sightline? Wait, let's re-read carefully. "Two share a diagonal sightline, and a third lurks at a corner of their invisible rectangle, forming a secret triangle."
    *   Actually, the description says: "The three conspiring stones awaken a constellation between them. Azure light races along the two straight edges of their right triangle — one beam horizontal, one vertical — meeting at the empty corner where no stone stands but where the angle bends."
    *   "A third beam of azure streaks diagonally between the two stones that anchor the longest side."
    *   "The light fills every cell it crosses but dares not cover the stones themselves."

    Let's break down the geometry implied by the text and the example.
    *   **Right Triangle:** The text explicitly mentions a "right triangle".
    *   **Edges:**
        1.  Horizontal edge.
        2.  Vertical edge.
        3.  Diagonal edge (hypotenuse).
    *   **Vertices:**
        *   Two vertices are occupied by stones (`X`).
        *   One vertex is the "empty corner" (the right angle corner).
        *   Wait, the text says: "meeting at the empty corner where no stone stands". This implies the right angle is at an empty spot.
        *   "A third beam... between the two stones that anchor the longest side." This implies the hypotenuse connects two stones.
        *   So, the vertices of the triangle are:
            1.  Stone 1 (at one end of hypotenuse).
            2.  Stone 2 (at other end of hypotenuse).
            3.  Empty spot (at the right angle).
    *   **The Fourth Stone:** "The fourth stone is a hermit and takes no part in the ritual." It stays `X` and doesn't affect the lines.

**3. Analyze the Training Example:**

*   **Input Grid:**
    ```
    X O O X O O O O  (Row 0)
    O O O O O O O O  (Row 1)
    O X O O O O O O  (Row 2)
    O O O X O O O O  (Row 3)
    O O O O O O O O  (Row 4)
    O O O O O O O O  (Row 5)
    O O O O O O O O  (Row 6)
    O O O O O O O O  (Row 7)
    ```
    Stones (`X`) are at:
    1.  (0, 0)
    2.  (0, 3)
    3.  (2, 1)
    4.  (3, 3)

    Let's check the coordinates (row, col):
    - Stone A: (0, 0)
    - Stone B: (0, 3)
    - Stone C: (2, 1)
    - Stone D: (3, 3)

*   **Output Grid:**
    ```
    X O O X O O O O
    A A O O O O O O
    A X A O O O O O
    A A A X O O O O
    O O O O O O O O
    ...
    ```
    Let's look at the Azure (`A`) cells.
    - Row 1: (1, 0), (1, 1)
    - Row 2: (2,

... [34617 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.58)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 69: "Two teams combine their footprints to map everywhere anyone ... [10 chars truncated]" k=1 alts: 0/0 195ba7dc

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Literal Description

See: The input is a rectangular grid composed of three colors: orange (O), black (.), and a single vertical column of red (R) that divides the grid into a left half and a right half of equal dimensions.

Do: Remove the red divider column to obtain two equally-sized subgrids (left and right). Combine them cell by cell using a logical OR: if a cell is orange in the left subgrid, the right subgrid, or both, output blue (B). If the cell is black (.) in both subgrids, output black (.).

Grid: The input grid has dimensions R rows by (2C+1) columns, where the middle column is entirely red. The output grid has dimensions R rows by C columns, containing only blue (B) and black (.).

Figurative Descriptions (1 variants)

"Two teams combine their footprints to map everywhere anyone has stood."

qwen3.6-35b: k=1

See: A red curtain hangs down the center of a stage, separating two dance troupes. On each side, orange footprints mark where dancers have stepped, while black tiles show untouched floor.

Do: Raise the curtain. Wherever either troupe — or both — left an orange footprint, the tile glows blue with the memory of movement. Only tiles that neither troupe ever touched remain dark and silent.

Grid: The stage is split evenly by the curtain. Once it lifts, the two halves overlay into a single floor plan of blue light and black stillness.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (27369 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Input:** A grid with a "red curtain" (R) down the center.
*   **Left side:** "Orange footprints" (O) and "black tiles" (.).
*   **Right side:** "Orange footprints" (O) and "black tiles" (.).
*   **Action:** "Raise the curtain" (remove the R column).
*   **Transformation:** "Wherever either troupe — or both — left an orange footprint, the tile glows blue (B) with the memory of movement."
*   **Result:** "Only tiles that neither troupe ever touched remain dark and silent (black, .)."
*   **Grid details:** "The stage is split evenly by the curtain. Once it lifts, the two halves overlay into a single floor plan."

**2. Analyze the Training Examples:**

*   **Example 1 Input:**
    ```
    O . O O . O R O O . . . .
    O . . O . . R . . . O . .
    . O O . . . R . . O O . .
    . O O O O . R O . . . O .
    O . O . O O R O O O O O O
    ```
    *   Dimensions: 5 rows, 13 columns.
    *   The 'R' is in column 7 (index 6).
    *   Left side (cols 0-5): 6 columns.
    *   Right side (cols 8-12): 5 columns.
    *   Wait, the description says "split evenly". Let's check the column counts.
    *   Row 1: `O . O O . O` (6 chars) | `R` | `O O . . . .` (6 chars). Total 13.
    *   Row 2: `O . . O . .` (6 chars) | `R` | `. . . O . .` (6 chars). Total 13.
    *   Row 3: `. O O . . .` (6 chars) | `R` | `. . O O . .` (6 chars). Total 13.
    *   Row 4: `. O O O O .` (6 chars) | `R` | `O . . . O .` (6 chars). Total 13.
    *   Row 5: `O . O . O O` (6 chars) | `R` | `O O O O O O` (6 chars). Total 13.
    *   Okay, the grid is 5x13. The 'R' is exactly in the middle (column index 6).
    *   Left half: 6 columns. Right half: 6 columns.
    *   Wait, looking at the output:
    ```
    B B B B . B
    B . . B . .
    . B B B . .
    B B B B B .
    B B B B B B
    ```
    *   Output dimensions: 5 rows, 6 columns.
    *   This confirms the "overlay" concept. The left half (6 cols) and right half (6 cols) are superimposed.
    *   Let's check the logic: "Wherever either troupe ... left an orange footprint (O), the tile glows blue (B)."
    *   This sounds like a logical OR operation on the presence of 'O'.
    *   If Left[i][j] == 'O' OR Right[i][j] == 'O', then Output[i][j] = 'B'.
    *   Otherwise (if both are '.'), Output[i][j] = '.'.
    *   Let's verify with Example 1.
    *   Row 1:
        *   Left: `O . O O . O`
        *   Right: `O O . . . .`
        *   Overlay:
            *   Col 0: L='O', R='O' -> 'B'
            *   Col 1: L='.', R='O' -> 'B'
            *   Col 2: L='O', R='.' -> 'B'
            *   Col 3: L='O', R='.' -> 'B'
            *   Col 4: L='.', R='.' -> '.'
            *   Col 5: L='O', R='.' -> 'B'
        *   Result: `B B B B . B`. Matches output.
    *   Row 2:
        *   Left: `O . . O . .`
        *   Right: `. . . O . .`
        *   Overlay:
   

... [24969 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.70)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 82: "Two monarchs divide a kingdom, each stamping their seal upon ... [22 chars truncated]" k=1 alts: 0/0 1bfc4729

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Literal Description

See: The input is a 10x10 grid with a black background containing exactly two colored dots. One dot is located in the upper half of the grid (rows 0–4) and the other in the lower half (rows 5–9). Their exact positions within their respective halves do not matter — only which half each belongs to and what color each is.

Do: Divide the grid into a top half (rows 0–4) and a bottom half (rows 5–9). For the top half, use the color of the upper dot to draw a rectangular border frame with this specific pattern: row 0 is entirely filled, row 1 has only the leftmost and rightmost cells filled, row 2 is entirely filled, row 3 has only the leftmost and rightmost cells filled, and row 4 has only the leftmost and rightmost cells filled. For the bottom half, use the color of the lower dot to draw a rectangular border frame with this pattern: row 5 has only the leftmost and rightmost cells filled, row 6 has only the leftmost and rightmost cells filled, row 7 is entirely filled, row 8 has only the leftmost and rightmost cells filled, and row 9 is entirely filled. All other cells remain black.

Grid: The grid is 10x10. The background is black. The output grid has the same dimensions as the input. The grid is conceptually split into two 5-row halves (rows 0–4 and rows 5–9), each governed by one of the two colored dots from the input.

Figurative Descriptions (1 variants)

"Two monarchs divide a kingdom, each stamping their seal upon their domain's walls."

qwen3.6-35b: k=1

See: A dark, empty kingdom stretches across the land. Two monarchs — one ruling from somewhere in the northern provinces, the other holding court in the southern territories — each mark their presence with a single colored banner planted in the void.

Do: Each monarch claims their half of the kingdom and constructs fortress walls along its borders in their royal color. But their architectural styles differ: the northern ruler builds a crown-like fortification — solid battlements at the top, open corridors, then another solid wall, trailing down to simple flanking towers. The southern ruler mirrors this in reverse — flanking towers give way to a grand solid wall below, then more towers, and a final solid foundation sealing the bottom. Each ruler's walls enclose their domain but leave the interior dark and open.

Grid: The kingdom is a 10×10 realm of darkness. It splits into two equal fiefdoms — north and south. Each monarch's single banner disappears, replaced by the fortress walls they command. The interior of each fiefdom remains untouched black ground.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (33097 chars)

The user wants me to solve a grid transformation puzzle.

**1. Analyze the Input and Output format:**
- Input: A 10x10 grid of characters.
- Characters: `.` (black), `B` (blue), `R` (red), `G` (green), `Y` (yellow), `X` (grey), `M` (magenta), `O` (orange), `A` (azure), `W` (maroon).
- Output: A 10x10 grid of characters.

**2. Analyze the Metaphorical Description:**
- **Setting:** A 10x10 grid of darkness (`.`).
- **Actors:** Two monarchs.
    - One in the "northern provinces" (top half).
    - One in the "southern territories" (bottom half).
- **Input markers:** Each monarch is represented by a single colored banner (a single colored character) in the void.
- **Transformation:**
    - The banners disappear.
    - Each monarch claims their half of the kingdom (5 rows each, presumably).
    - They build fortress walls along the borders of their domain in their royal color.
    - **Northern Ruler's Style:** "crown-like fortification — solid battlements at the top, open corridors, then another solid wall, trailing down to simple flanking towers."
    - **Southern Ruler's Style:** "mirrors this in reverse — flanking towers give way to a grand solid wall below, then more towers, and a final solid foundation sealing the bottom."
    - **Result:** Walls enclose the domain, interior remains black (`.`).

**3. Analyze the Training Examples:**
- **Example 1 Input:**
    - 10x10 grid.
    - Blue (`B`) at row 2, col 5 (0-indexed: row 2, col 5). Wait, let's count carefully.
    - Row 0: `.`
    - Row 1: `.`
    - Row 2: `.` `.` `.` `.` `.` `B` `.` `.` `.` `.` -> B is at index 5.
    - Row 3-5: `.`
    - Row 6: `.`
    - Row 7: `.` `.` `.` `.` `.` `Y` `.` `.` `.` `.` -> Y is at index 5.
    - Row 8-9: `.`
    - So, Blue is in the top half (rows 0-4), Yellow is in the bottom half (rows 5-9).
    - Actually, looking at the output, the split seems to be horizontal.
    - Top half: Rows 0-4.
    - Bottom half: Rows 5-9.
    - Wait, let's look at the output structure.

- **Example 1 Output:**
    - Rows 0-4 are Blue (`B`).
    - Rows 5-9 are Yellow (`Y`).
    - Let's look at the pattern for Blue (Top):
        - Row 0: `B B B B B B B B B B` (Solid wall)
        - Row 1: `B . . . . . . . . B` (Open corridor with side walls)
        - Row 2: `B B B B B B B B B B` (Solid wall)
        - Row 3: `B . . . . . . . . B` (Open corridor with side walls)
        - Row 4: `B . . . . . . . . B` (Open corridor with side walls) -- Wait, description said "trailing down to simple flanking towers".
        - Let's re-read the description carefully.
        - "solid battlements at the top" -> Row 0 is solid.
        - "open corridors" -> Row 1 is open (with walls on sides).
        - "then another solid wall" -> Row 2 is solid.
        - "trailing down to simple flanking towers" -> Rows 3 and 4?
        - In the output:
            - Row 0: Solid B
            - Row 1: B . . . . . . . . B (Side walls)
            - Row 2: Solid B
            - Row 3: B . 

... [30198 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.50)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 96: "A king in his castle banishes all imposters wearing his colo ... [20 chars truncated]" k=2 alts: 0/0 1e81d6f9

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The grid contains a cross-shaped barrier made of grey (X) cells occupying row 3 (columns 0-3) and column 3 (rows 0-3), forming an L or cross that encloses a 3×3 region in the top-left corner (rows 0-2, columns 0-2). Inside this enclosed region, position (1,1) contains a single colored cell — this is the 'target' color. The rest of the grid outside the enclosed region is populated with scattered colored cells on a black background.

Do: 1. Identify the color of the cell at row 1, column 1 (the center of the 3×3 region enclosed by the grey cross in the top-left corner). 2. Scan every cell in the grid that lies outside the enclosed top-left 3×3 region (i.e., outside rows 0-2, columns 0-2). 3. For each such cell, if its color matches the target color identified in step 1, replace it with black (.). 4. Leave all other cells unchanged, including the target-colored cell at (1,1) itself and any other cells within the enclosed corner region.

Grid: The grid is 15 rows by 15 columns with a black (.) background. A grey (X) cross structure always occupies the same positions: row 3 columns 0-3 and column 3 rows 0-3. This cross partitions off a 3×3 region in the top-left corner (rows 0-2, columns 0-2). The grid dimensions and cross position are fixed across all instances.

Figurative Descriptions (1 variants)

"A king in his castle banishes all imposters wearing his colors from the kingdom."

qwen3.6-35b: k=2

See: In the top-left corner of the world, a small fortress is walled off by grey stone ramparts — a cross-shaped battlement sealing three rows and three columns into a protected keep. Inside this keep sits a lone monarch on their throne at the center, dressed in a single distinctive color. Beyond the walls, the open kingdom sprawls across the remaining grid, dotted with scattered figures of many colors going about their lives.

Do: The monarch gazes out from behind the fortress walls and is displeased: there are pretenders out in the kingdom wearing the royal color — the same hue as the monarch's own garments. By royal decree, every impostor bearing the monarch's color beyond the castle walls is cast into shadow, erased from the land and replaced by empty darkness. Those wearing any other color are loyal subjects and remain untouched. The monarch, safe within the keep, remains on the throne — it is only the copies outside the walls that are banished.

Grid: The kingdom is a 15×15 realm of darkness dotted with colorful inhabitants. The grey stone ramparts always stand in the same place — a horizontal wall across the fourth row and a vertical wall down the fourth column, meeting to seal off the royal 3×3 keep in the top-left corner. This architecture never changes; only the monarch's color and the population of the kingdom shift from one instance to the next.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (29470 chars)

The user wants me to solve a grid transformation puzzle.

**1. Understand the Goal:**
The goal is to transform an input grid into an output grid based on a specific set of rules described metaphorically.

**2. Analyze the Metaphorical Description:**
*   **Grid Size:** 15x15.
*   **The "Keep" (Fortress):** Located in the top-left corner. It's a 3x3 area.
    *   The description says "a cross-shaped battlement sealing three rows and three columns".
    *   Looking at the grid details: "a horizontal wall across the fourth row and a vertical wall down the fourth column".
    *   Wait, let's verify the coordinates.
    *   Rows are 0-indexed or 1-indexed? Let's assume 0-indexed for calculation, but the description says "fourth row" and "fourth column".
    *   If it's 1-indexed: Row 4 is index 3. Column 4 is index 3.
    *   Let's check the training examples to confirm the wall location.
    *   In Example 1 Input:
        Row 0: `. . . X . . . . . . . . B . .` -> Index 3 is 'X'.
        Row 1: `. Y . X . . . . . . . . . . .` -> Index 3 is 'X'.
        Row 2: `. . . X . . . . W R Y . . . .` -> Index 3 is 'X'.
        Row 3: `X X X X . . . . . . . . . . .` -> Indices 0, 1, 2, 3 are 'X'.
    *   So, the "walls" are made of 'X' (grey).
    *   The vertical wall is at column index 3 (4th column).
    *   The horizontal wall is at row index 3 (4th row).
    *   The "keep" is the 3x3 area in the top-left corner. This corresponds to rows 0, 1, 2 and columns 0, 1, 2.
    *   The walls (X) surround this keep. Specifically, row 3 is all X (or at least the first 4 are X), and column 3 is X for rows 0, 1, 2.
    *   Actually, looking at the input grids, the walls are explicitly 'X'.
    *   The "monarch" is at the center of the keep. The keep is 3x3. The center is at (row 1, col 1) relative to the grid (0-indexed).
    *   The monarch has a "distinctive color". This is the color of the cell at (1, 1).

*   **The "Kingdom" (Outside the Keep):**
    *   Everything outside the 3x3 keep (rows 0-2, cols 0-2) and the walls (row 3, col 3).
    *   Actually, the walls are part of the grid structure. The "open kingdom" is the rest of the grid.
    *   The description says "Beyond the walls, the open kingdom sprawls across the remaining grid".
    *   So, cells outside the 3x3 top-left block are the kingdom.

*   **The Transformation Rule:**
    *   "The monarch gazes out... displeased: there are pretenders out in the kingdom wearing the royal color".
    *   "Royal color" = color of the monarch at (1, 1).
    *   "Pretenders" = cells in the kingdom (outside the 3x3 keep) that have the same color as the monarch.
    *   "Cast into shadow, erased from the land and replaced by empty darkness".
    *   "Empty darkness" = '.' (black).
    *   "Those wearing any other color are loyal subjects and remain untouched."
    *   "The monarch, safe within the keep, remains on the throne".
    *   "Only the copies outside the walls that are banished."

**3. Identify CAST, A

... [26694 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.07)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 119: "A drumline marches in formation, and every third beat strike ... [36 chars truncated]" k=1 alts: 0/0 22a4bbc2

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Literal Description

See: The grid consists of rows where each non-black cell is either azure (A) or blue (B). Consecutive rows that share the same non-black color form a 'block' (a block may be 1, 2, 3, or more rows). Blocks alternate between A-colored and B-colored as you move down the grid. Black (.) cells serve as padding within rows and are not considered when determining a row's color identity — each row contains exactly one non-black color.

Do: 1. Scan the grid top to bottom and group consecutive rows into blocks, where each block's rows all share the same non-black color (A or B). A new block starts whenever the non-black color changes from the previous row. 2. Number the blocks sequentially starting from 1. 3. For every block whose position number follows the pattern 1, 4, 7, 10, 13, 16, ... (i.e., positions where (position - 1) mod 3 == 0), replace all non-black cells in that block with red (R). Black cells remain black. 4. All other blocks are left unchanged.

Grid: The grid width is fixed across all rows but varies by puzzle instance (3 to 5 columns observed). The grid height varies. Every cell is one of: black (.), azure (A), blue (B), or red (R, in output only). Each row contains exactly one non-black color (A or B) mixed with zero or more black cells.

Figurative Descriptions (1 variants)

"A drumline marches in formation, and every third beat strikes the snare — painting it red."

qwen3.6-35b: k=1

See: A parade of marching bands files down the street in colored uniforms — some squads wear azure, others wear blue. Each squad occupies one or more rows, standing shoulder to shoulder, with gaps in the crowd (black) where spectators can see through. The squads alternate colors as you look from the front of the parade to the back.

Do: A spotlight sweeps down the parade from front to back. It has a rhythm: it fires on the first squad, skips two, fires again, skips two, fires again — like a heartbeat every third beat. Every squad caught in the spotlight has its uniforms dyed red on the spot, while the gaps in the crowd stay empty. The squads the spotlight passes over keep marching in their original colors, undisturbed.

Grid: The street is a fixed number of lanes wide, and the parade stretches as long as it needs to. Every lane holds either a gap in the crowd (black) or a uniformed marcher — never a mix of azure and blue in the same row. Red only appears where the spotlight has touched.

qwen3.6-35b — MARC valid, solved with 1 example

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Prediction

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Expected

Reasoning (27292 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**

*   **Visuals:** A parade of marching bands.
    *   Squads wear azure (A) or blue (B).
    *   Squads occupy rows.
    *   Gaps are black (.)
    *   Squads alternate colors (A then B, or B then A) as you look from front to back (top to bottom).
    *   "Every lane holds either a gap in the crowd (black) or a uniformed marcher — never a mix of azure and blue in the same row." -> This implies rows are homogeneous in color (all A or all B) or empty (all .).
*   **Action:** A spotlight sweeps down the parade (top to bottom).
    *   Rhythm: Fires on the first squad, skips two, fires again, skips two...
    *   Pattern: Fire, Skip, Skip, Fire, Skip, Skip...
    *   Effect: Squads caught in the spotlight are dyed **Red (R)**.
    *   Squads not caught keep their original color (A or B).
    *   Gaps (.) stay empty.
*   **Grid Details:**
    *   Fixed width.
    *   Rows are the "squads".
    *   Red only appears where the spotlight touched.

**2. Analyze the Training Examples:**

Let's look at Example 1 to verify the "Fire, Skip, Skip" pattern.

Input Grid (Example 1):
Row 0: B B B .
Row 1: B B B .
Row 2: A A A A
Row 3: . . B B
Row 4: . . B B
Row 5: A A A A
Row 6: A A A A
Row 7: . B B .
Row 8: A A . .
Row 9: B B B B
Row 10: . A A .
Row 11: . A A .
Row 12: B B B B
Row 13: A A A .
Row 14: A A A .
Row 15: . B B B
Row 16: . B B B
Row 17: A A A .
Row 18: . B B .
Row 19: A A A A

Output Grid (Example 1):
Row 0: R R R .  (Changed B -> R)
Row 1: R R R .  (Changed B -> R)
Row 2: A A A A  (Unchanged A)
Row 3: . . B B  (Unchanged B)
Row 4: . . B B  (Unchanged B)
Row 5: R R R R  (Changed A -> R)
Row 6: R R R R  (Changed A -> R)
Row 7: . B B .  (Unchanged B)
Row 8: A A . .  (Unchanged A)
Row 9: R R R R  (Changed B -> R)
Row 10: . A A .  (Unchanged A)
Row 11: . A A .  (Unchanged A)
Row 12: B B B B  (Unchanged B)
Row 13: R R R .  (Changed A -> R)
Row 14: R R R .  (Changed A -> R)
Row 15: . B B B  (Unchanged B)
Row 16: . B B B  (Unchanged B)
Row 17: A A A .  (Unchanged A)
Row 18: . R R .  (Changed B -> R)
Row 19: A A A A  (Unchanged A)

Let's check the row indices (0-indexed) that changed to Red (R):
0, 1, 5, 6, 9, 13, 14, 18.

Let's check the pattern "Fire, Skip, Skip".
If the pattern applies to *rows* (squads):
Row 0: Fire (Change) -> Yes.
Row 1: Skip? No, Row 1 changed.
Row 2: Skip? No, Row 2 didn't change.
Row 3: Fire? No, Row 3 didn't change.

Wait, the description says "Each squad occupies one or more rows".
Maybe the "squad" is a contiguous block of rows with the same color?
Let's look at the rows in the input.
Row 0: B
Row 1: B
Row 2: A
Row 3: B (partially)
Row 4: B (partially)
Row 5: A
Row 6: A
Row 7: B (partially)
Row 8: A
Row 9: B
Row 10: A
Row 11: A
Row 12: B
Row 13: A
Row 14: A
Row 15: B
Row 16: B
Row 17: A
Row 18: B
Row 19: A

The description says: "never a 

... [24901 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.07)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 128: "Lighthouses signaling across the darkness" k=1 alts: 0/0 253bf280

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Example 5

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Example 6

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Example 7

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Example 8

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Literal Description

See: The input grid has a black (.) background with several azure (A) cells scattered across it. Some pairs of A cells share the same row or the same column, while other A cells have no partner aligned with them in any row or column.

Do: For each pair of azure (A) cells that share the same row, fill all cells strictly between them with green (G), leaving the A cells themselves unchanged. For each pair of azure (A) cells that share the same column, fill all cells strictly between them with green (G), leaving the A cells themselves unchanged. Any azure cell that has no other azure cell in its row or column remains as-is with no green fill. If a row or column contains exactly two A cells, they form one pair. All other cells remain black.

Grid: The grid dimensions vary across instances. The background is black (.). The only non-background colors are azure (A) as fixed markers and green (G) as filled connectors. The grid uses a standard row-column coordinate system with no wrapping or special boundary behavior.

Figurative Descriptions (1 variants)

"Lighthouses signaling across the darkness"

qwen3.6-35b: k=1

See: Scattered across a dark sea, azure lighthouses stand on their lonely posts. Some lighthouses happen to gaze directly at another across the water — perfectly aligned along the same shipping lane, either north-south or east-west. Others stand alone, their beams finding no companion on the horizon.

Do: When two lighthouses face each other along the same lane, their beams meet and the water between them glows green with reflected light. The lighthouses themselves remain azure — only the dark water between paired beacons is illuminated. A lighthouse with no partner in its lane keeps its light to itself, illuminating nothing. The beams travel only in straight cardinal lines and never bend or wrap around the edges of the sea.

Grid: The sea varies in size. The dark water is black (.), the lighthouses are azure (A), and the glow of their joined beams is green (G). Each lighthouse can potentially signal in two directions — along its row and along its column — so it may participate in up to two connections.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

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Reasoning (26201 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   `.` (black): Empty space / dark water.
    *   `A` (azure): Lighthouse.
    *   `G` (green): Glowing water (result of interaction).
    *   Other colors (B, R, G, Y, X, M, O, W) are defined in the key but not present in the examples or description, likely distractors or for other puzzles.

*   **AFFORDANCES (Capabilities):**
    *   Lighthouses (`A`) are stationary.
    *   Lighthouses emit beams in cardinal directions (North, South, East, West).
    *   Beams travel in straight lines.
    *   Beams do not wrap around edges.
    *   Beams stop or interact? The description says "When two lighthouses face each other along the same lane, their beams meet and the water between them glows green". This implies a connection is formed between two `A`s in the same row or column with only `.`s between them.

*   **TRANSFORMATION RULE:**
    *   Scan the grid for pairs of Azure lighthouses (`A`) that are aligned horizontally (same row) or vertically (same column).
    *   Check if they are "facing each other". The description says "perfectly aligned along the same shipping lane". It doesn't explicitly mention obstacles blocking the view, but usually in these puzzles, if there's another object in between, it might block. However, looking at the training example:
        *   Input has `A` at (1, 2) and (7, 2) (0-indexed).
        *   Output has `G` at (2, 2), (3, 2), (4, 2), (5, 2), (6, 2).
        *   The cells between the two `A`s are filled with `G`.
        *   The `A`s remain `A`.
        *   The rest of the grid remains `.`.
    *   Let's check the logic:
        *   Find all `A`s.
        *   For each `A`, look in all 4 directions.
        *   If another `A` is found in that direction, fill the cells strictly between them with `G`.
        *   Wait, what if there are multiple `A`s in a line? E.g., A . A . A.
        *   The description says "When two lighthouses face each other...". It implies pairwise connections.
        *   Let's look at the test input to see if there are complex cases.
        *   Test Input:
            Row 1: . . A . . . . . . . A . . (Indices: 2, 10) -> Two As.
            Row 5: . . . . . . A . . . . . A (Indices: 6, 12) -> Two As.
            Row 7: . A . . . . . . . . . . . (Index: 1) -> One A.
            Row 9: . . . . . . . . A . . . . (Index: 8) -> One A.
            Row 10: . A . . . . . . . . . . . (Index: 1) -> One A.
            Wait, let's re-read the grid carefully.

**2. Analyzing the Test Input**

Grid dimensions: 12 rows, 13 columns.

Let's list coordinates of `A`s (0-indexed, row, col):
1.  Row 1: `A` at col 2. `A` at col 10.
    *   Row 1: `. . A . . . . . . . A . .`
    *   Indices: (1, 2) and (1, 10).
    *   Are there any obstacles? The cells between are `.`.
    *   So, cells (1, 3) to (1, 9) should become `G`.

2.  Row 

... [23330 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.98)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 132: "A volcano erupts a beam of light through its crater in the d ... [18 chars truncated]" k=3 alts: 0/0 25d487eb

Training Examples

Example 1

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Example 2

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Example 3

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Literal Description

See: The input grid contains a single diamond or triangular shape made of one dominant color, set against a black background. Embedded within the shape is exactly one cell of a different color — the 'marker'. The shape has a clear tip (pointed end) on the side opposite to where the marker sits. For example, if the marker is at the bottom edge of the shape, the tip points upward; if the marker is on the left edge, the tip points to the right.

Do: 1. Identify the diamond or triangular shape and its dominant color. 2. Find the single cell within the shape whose color differs from the dominant color — this is the marker. 3. Determine which side of the shape the marker is on (top, bottom, left, or right). 4. Locate the tip of the shape on the opposite side from the marker. 5. From the cell just beyond that tip, draw a straight line of the marker's color extending outward in the direction away from the shape, continuing until the edge of the grid. 6. Leave the original shape unchanged.

Grid: The grid dimensions vary but the background is always black (.). The shape and its emitted line are the only non-background elements. The line extends from the tip of the shape to the grid boundary along the row or column of the tip, depending on direction.

Figurative Descriptions (1 variants)

"A volcano erupts a beam of light through its crater in the direction it faces."

qwen3.6-35b: k=3

See: A mountain rises from the dark plain, built from a single mineral. Buried within its slopes is a glowing ember — a single cell of a different color, like magma hidden inside rock. The mountain has a steep peak on one side and a broad base on the other, with the ember always nestled near the base.

Do: The ember superheats the mountain from within, and the peak acts as a vent. The mountain channels all that energy outward through its pointed summit, erupting a beam of the ember's color that streaks across the dark sky from the peak until it hits the edge of the world. The mountain itself remains perfectly intact — only the beam is new.

Grid: The dark plain is the black background. The mountain is the cluster of one color, and the ember is the single odd-colored cell within it. The eruption is a straight trail of the ember's color shooting from just beyond the peak, extending to the grid's edge along the peak's row or column.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

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Reasoning (37171 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Dark plain:** The background, represented by `.` (black).
    *   **Mountain:** A cluster of cells of a single color (e.g., `A` in Ex 1, `R` in Ex 2, `G` in Ex 3). It has a specific shape (steep peak, broad base).
    *   **Ember:** A single cell of a different color inside the mountain cluster (e.g., `G` in Ex 1, `B` in Ex 2, `R` in Ex 3).
    *   **Eruption/Beam:** A trail of the ember's color extending from the mountain.

*   **AFFORDANCES (Capabilities/Properties):**
    *   **Mountain:** Has a "peak" (a specific cell or direction). The description says "steep peak on one side and a broad base on the other".
    *   **Ember:** Located "near the base". It "superheats" the mountain.
    *   **Peak:** Acts as a "vent".
    *   **Eruption:** Shoots from "just beyond the peak" in a straight line (row or column) until it hits the grid edge.

*   **TRANSFORMATION RULE:**
    *   Identify the main cluster (Mountain) color.
    *   Identify the single different color cell inside it (Ember).
    *   Determine the "Peak" of the mountain. The description says "steep peak on one side". Looking at the examples:
        *   Ex 1: Mountain is `A`. Shape is roughly triangular. The peak seems to be the top-most cell or the cell with the highest y-coordinate (if y increases downwards). Wait, let's look at coordinates.
            *   Input Ex 1:
                Row 5: `A` at (5, 6) [0-indexed: row 5, col 6]
                Row 6: `A` at (6, 5), (6, 6), (6, 7)
                Row 7: `A` at (7, 4), (7, 5), (7, 6), (7, 7), (7, 8)
                Row 8: `A` at (8, 3), (8, 4), (8, 5), (8, 6), (8, 7), (8, 8), (8, 9)
                Ember `G` is at (8, 6).
            *   Output Ex 1:
                A vertical beam of `G` appears going *upwards* from the top of the mountain.
                The top of the mountain is at Row 5, Col 6.
                The beam is at Col 6, rows 0 to 4.
                Wait, the beam is `G` (ember color). It goes from the peak upwards.
                Let's check the peak location. The highest `A` is at (5, 6). The beam is in column 6.
        *   Ex 2: Mountain is `R`.
            *   Input Ex 2:
                Row 2: `R` at (2, 3)
                Row 3: `R` at (3, 3), (3, 4)
                Row 4: `R` at (4, 3), (4, 4) ... wait, let's look closer.
                Row 4: `B` at (4, 3), `R` at (4, 4), `R` at (4, 5). Wait, `B` is the ember?
                Let's re-read Ex 2 Input carefully.
                Row 2: `R` at col 3.
                Row 3: `R` at col 3, 4.
                Row 4: `B` at col 3, `R` at col 4, `R` at col 5.
                Row 5: `R` at col 3, 4.
                Row 6: `R` at col 3.
                The cluster is `R`. The single different cell is `B` at (4, 3).
                Wait, `B` is at (4, 3). Is it inside?
                The shape

... [34240 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.94)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 146: "Four royal courts compete for territory, and the strongest c ... [28 chars truncated]" k=1 alts: 0/0 281123b4

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Example 5

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Example 6

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Literal Description

See: The input grid consists of four 4×4 panels arranged side by side, separated by single green (G) columns. Each panel is associated with a distinct color: the first panel uses azure (A), the second uses grey (X), the third uses maroon (W), and the fourth uses yellow (Y). Within each panel, some cells are filled with that panel's color and some are empty (black/.).

Do: Construct a 4×4 output grid. For each cell position (row, column), check which of the four panels have a filled (non-empty) cell at that same position. Among the panels that are filled at that position, select the color with the highest priority according to this fixed ranking: W (maroon) > Y (yellow) > A (azure) > X (grey). Place that color in the output cell. If no panel is filled at that position, output black (.).

Grid: The input is a 4×19 grid composed of four 4×4 colored panels separated by three single-column green (G) dividers. The output is a single 4×4 grid. The panels and output share the same row-column coordinate system, so position (r, c) in the output corresponds to position (r, c) within each panel.

Figurative Descriptions (1 variants)

"Four royal courts compete for territory, and the strongest claim wins each plot of land."

qwen3.6-35b: k=1

See: Four kingdoms sit side by side, separated by emerald fortress walls. Each kingdom flies a single banner color — one azure, one grey, one maroon, one yellow. Within each kingdom's 4×4 domain, some plots are claimed (bearing the kingdom's banner) and some lie fallow (dark and empty).

Do: The fortress walls crumble and all four kingdoms collapse onto the same contested land. Wherever multiple kingdoms have staked a claim to the same plot, only the mightiest ruler plants their flag. Maroon is the emperor, yellow the duke, azure the baron, and grey the commoner — rank always decides. Where no kingdom ever bothered to claim a plot, the land remains dark and abandoned.

Grid: The four walled kingdoms span a wide banner, each a 4×4 fief divided by emerald columns. When the dust settles, a single 4×4 territory remains — each plot showing only the highest-ranking banner that once flew over that same position in any of the four kingdoms.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

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Reasoning (34310 chars)

The user wants me to solve a grid transformation puzzle.

**1. Analyze the Input and Metaphorical Description**

*   **Input Grid:** A large grid containing multiple colors.
*   **Metaphorical Description:**
    *   "Four kingdoms sit side by side, separated by emerald fortress walls."
    *   "Each kingdom flies a single banner color — one azure, one grey, one maroon, one yellow."
    *   "Within each kingdom's 4×4 domain, some plots are claimed (bearing the kingdom's banner) and some lie fallow (dark and empty)."
    *   "The fortress walls crumble and all four kingdoms collapse onto the same contested land."
    *   "Wherever multiple kingdoms have staked a claim to the same plot, only the mightiest ruler plants their flag."
    *   **Ranking:** Maroon (Emperor) > Yellow (Duke) > Azure (Baron) > Grey (Commoner).
    *   "Where no kingdom ever bothered to claim a plot, the land remains dark and abandoned." (Black/.)
    *   "The four walled kingdoms span a wide banner, each a 4×4 fief divided by emerald columns."
    *   "When the dust settles, a single 4×4 territory remains."

*   **Grid Details:**
    *   The input grid seems to be composed of four 4x4 blocks separated by columns of 'G' (green/emerald).
    *   Let's check the dimensions of the test input.
    *   Input rows: 4.
    *   Input columns: Let's count.
        Row 1: `A A A . G X . X X G W . . . G . . . .`
        Wait, looking at the spacing in the prompt, it looks like space-separated characters.
        Let's parse the string carefully.
        `A A A . G X . X X G W . . . G . . . .`
        Count: 1(A) 2(A) 3(A) 4(.) 5(G) 6(X) 7(.) 8(X) 9(X) 10(G) 11(W) 12(.) 13(.) 14(.) 15(G) 16(.) 17(.) 18(.) 19(.)
        That's 19 characters.
        Wait, the description says "Four kingdoms... each a 4x4 fief divided by emerald columns".
        If there are 4 kingdoms, there are 4 blocks of 4x4.
        Separated by emerald columns.
        If they are side by side, the structure is likely: [4x4] [G] [4x4] [G] [4x4] [G] [4x4].
        Or maybe the G columns are part of the grid structure.
        Let's look at the input string again.
        `A A A . G X . X X G W . . . G . . . .`
        Indices:
        0: A
        1: A
        2: A
        3: .
        4: G
        5: X
        6: .
        7: X
        8: X
        9: G
        10: W
        11: .
        12: .
        13: .
        14: G
        15: .
        16: .
        17: .
        18: .
        
        This looks like 4 blocks of width 4, separated by width 1 columns of G.
        Block 1: cols 0-3 (A A A .)
        Separator: col 4 (G)
        Block 2: cols 5-8 (X . X X)
        Separator: col 9 (G)
        Block 3: cols 10-13 (W . . .)
        Separator: col 14 (G)
        Block 4: cols 15-18 (. . . .)
        
        Wait, the input has 4 rows.
        Let's check the other rows to confirm the structure.
        Row 2: `A . A A G X X X X G . . W W G Y Y . Y`
        Indices:
        0: A
   

... [31663 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.19)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 161: "A ghost haunts a lonely grave, conjuring an echo of the cath ... [24 chars truncated]" k=3 alts: 0/0 2c737e39

Training Examples

Example 1

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Example 2

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Example 3

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Literal Description

See: The input grid contains exactly two grey (X) cells. One X is embedded within a multi-colored pattern of adjacent non-background cells — this is the 'template X.' The other X stands alone with no colored neighbors — this is the 'anchor X.' The template pattern consists of the template X plus all colored (non-black, non-X) cells that form a connected cluster around it.

Do: 1. Identify the two X cells. The template X is the one adjacent to or surrounded by other colored cells; the anchor X is the isolated one. 2. For every colored (non-black) cell in the template pattern (excluding the template X itself), compute its row and column offset relative to the template X's position. 3. For each such offset, place the same color at the corresponding offset from the anchor X's position. 4. Replace the anchor X itself with background (black/dot) — do not copy X to the new location. 5. Leave the original template pattern (including its X) unchanged in place.

Grid: The grid dimensions match the input (variable size, rectangular). The background color is black (.). The grid uses a standard row-column coordinate system with (0,0) at the top-left. The copied pattern must fit within the grid boundaries.

Figurative Descriptions (1 variants)

"A ghost haunts a lonely grave, conjuring an echo of the cathedral it once inhabited."

qwen3.6-35b: k=3

See: On the black night of the grid, there is a small cathedral built of colored stained glass, with a grey cornerstone (X) mortared into its walls. Somewhere else in the darkness, a second grey stone sits alone — a forgotten grave marker with no church around it.

Do: The ghost that dwells in the cathedral's cornerstone senses the lonely grave marker and flies to it, carrying the memory of every stained-glass window and colored brick that surrounded it. Upon arriving, the ghost rebuilds the cathedral from memory around the grave — each colored piece reappearing at the same relative position it held back home. But the grave marker itself dissolves into the dark earth once the ghost departs, leaving no grey stone behind. The original cathedral remains standing, untouched and whole, its cornerstone still in place.

Grid: The night sky is the black (.) background. The cathedral's stained glass may be any color — blue, red, green, yellow, and others — arranged in a cluster around one grey cornerstone. The ghost's reconstruction preserves the exact arrangement of colors as seen from the cornerstone's perspective. The grid's edges are the walls of the world; nothing can be built beyond them.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

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Expected

Reasoning (25424 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Black background (.):** Empty space.
    *   **Cathedral:** A cluster of colored cells (stained glass) surrounding a specific grey cell (X). This is the "source" pattern.
    *   **Cornerstone (X):** The specific grey cell that acts as the center or anchor for the cathedral pattern.
    *   **Grave marker (X):** Another isolated grey cell (X) somewhere else in the grid. This is the "target" location.
    *   **Ghost:** The agent performing the transformation. It carries the pattern from the cathedral to the grave marker.

*   **AFFORDANCES (Capabilities):**
    *   The "ghost" reads the relative positions of all colored cells with respect to the cathedral's cornerstone (X).
    *   The "ghost" moves to the location of the second X (grave marker).
    *   The "ghost" reconstructs the pattern around the grave marker's location using the relative offsets found in the first step.
    *   The original cathedral (source) remains unchanged.
    *   The grave marker (target X) disappears (becomes black `.`) after the reconstruction.

*   **TRANSFORMATION RULE:**
    1.  Identify the "Cathedral" group: Find the X that is surrounded by colored cells. Let's call its coordinates $(r_c, c_c)$.
    2.  Identify the "Grave Marker": Find the isolated X that is not part of the cathedral cluster. Let's call its coordinates $(r_g, c_g)$.
    3.  Extract the pattern: For every colored cell at $(r, c)$ in the cathedral, calculate the offset $(dr, dc) = (r - r_c, c - c_c)$.
    4.  Apply the pattern: For each offset $(dr, dc)$, place the color of the cell at $(r_c + dr, c_c + dc)$ into the new location $(r_g + dr, c_g + dc)$.
    5.  Cleanup: The target X at $(r_g, c_g)$ becomes `.` (black). The source X at $(r_c, c_c)$ remains `X`. All other cells remain as they were, except for the newly placed colored cells.

**2. Analyzing the Test Input**

Input Grid:
```
. . . . . . . . . .
. . . . . . . . . .
. . . . . . X . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . X . . . . . .
. R R G G . . . . .
. B . G G A A . . .
```

Let's parse the grid coordinates (row, col) starting from 0.
Rows: 0 to 10 (11 rows).
Cols: 0 to 9 (10 columns).

**Step 1: Identify the Cathedral (Source)**
I see a cluster of colors at the bottom.
Row 9: `. R R G G . . . . .` -> Cells at (9,1)=R, (9,2)=R, (9,3)=G, (9,4)=G.
Row 10: `. B . G G A A . . .` -> Cells at (10,1)=B, (10,2)=., (10,3)=G, (10,4)=G, (10,5)=A, (10,6)=A.

Wait, looking at the description: "a small cathedral built of colored stained glass, with a grey cornerstone (X) mortared into its walls."
I need to find an X that is surrounded by these colors.
Looking at the grid, there are two X's.
1.  At (2, 6): `. . . . . . X . . .`
2.  At (8, 2): `. . . X . . . . . .`

Let's check the surroundings of X at (2, 6).
Neighbors: (1,6)=., (3,6)=., (2,5)=., (2,7)=.

... [22748 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 173: "Every creature casts a shadow at sunset, and the wallpaper r ... [24 chars truncated]" k=1 alts: 0/0 310f3251

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Example 4

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Output

Example 5

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Output

Literal Description

See: The input is a small grid (H rows × W columns) with a black (.) background containing one or more colored cells (non-black, non-red) at various positions.

Do: 1. Start with the input grid (H × W). 2. For each colored (non-black) cell at position (r, c), place a red (R) cell at the position one step diagonally up-left, wrapping around the grid edges: ((r−1) mod H, (c−1) mod W). This red cell is added to the grid without removing anything. 3. Tile this modified grid in a 3×3 arrangement to produce the output grid of size 3H × 3W. Each tile is an identical copy of the modified grid, laid out in a regular 3-row by 3-column grid of tiles.

Grid: The output grid has dimensions 3H × 3W, where H and W are the height and width of the input grid. The background is black (.). The output consists of 9 identical tiles arranged 3×3, each tile being the input grid augmented with red markers at the wrapped diagonal-up-left neighbor of every colored cell.

Figurative Descriptions (1 variants)

"Every creature casts a shadow at sunset, and the wallpaper repeats itself endlessly."

qwen3.6-35b: k=1

See: A small swatch of dark wallpaper with a few colorful creatures resting on it.

Do: As the sun sets from the upper-left, each creature casts a red shadow one diagonal step toward the fading light — if the shadow falls off the edge, it wraps around to the opposite side of the swatch, as if the wallpaper were already a cylinder. Then the completed swatch is stamped out as a 3×3 block of identical copies, like a wallpaper roll unspooling across a wall.

Grid: The finished wall is three swatches tall and three swatches wide. Every tile is the same: the original dark background, the colorful creatures where they stood, and each creature's red sunset shadow sitting one step up and to the left (wrapping at the edges).

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (33476 chars)

The user wants me to solve a grid transformation puzzle.

**1. Analyze the Input and Output format:**
- Input: A grid of characters representing colors.
- Output: A larger grid of characters.
- Colors: `.` (black), `B` (blue), `R` (red), `G` (green), `Y` (yellow), `X` (grey), `M` (magenta), `O` (orange), `A` (azure), `W` (maroon).

**2. Analyze the Metaphorical Description:**
- **Input:** "A small swatch of dark wallpaper with a few colorful creatures resting on it." -> This is the input grid.
- **Action 1 (Shadows):** "As the sun sets from the upper-left, each creature casts a red shadow one diagonal step toward the fading light — if the shadow falls off the edge, it wraps around to the opposite side of the swatch, as if the wallpaper were already a cylinder."
    - "Sun sets from the upper-left" implies light comes from top-left? Or shadows go towards the light?
    - "casts a red shadow one diagonal step toward the fading light". If light is upper-left, shadows go towards upper-left.
    - "one diagonal step": usually means (-1, -1) in matrix coordinates (row, col).
    - "wraps around": Toroidal boundary conditions.
    - "red shadow": The shadow color is 'R'.
    - "if the shadow falls off the edge": Handle wrapping.
- **Action 2 (Tiling):** "Then the completed swatch is stamped out as a 3×3 block of identical copies, like a wallpaper roll unspooling across a wall."
    - The processed swatch (input grid + shadows) is repeated 3 times horizontally and 3 times vertically.
    - Resulting grid size: $3 \times H_{input}$ rows and $3 \times W_{input}$ columns.

**3. Analyze the Grid Details:**
- "The finished wall is three swatches tall and three swatches wide." -> Confirms 3x3 tiling.
- "Every tile is the same: the original dark background, the colorful creatures where they stood, and each creature's red sunset shadow sitting one step up and to the left (wrapping at the edges)."
    - Wait, "sitting one step up and to the left".
    - If light is upper-left, shadows usually go opposite to light. If light is upper-left, shadows go to bottom-right.
    - But the text says "casts a red shadow one diagonal step toward the fading light". If light is upper-left, fading light is upper-left. So shadow goes to upper-left.
    - Let's check the training example to verify direction.

**4. Analyze Training Example 1:**
- **Input:**
  ```
  . . . .
  . . X .
  . . . .
  . X . .
  ```
  Size: 4 rows, 4 columns.
  Creatures: 'X' at (1, 2) and (3, 1) (0-indexed).
  Wait, let's look closer.
  Row 0: `.` `.` `.` `.`
  Row 1: `.` `.` `X` `.` -> X at (1, 2)
  Row 2: `.` `.` `.` `.`
  Row 3: `.` `X` `.` `.` -> X at (3, 1)

- **Output:**
  Size: 12 rows, 12 columns. (4*3 x 4*3).
  Let's look at the first 4x4 block (top-left swatch).
  ```
  . R . .
  . . X .
  R . . .
  . X . .
  ```
  Wait, let's parse the output string carefully.
  Output rows:
  1. `. R . . . R . . . R . .` -> First 4 chars: `. R . .`
  2. `. . X . . . X . . . X .` ->

... [30631 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.10)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 178: "Two dancers audition for the same spotlight — only a s ... [28 chars truncated]" k=1 alts: 0/0 31d5ba1a

Training Examples

Example 1

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Output

Example 2

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Example 3

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Example 4

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Example 5

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Output

Literal Description

See: The input is a 6-row by 5-column grid divided into two halves. The top half (rows 1-3) contains a pattern of maroon (W) cells on a black (.) background. The bottom half (rows 4-6) contains a pattern of yellow (Y) cells on a black (.) background. Each half acts as a binary mask over the same 3×5 grid positions.

Do: Produce a 3×5 output grid by comparing the top half (W mask) and bottom half (Y mask) cell by cell at each corresponding position. Apply an XOR rule: if exactly one of the two cells is colored (W in the top half or Y in the bottom half) and the other is black, output magenta (M). If both are colored or both are black, output black (.). In other words, M appears only where W and Y disagree.

Grid: The output grid is 3 rows by 5 columns, matching the dimensions of each half of the input. It uses only two values: magenta (M) for active cells and black (.) for inactive cells.

Figurative Descriptions (1 variants)

"Two dancers audition for the same spotlight — only a solo performer gets to shine."

qwen3.6-35b: k=1

See: The stage is split into an upper balcony and a lower floor, each holding a troupe of performers. Maroon dancers (W) rehearse above, yellow dancers (Y) rehearse below, both moving across the same five-column, three-row grid of spotlight marks. The black spaces are empty marks where no one stands.

Do: When the curtain rises, only solo acts earn the magenta spotlight. Where a dancer stands alone on a mark — one troupe claiming it while the other leaves it empty — the spotlight blazes magenta. But where both troupes crowd the same mark, they block each other's light and the spot goes dark. And where neither troupe shows up, the stage stays dark too. The spotlight rewards those who dance where their rival dares not.

Grid: The final playbill is a 3-row by 5-column seating chart of spotlights: magenta (M) where a lone performer earned the light, black (.) where the mark sits dark — either contested or abandoned.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (27577 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Input and Output Grids:**

*   **Input Grids:**
    *   The input grids seem to be composed of two distinct parts or layers, or perhaps just a single grid with different characters.
    *   Looking at the training examples:
        *   Example 1 Input:
            ```
            W . . W W
            . . . . .
            . . W . W
            . . Y Y .
            Y Y Y . .
            Y . Y . Y
            ```
            This is a 6x5 grid.
        *   Example 1 Output:
            ```
            M . M . M
            M M M . .
            M . . . .
            ```
            This is a 3x5 grid.

    *   Wait, the input is 6 rows, output is 3 rows.
    *   Let's check the structure.
    *   Input rows 1-3:
        ```
        W . . W W
        . . . . .
        . . W . W
        ```
        Contains 'W' (Maroon) and '.' (Black).
    *   Input rows 4-6:
        ```
        . . Y Y .
        Y Y Y . .
        Y . Y . Y
        ```
        Contains 'Y' (Yellow) and '.' (Black).

    *   The description says: "The stage is split into an upper balcony and a lower floor... five-column, three-row grid".
    *   This implies the input is actually two 3x5 grids stacked vertically.
    *   Top half (Rows 1-3): Maroon dancers (W).
    *   Bottom half (Rows 4-6): Yellow dancers (Y).
    *   The output is a single 3x5 grid.

**2. Analyze the Metaphorical Description:**

*   **Cast:**
    *   Maroon dancers (W) -> Top half of input.
    *   Yellow dancers (Y) -> Bottom half of input.
    *   Black spaces (.) -> Empty marks.
    *   Magenta (M) -> The result/spotlight.
*   **Affordances:**
    *   Dancers occupy specific cells in their respective 3x5 grids.
    *   'W' means a Maroon dancer is present.
    *   'Y' means a Yellow dancer is present.
    *   '.' means no dancer.
*   **Transformation Rule:**
    *   "When the curtain rises, only solo acts earn the magenta spotlight."
    *   "Where a dancer stands alone on a mark — one troupe claiming it while the other leaves it empty — the spotlight blazes magenta."
    *   "But where both troupes crowd the same mark, they block each other's light and the spot goes dark."
    *   "And where neither troupe shows up, the stage stays dark too."
    *   "The spotlight rewards those who dance where their rival dares not."

    *   **Interpretation:**
        *   We have two 3x5 grids. Let's call them Grid A (Top, W) and Grid B (Bottom, Y).
        *   For each cell $(r, c)$ where $r \in \{0, 1, 2\}$ and $c \in \{0, 1, 2, 3, 4\}$:
            *   Check if Grid A has a dancer at $(r, c)$ (i.e., is 'W').
            *   Check if Grid B has a dancer at $(r, c)$ (i.e., is 'Y').
            *   **Case 1:** Grid A has 'W' AND Grid B has 'Y'. -> "Both troupes crowd the same mark". Result: Dark (.)
            *   **Case 2:** Grid A has 'W' AND Grid B has '.'. -&g

... [25159 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.20)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 194: "A curtain divides two dancers, and the spotlight finds whoev ... [16 chars truncated]" k=3 alts: 9/15 34b99a2b

Training Examples

Example 1

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Output

Example 2

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Example 3

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Example 4

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Output

Literal Description

See: The input grid contains a single vertical column of yellow (Y) cells that divides the grid into two equal halves: a left half and a right half. The left half contains azure (A) cells and black (.) background cells. The right half contains grey (X) cells and black (.) background cells.

Do: Remove the yellow divider column and compare the left and right halves cell by cell. For each position, apply an XOR rule: if exactly one of the two sides has a colored cell (A on the left or X on the right) and the other side is black (.), output red (R). If both sides have a colored cell or both sides are black, output black (.). The result is a grid with only red (R) and black (.) cells.

Grid: The output grid has the same number of rows as the input and a width equal to half the input width minus the divider column. For example, a 5×9 input with a 1-cell-wide divider produces a 5×4 output. The background is black (.) and the only foreground color is red (R).

Figurative Descriptions (16 variants)

"A curtain divides two dancers, and the spotlight finds whoever dances alone."

qwen3.6-35b: k=3

See: A golden curtain hangs down the center of a stage, splitting it into two wings. In the left wing, azure performers take their positions among empty squares. In the right wing, grey performers mirror the same stage layout. The black squares are darkness — empty stage floor.

Do: Raise the curtain and let the two troupes face each other. Wherever a performer on one side finds only darkness across from them — no partner, no mirror — a red spotlight ignites on that square, marking the lonesome dancer. But where two performers lock eyes across the divide, or where darkness meets darkness, the stage stays dark. The spotlight only loves the unmatched.

Grid: The curtain vanishes and the two wings collapse into one stage. What remains is a smaller floor plan lit only by red spotlights where solitary dancers stood, surrounded by the darkness of matched pairs and empty silence.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (30643 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and some training examples.

**1. Analyze the Metaphorical Description:**

*   **Input Grid Structure:**
    *   "A golden curtain hangs down the center of a stage, splitting it into two wings." -> This suggests a vertical line of symmetry or a separator in the middle of the grid. Looking at the color key, 'Y' is yellow (golden). So, the column containing 'Y' is the curtain.
    *   "In the left wing, azure performers take their positions among empty squares." -> 'A' is azure. So, the left side of the 'Y' column contains 'A's and '.'s (black/empty).
    *   "In the right wing, grey performers mirror the same stage layout." -> 'X' is grey. So, the right side of the 'Y' column contains 'X's and '.'s.
    *   "The black squares are darkness — empty stage floor." -> '.' represents empty space.
*   **Transformation Rule:**
    *   "Raise the curtain and let the two troupes face each other." -> The 'Y' column (curtain) is removed. The left and right sides are brought together.
    *   "Wherever a performer on one side finds only darkness across from them — no partner, no mirror — a red spotlight ignites on that square, marking the lonesome dancer." -> This implies a comparison between the left side and the right side.
    *   "But where two performers lock eyes across the divide, or where darkness meets darkness, the stage stays dark." -> If there is a match (performer vs performer or darkness vs darkness), the result is '.' (black/darkness).
    *   "The spotlight only loves the unmatched." -> If there is a mismatch (performer vs darkness), the result is 'R' (red).
    *   "The curtain vanishes and the two wings collapse into one stage." -> The output grid width will be the sum of the widths of the left and right wings.
    *   "What remains is a smaller floor plan lit only by red spotlights where solitary dancers stood, surrounded by the darkness of matched pairs and empty silence." -> The output grid consists of '.' and 'R'.

**2. Analyze the Grid Details & Dimensions:**

Let's look at the input grids in the examples to understand the dimensions.
*   **Example 1 Input:**
    Row 1: `. A . . Y . X X .` (Length 9)
    Left of Y: `. A . .` (Length 4)
    Right of Y: `. X X .` (Length 4)
    Output:
    Row 1: `. . R .` (Length 4)
    Wait, the output width is 4. The input width is 9. The 'Y' is at index 4 (0-indexed). Left part is indices 0-3 (4 chars). Right part is indices 5-8 (4 chars).
    So, the output grid has the same height as the input, and the width is half of (Input Width - 1).
    Let's check the logic.
    Left Wing: `L`
    Right Wing: `R`
    Output Cell `O[i][j]` corresponds to comparing `L[i][j]` and `R[i][j]`.
    Wait, usually "facing each other" might mean mirroring or direct alignment.
    Let's check the text: "In the right wing, grey performers mirror the same stage layout." This might j

... [28679 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.60)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 199: "A rubber stamp prints its design wherever ink drops have fal ... [16 chars truncated]" k=3 alts: 0/0 363442ee

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

Input

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Output

Literal Description

See: The input grid is 9 rows by 13 columns, divided into two regions by a vertical column of grey (X) at column 3. The left region (columns 0-2, rows 0-2) contains a 3×3 colorful pattern; the rest of the left region (rows 3-8) is black. The right region (columns 4-12) is a 9×6 area on a black background containing scattered blue (B) dots.

Do: 1. Extract the 3×3 pattern from the top-left corner (rows 0-2, columns 0-2). 2. Divide the right region (columns 4-12) into a 3×3 grid of 3×3 blocks. The nine blocks correspond to positions (row-block 0-2, col-block 0-2), where block (r,c) spans rows r*3 to r*3+2 and columns 4+c*3 to 4+c*3+2. 3. For each of the nine blocks, check whether it contains a blue (B) cell anywhere within it. 4. If a block contains a blue cell, replace the entire 3×3 block with the extracted pattern. 5. If a block contains no blue cell, fill the entire 3×3 block with black (.). 6. The left region and the grey column remain unchanged.

Grid: The grid is 9 rows by 13 columns. Column 3 is always grey (X), serving as a fixed vertical divider. The background color is black (.). The left side (columns 0-2) holds a 3×3 pattern in the top three rows. The right side (columns 4-12) is structured as a 3×3 arrangement of 3×3 blocks, giving it a modular tiled structure.

Figurative Descriptions (1 variants)

"A rubber stamp prints its design wherever ink drops have fallen on the page."

qwen3.6-35b: k=3

See: A grey wall divides the world in two. On the left side, a colorful rubber stamp sits in its holder at the top — a 3×3 design ready to be used. The right side is a blank page divided into nine equal panels, mostly empty and dark. Scattered across some of these panels, lone blue ink drops have splattered onto the page, marking where something should be printed.

Do: The stamp-maker picks up the 3×3 design from the left side of the wall and walks to the right. She examines each of the nine panels on the page. Wherever she finds even a single blue ink drop — no matter where it landed within that panel — she presses the stamp down firmly, imprinting the full colorful design over the entire panel, ink drop and all. Panels that remain dry and unmarked are left blank and dark, untouched by the stamp. The wall and the stamp's original home on the left are never disturbed.

Grid: The world is 9 rows by 13 columns. A grey stone wall at column 3 permanently separates the stamp holder (left) from the page (right). The stamp is always a 3×3 colorful design resting in the top-left corner. The page to the right is a 3×3 arrangement of equally sized panels — nine little canvases waiting to receive the stamp's impression wherever blue ink has marked them.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (28167 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **The Wall:** A vertical line of 'X' (grey) characters at column index 3 (0-indexed). It separates the left side (columns 0-2) from the right side (columns 4-12).
    *   **The Stamp:** A 3x3 block of colored characters located in the top-left corner of the grid (rows 0-2, columns 0-2). This is the pattern to be copied.
    *   **The Page:** The area to the right of the wall (columns 4-12). It is divided into a 3x3 grid of panels. Each panel is 3x3 cells.
    *   **The Ink Drops:** 'B' (blue) characters scattered within the Page area. They act as triggers.
    *   **The Background:** '.' (black) characters filling the empty space.

*   **AFFORDANCES (Capabilities):**
    *   **The Stamp:** Can be "picked up" and "imprinted". It retains its original 3x3 pattern.
    *   **The Page Panels:** Can be "marked" by an ink drop ('B') or "imprinted" with the stamp pattern.
    *   **The Wall:** Static, acts as a separator.
    *   **Ink Drops:** Signal that a specific panel needs the stamp pattern.

*   **TRANSFORMATION RULE:**
    1.  **Identify the Stamp:** Extract the 3x3 pattern from the top-left corner (rows 0-2, cols 0-2). Let's call this pattern $S$.
    2.  **Identify the Page Structure:** The page is the region to the right of the wall (cols 4-12). It consists of 9 panels arranged in a 3x3 grid.
        *   Panel (0,0) covers rows 0-2, cols 4-6.
        *   Panel (0,1) covers rows 0-2, cols 7-9.
        *   Panel (0,2) covers rows 0-2, cols 10-12.
        *   Panel (1,0) covers rows 3-5, cols 4-6.
        *   Panel (1,1) covers rows 3-5, cols 7-9.
        *   Panel (1,2) covers rows 3-5, cols 10-12.
        *   Panel (2,0) covers rows 6-8, cols 4-6.
        *   Panel (2,1) covers rows 6-8, cols 7-9.
        *   Panel (2,2) covers rows 6-8, cols 10-12.
    3.  **Check for Ink Drops:** For each of the 9 panels, check if there is any 'B' character inside its boundaries.
    4.  **Apply Stamp:** If a panel contains at least one 'B', replace the entire 3x3 content of that panel with the Stamp pattern $S$.
    5.  **Leave Blank:** If a panel contains no 'B', leave it as is (which is usually all '.' or black).
    6.  **Preserve Left Side:** The left side (cols 0-2) and the wall (col 3) remain unchanged.

**2. Analyzing the Test Input**

*   **Input Grid:**
    ```
    Row 0: G G W X . . . . . . . . .
    Row 1: A Y Y X . . . . B . . B .
    Row 2: A W A X . . . . . . . . .
    Row 3: . . . X . . . . . . . . .
    Row 4: . . . X . B . . . . . B .
    Row 5: . . . X . . . . . . . . .
    Row 6: . . . X . . . . . . . . .
    Row 7: . . . X . B . . B . . . .
    Row 8: . . . X . . . . . . . . .
    ```

*   **Step 1: Identify the Stamp ($S$)**
    *   Located at rows 0-2, cols 0-2.
    *   Row 0: G G W
    *   Row 1: A Y Y
    *   Row 2: A W A
    *   So, $S = \begin{bmatrix} G & G & W \\ A & Y & Y \\ A & W & A \end{b

... [25333 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 207: "A talent show where the most popular act wins the encore." k=1 alts: 2/15 39a8645d

Training Examples

Example 1

Input

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Output

Example 2

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Output

Example 3

Input

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Output

Literal Description

See: The input grid contains several small 3×3 shapes scattered on a black background. Each shape is a distinct pattern of colored cells within a 3×3 bounding box, with the remaining cells black. Multiple colors may be present (e.g., red, green, azure, blue, yellow, magenta), and some shape patterns appear more than once as exact duplicates — same color and same spatial arrangement of colored cells within their 3×3 bounding box.

Do: 1. Scan the input grid and identify every distinct 3×3 shape by extracting each connected or nearby cluster of non-black cells and reading its 3×3 bounding box pattern. 2. Group these shapes by their exact pattern (same color and same cell arrangement within the 3×3 box). 3. Count how many identical copies exist for each distinct shape pattern. 4. Select the shape pattern that has the highest number of identical copies in the grid. 5. Output that 3×3 pattern as the result.

Grid: The input is a rectangular grid (typically 14×14) with a black (.) background. The output is always a 3×3 grid showing the extracted shape pattern on a black background. Each shape occupies exactly a 3×3 bounding box within the input grid.

Figurative Descriptions (16 variants)

"A talent show where the most popular act wins the encore."

qwen3.6-35b: k=1

See: A dark stage is scattered with small troupes of performers, each wearing matching costumes of a single color — blue dancers, red acrobats, yellow jugglers, azure mimes. Each troupe strikes a unique pose within its own small spotlight. Some acts are one-of-a-kind, but others have sent identical understudy groups who mirror the original's pose and costume perfectly, scattered elsewhere across the stage.

Do: The audience votes by recognition: whichever act has sent the most identical understudy copies of itself onto the stage is clearly the crowd favorite. That winning troupe — the one whose exact pose and costume appears more times than any other — earns the encore. Pull them into the spotlight alone and let the rest of the stage go dark.

Grid: The stage is a wide dark floor where each troupe occupies a small spotlight just large enough for a few performers. The encore spotlight shrinks to show only the winning troupe's formation against the darkness, exactly as they stood during the show.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

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Reasoning (39712 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Grid Elements):**
    *   `.` (black): Empty space / background.
    *   `B` (blue), `R` (red), `Y` (yellow), `G` (green), `A` (azure), etc.: Colored pixels representing "performers" or "troupes".
    *   The description mentions "troupes of performers, each wearing matching costumes of a single color". This implies that connected components or specific shapes of the same color form a "troupe".
    *   "Each troupe strikes a unique pose within its own small spotlight." This suggests that the shape formed by the colored pixels is the "pose".
    *   "Some acts are one-of-a-kind, but others have sent identical understudy groups who mirror the original's pose and costume perfectly, scattered elsewhere across the stage." This means there are multiple instances of the same shape (pattern) of the same color located at different positions in the grid.

*   **AFFORDANCES (Capabilities):**
    *   The grid contains various colored shapes.
    *   We need to identify distinct shapes (poses) defined by a specific color.
    *   We need to count how many times each distinct shape appears.
    *   We need to find the shape that appears the most frequently (the "crowd favorite").
    *   The output should be a grid containing *only* that winning shape, centered or positioned relative to the input? Or just the shape itself?
    *   Let's look at the "What to do" section: "Pull them into the spotlight alone and let the rest of the stage go dark." "The encore spotlight shrinks to show only the winning troupe's formation against the darkness, exactly as they stood during the show."
    *   This phrasing is slightly ambiguous. Does "exactly as they stood" mean keeping their relative positions? Or does it mean extracting the shape and displaying it?
    *   Let's look at the training examples to clarify.

*   **TRANSFORMATION RULE (Input -> Output):**
    *   **Example 1 Analysis:**
        *   **Input Grid:** 14x14.
        *   **Colors present:** B (blue), Y (yellow), R (red).
        *   Let's identify the shapes (troupes).
        *   **Blue (B) shapes:**
            *   Top right: `B . B` (row 0), `B B B` (row 1), `B` (row 2). Wait, let's look closer.
            *   Row 0: `...B.B...` -> Two isolated B's? Or connected?
            *   Row 1: `...BBB...` -> A horizontal line of 3.
            *   Row 2: `......B...` -> One B.
            *   Row 6: `.B.B...` -> Two isolated B's.
            *   Row 7: `.BBB...` -> Horizontal line of 3.
            *   Row 8: `..B...` -> One B.
            *   Row 11: `......B.B` -> Two isolated B's.
            *   Row 12: `......BBB` -> Horizontal line of 3.
            *   Row 13: `.......B.` -> One B.
            *   It looks like there are distinct clusters. Let's trace connectivity (4-way or 8-way? Usually 4-way in these puzzles, but let's

... [36997 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.22)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 211: "Seeds planted along a rooftop send roots zigzagging down thr ... [14 chars truncated]" k=1 alts: 0/0 3ac3eb23

Training Examples

Example 1

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Example 2

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Literal Description

See: The input is a grid where the top row contains one or more colored pixels (seeds) placed at various columns against a black (.) background. All rows below the top row are entirely black.

Do: For each colored seed at column c in row 0: on every even-numbered row (0, 2, 4, ...), place that seed's color at column c. On every odd-numbered row (1, 3, 5, ...), place that seed's color at columns c-1 and c+1 (if within grid bounds). Leave all other cells black. Each seed operates independently; process all seeds the same way.

Grid: The output grid has the same dimensions as the input grid. The background is black (.). The coordinate system is row-major with row 0 at the top. Column indices run left to right starting at 0.

Figurative Descriptions (1 variants)

"Seeds planted along a rooftop send roots zigzagging down through the soil."

qwen3.6-35b: k=1

See: Along the rooftop of an empty dark field, one or more colored seeds sit waiting. Below them stretches nothing but quiet black earth.

Do: Each seed sends roots downward through the soil. The roots don't fall straight — they sway side to side as they descend, like a pendulum. On each swing the root splits briefly into two tendrils reaching to either side, then reconverges on the next level before splitting again. Each seed's roots grow independently, painting the earth with their own color.

Grid: The field keeps its original size. The dark earth remains wherever no root has touched it. The rooftop is at the top and roots grow downward row by row.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

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Reasoning (29829 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Input:** "Along the rooftop of an empty dark field, one or more colored seeds sit waiting. Below them stretches nothing but quiet black earth."
    *   This implies the input grid has a top row (rooftop) with some colored cells (seeds) and the rest is black (dots).
*   **Action:** "Each seed sends roots downward through the soil. The roots don't fall straight — they sway side to side as they descend, like a pendulum. On each swing the root splits briefly into two tendrils reaching to either side, then reconverges on the next level before splitting again."
    *   Roots grow downwards from the seeds.
    *   "Sway side to side" suggests a zig-zag or alternating pattern.
    *   "Splits briefly into two tendrils reaching to either side" suggests branching.
    *   "Reconverges on the next level" suggests the branches meet back up or the pattern shifts.
    *   "Each seed's roots grow independently, painting the earth with their own color."
*   **Output:** "The field keeps its original size. The dark earth remains wherever no root has touched it. The rooftop is at the top and roots grow downward row by row."

**2. Analyze the Training Examples:**
*   **Example 1:**
    *   Input:
        ```
        . Y . . . . .
        . . . . . . .
        . . . . . . .
        . . . . . . .
        . . . . . . .
        . . . . . . .
        ```
        (6 rows, 7 columns). Top row has a 'Y' at index 1 (0-indexed).
    *   Output:
        ```
        . Y . . . . .
        Y . Y . . . .
        . Y . . . . .
        Y . Y . . . .
        . Y . . . . .
        Y . Y . . . .
        ```
    *   **Observation:**
        *   The seed 'Y' is at (0, 1).
        *   Row 1: 'Y' at (1, 0) and (1, 2).
        *   Row 2: 'Y' at (2, 1).
        *   Row 3: 'Y' at (3, 0) and (3, 2).
        *   Row 4: 'Y' at (4, 1).
        *   Row 5: 'Y' at (5, 0) and (5, 2).
    *   **Pattern:**
        *   The seed at column $c$ in row $r$ seems to generate a pattern in subsequent rows.
        *   Row 0: Seed at col 1.
        *   Row 1: Seeds at col 0 and 2. (Left and Right of 1).
        *   Row 2: Seed at col 1. (Center of 0 and 2).
        *   Row 3: Seeds at col 0 and 2.
        *   Row 4: Seed at col 1.
        *   Row 5: Seeds at col 0 and 2.
    *   **Interpretation of "Sway side to side" and "Splits":**
        *   It looks like a zig-zag or a diamond shape expanding and contracting?
        *   Actually, looking at the coordinates:
            *   (0, 1) -> (1, 0), (1, 2) -> (2, 1) -> (3, 0), (3, 2) -> (4, 1) -> (5, 0), (5, 2).
        *   Wait, the description says "On each swing the root splits briefly into two tendrils reaching to either side, then reconverges on the next level before splitting again."
        *   Let's trace a single root.
            *   Start at (0, 1).
            *   "Sw

... [26970 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.67)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 214: "A jeweler counts the perfect emeralds among rough stones and ... [38 chars truncated]" k=4 alts: 0/0 3b4c2228

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Example 5

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Literal Description

See: The input grid contains three types of colored elements on a black background: solid 2x2 green (G) blocks, solid 2x2 red (R) blocks, and isolated single green or red cells that do not form part of any 2x2 block. Only the solid 2x2 green blocks are meaningful; the 2x2 red blocks and all isolated single-color cells are distractors.

Do: 1. Scan the entire input grid to find all distinct, non-overlapping 2x2 regions composed entirely of green (G) cells. 2. Count the total number of such 2x2 green blocks. Call this count N. 3. Create a 3x3 output grid filled with black (.) cells. 4. Place N blue (B) cells along the main diagonal of the output grid, starting from the top-left corner: position (0,0), then (1,1), then (2,2), filling as many diagonal positions as N requires (N will be between 1 and 3).

Grid: The input grid varies in size (rows and columns differ across instances) and uses a black (.) background with green (G) and red (R) colored cells. The output grid is always exactly 3x3 with a black (.) background, containing between 1 and 3 blue (B) cells placed along the main diagonal from top-left to bottom-right.

Figurative Descriptions (1 variants)

"A jeweler counts the perfect emeralds among rough stones and lights candles down a dark staircase."

qwen3.6-35b: k=4

See: Scattered across a dark workbench are green and red stones of various sizes. Some stones are perfectly cut — flawless 2×2 emeralds that catch the light. Others are rough chunks of red garnet in similar shapes, and lone gem chips of both colors lie strewn about like shavings from the cutting wheel. Only the master jeweler's trained eye can distinguish the true emeralds from the noise.

Do: The jeweler inspects the workbench and counts only the perfect emeralds — the ones with that unmistakable 2×2 cut. For each true emerald found, the jeweler descends one step into the cellar, lighting a blue candle on each landing as they go. The staircase runs diagonally from the top landing to the bottom, and only as many candles are lit as emeralds were counted above.

Grid: The workbench above varies in size and is cluttered with green and red stones of different shapes against a dark surface. The cellar staircase below is always a small 3×3 chamber of darkness, where blue candle flames mark each step taken along the diagonal descent from the upper-left landing to the lower-right.

qwen3.6-35b — MARC valid, solved with 4 examples

Input

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Prediction

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Reasoning (29744 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Input Grid:** Represents a "workbench" cluttered with stones.
    *   **Green stones (G):** Represent "emeralds".
    *   **Red stones (R):** Represent "garnets" (noise/rough chunks).
    *   **Black background (.):** Represents the "dark workbench" or "cellar darkness".
    *   **Output Grid:** Represents the "cellar staircase" with "blue candles" (B).

*   **AFFORDANCES (Capabilities/Actions):**
    *   **Green stones (G):** Can form specific shapes. Specifically, "perfectly cut — flawless 2×2 emeralds".
    *   **Red stones (R):** Can form shapes, but are described as "rough chunks" or "noise".
    *   **2x2 Green Block:** This is the target object. It's a square of 4 'G's.
    *   **Blue Candle (B):** Represents a count of the target objects.

*   **TRANSFORMATION RULE:**
    *   **Step 1: Identify Target Objects.** Look for "perfect emeralds". The description says "flawless 2×2 emeralds". This implies finding 2x2 subgrids consisting entirely of 'G's.
    *   **Step 2: Count Target Objects.** Count how many distinct 2x2 blocks of 'G's exist in the input grid.
    *   **Step 3: Generate Output.** The output is a 3x3 grid (the "cellar staircase").
    *   **Step 4: Place Candles.** "For each true emerald found, the jeweler descends one step into the cellar, lighting a blue candle on each landing as they go." "The staircase runs diagonally from the top landing to the bottom".
    *   **Interpretation of Output Placement:**
        *   The output grid is always 3x3.
        *   The candles (B) are placed on the diagonal from top-left to bottom-right.
        *   The number of candles equals the count of 2x2 'G' blocks found.
        *   If count = 1, place B at (0,0).
        *   If count = 2, place B at (0,0) and (1,1).
        *   If count = 3, place B at (0,0), (1,1), and (2,2).
        *   If count > 3? The examples show counts up to 3. Let's check the examples to confirm the counting logic and output size.

**2. Analyzing Training Examples**

*   **Example 1:**
    *   Input:
        ```
        . G G . .
        . G G . .
        . . . . .
        R R . . R
        R R . . .
        . . . R R
        . . . R R
        ```
    *   Scanning for 2x2 'G' blocks:
        *   Top-left area: Rows 0-1, Cols 1-2 contain `G G` / `G G`. That's one 2x2 block.
        *   Are there others? No other 'G's.
    *   Count = 1.
    *   Output:
        ```
        B . .
        . . .
        . . .
        ```
    *   Logic check: 1 candle on the diagonal (0,0). Matches.

*   **Example 2:**
    *   Input:
        ```
        . G G . . . G
        . G G . . . .
        . . . . R . .
        G . . . G G .
        . . G . G G .
        ```
    *   Scanning for 2x2 'G' blocks:
        *   Top-left: Rows 0-1, Cols 1-2 contain `G G` / `G G`. (Count = 1).
        *   Bottom-

... [26886 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.11)

Prediction

Expected

Figurative + 4 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 223: "Scattered seeds fall and pile into pyramids on the ground." k=3 alts: 1/15 3d6c6e23

Training Examples

Example 1

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Example 2

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Example 3

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Literal Description

See: The input grid has a black background with one or more columns containing colored cells. Each such column has colored cells scattered vertically in its upper portion, separated by gaps of black cells, with empty space below. A column may contain cells of a single color or multiple colors. When multiple colors appear in a column, they are grouped contiguously from top to bottom (e.g., all red cells appear above all blue cells). The total number of colored cells in each column is always a perfect square (1, 4, 9, 16, ...).

Do: For each column that contains colored cells, do the following independently: (1) Count the total number of colored cells N in that column. Compute the triangle size as sqrt(N), call it S. (2) Record the colors from top to bottom in the column, preserving their order. (3) Clear the entire column. (4) Build a triangle of S rows at the very bottom of the grid, centered on that column. The bottom row of the triangle sits on the last row of the grid. Row widths from top to bottom are 1, 3, 5, ..., 2S-1 (odd numbers). Each row is horizontally centered on the column. (5) Fill the triangle rows with colors from top (narrowest) to bottom (widest). Assign colors in the same top-to-bottom order as they appeared in the input column: the first color fills cells starting from the top row of the triangle, consuming one cell per triangle position left-to-right, top-to-bottom, until that color's count is exhausted, then continue with the next color. All cells not part of any triangle become black.

Grid: The output grid has the same dimensions as the input grid. The background is entirely black except for the triangle(s) drawn at the bottom. Multiple columns may each produce their own independent triangle, and these triangles coexist on the grid without overlapping. Triangles are always bottom-aligned (touching the last row) and horizontally centered on their source column.

Figurative Descriptions (16 variants)

"Scattered seeds fall and pile into pyramids on the ground."

qwen3.6-35b: k=3

See: Against a night sky, colored seeds float in vertical columns — hovering in the upper air, spaced unevenly as if suspended by invisible threads. Some columns hold seeds of a single hue; others carry layers of different colors stacked like geological strata, one color giving way to the next below it. The ground below sits empty, waiting.

Do: Gravity finally switches on. Every floating seed in a column falls, but rather than simply dropping straight down, the seeds accumulate into a neat triangular mound resting on the ground floor — like sand pouring through an hourglass and forming a perfect pile. The colors preserve their original layering: whatever was highest in the sky settles at the peak of the mound, and the deepest colors spread across its wide base. The more seeds that fall, the taller and broader the pyramid they build.

Grid: The sky clears completely — all black — and only the triangular mounds remain, each sitting flush against the bottom edge of the grid, centered beneath where its seeds once floated. If multiple columns had seeds, multiple independent pyramids form side by side, each loyal to its own column. The night reclaims everything the pyramids don't touch.

qwen3.6-35b — MARC valid, solved with 3 examples

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Reasoning (28928 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Background:** Black (`.`). Represents empty space or the "night sky".
    *   **Seeds:** Colored characters (`R`, `O`, `B`, etc.). These are the objects that move.
    *   **Ground:** The bottom row(s) of the grid.
    *   **Pyramids/Mounds:** The resulting structures formed by the seeds.

*   **AFFORDANCES (Capabilities/Actions):**
    *   **Seeds:** They "float" initially in columns. They "fall" due to gravity. They "accumulate" into a triangular mound.
    *   **Columns:** Seeds are grouped by their column index.
    *   **Pyramids:** They sit on the bottom edge. They are centered. They are triangular.

*   **TRANSFORMATION RULE:**
    *   **Input:** A grid with colored seeds scattered in columns against a black background.
    *   **Process:**
        1.  Identify columns containing seeds.
        2.  For each column, count the number of seeds.
        3.  The seeds in a column fall to the bottom.
        4.  They form a "neat triangular mound" (pyramid).
        5.  The pyramid is centered horizontally relative to the original column position? Or just centered in the grid? The description says "centered beneath where its seeds once floated". This implies the pyramid's base is centered on the column index.
        6.  The pyramid shape is triangular. Let's look at the examples to determine the exact shape.
        7.  **Color Preservation:** "The colors preserve their original layering: whatever was highest in the sky settles at the peak of the mound, and the deepest colors spread across its wide base." This means the order of colors from top to bottom in the input column is preserved from the peak (top) to the base (bottom) of the pyramid.
        8.  **Multiple Columns:** "If multiple columns had seeds, multiple independent pyramids form side by side". This suggests the pyramids don't merge; they stay in their respective columns.
        9.  **Grid Size:** The output grid size seems to match the input grid size.

**2. Analyzing Training Examples**

*   **Example 1:**
    *   Input: 15x15 grid.
    *   Seeds: `O` (orange) in column 6 (0-indexed? let's count).
    *   Let's check indices.
    *   Row 1: `.` `.` `.` `.` `.` `.` `O` `.` ... -> Index 6.
    *   Row 2: `O` at index 6.
    *   Row 4: `O` at index 6.
    *   Row 5: `O` at index 6.
    *   Row 6: `O` at index 6.
    *   Row 8: `O` at index 6.
    *   Row 10: `O` at index 6.
    *   Row 11: `O` at index 6.
    *   Row 12: `O` at index 6.
    *   Total `O` seeds: 9.
    *   Output:
        *   Row 13 (index 13): `.` `.` `.` `.` `.` `.` `O` `.` ... -> 1 seed at index 6.
        *   Row 14 (index 14): `.` `.` `.` `.` `.` `O` `O` `O` `.` ... -> 3 seeds at indices 5, 6, 7.
        *   Row 15 (index 15): `.` `.` `.` `.` `O` `O` `O` `O` `O` `.` ... -> 5 seeds at indices 4, 5, 6, 7, 8.
    *   Wait, the grid in Example 1 output has 16 rows? Let's count.
    *   I

... [26153 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.01)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 230: "A dam swells with the pressure of raindrops falling on eithe ... [7 chars truncated]" k=1 alts: 0/0 4093f84a

Training Examples

Example 1

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Example 2

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Example 3

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Literal Description

See: The input grid contains a solid rectangular barrier made of grey (X) cells that spans the full height or width of the grid, oriented either vertically or horizontally. The barrier is several cells thick. Scattered across the grid on both sides of the barrier are colored dots (a single non-black, non-grey color such as green, red, blue, or yellow) placed on the otherwise black (.) background.

Do: 1. Identify the solid rectangular grey (X) barrier and its orientation (vertical or horizontal). 2. Identify all colored dots in the grid. 3. For each row (if the barrier is vertical) or each column (if the barrier is horizontal), count how many colored dots appear on each side of the barrier. 4. Extend the barrier outward on that side by exactly as many cells as there are dots on that side in that row or column. For example, if a vertical barrier spans columns 5-6 and row 11 has two colored dots to the left of the barrier, extend the barrier leftward in row 11 by 2 cells (filling columns 3 and 4 with X). If the same row has one dot to the right, extend rightward by 1 cell (filling column 7 with X). 5. Remove all colored dots from the grid, replacing them with black (.).

Grid: The grid is rectangular, typically 14 columns wide and 14 rows tall. The background is black (.). The grey barrier is a contiguous rectangular block spanning the full length of one dimension (all rows or all columns) and is 2 to 5 cells thick in the other dimension. The output grid has the same dimensions as the input. The only changes are: the barrier grows locally in certain rows/columns, and all colored dots are erased.

Figurative Descriptions (1 variants)

"A dam swells with the pressure of raindrops falling on either side."

qwen3.6-35b: k=1

See: A thick grey dam stretches across the landscape, dividing the world in two. Scattered across the terrain on both sides, colored raindrops have fallen and pooled on the ground, each one exerting pressure against the dam's nearest face.

Do: The dam feels the weight of every raindrop pushing against it. Along each channel — each row or column running perpendicular to the dam — the structure bulges outward, absorbing one raindrop's worth of thickness for each drop pressing from that side. As the dam swells to accommodate the pressure, the raindrops themselves are consumed, soaked into the earth and vanishing entirely. The dam remembers where it was pushed but forgets what pushed it.

Grid: The world is a rectangular floodplain of black earth. The dam is a solid grey wall, several cells thick, running the full length of one dimension. Colored raindrops are single cells of one color, scattered on both sides. After the flood, only the original dam remains — now with local bulges where pressure was greatest — and the raindrops are gone, leaving bare earth behind.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (28937 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Visuals:** A "thick grey dam" (X) divides the world. "Colored raindrops" (other colors) are scattered on both sides.
*   **Action:** The dam feels pressure from raindrops.
*   **Mechanism:** "Along each channel — each row or column running perpendicular to the dam — the structure bulges outward, absorbing one raindrop's worth of thickness for each drop pressing from that side."
*   **Result:** Raindrops vanish. The dam swells (bulges) into the empty space (black earth `.`) where the raindrops were. The dam remembers where it was pushed.
*   **Grid details:** Rectangular floodplain (black `.`). Dam is solid grey (`X`), several cells thick, running full length of one dimension. Raindrops are single cells. Output contains only the modified dam and black earth.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   **Input Grid:** 14 rows, 15 columns.
    *   **Dam:** A vertical wall of `X`s. Let's locate it.
        *   Columns 4, 5, 6, 7, 8 (0-indexed) seem to be `X`. Wait, let's look closer.
        *   Row 0: `. . . . X X X X X . . . G .` -> Indices 4,5,6,7,8 are X.
        *   It looks like a vertical wall of width 5.
    *   **Raindrops:** `G` (green) cells scattered.
    *   **Transformation:**
        *   Look at Row 0: Input has `G` at index 13. Output has `X` at index 9. Wait, let's check the output carefully.
        *   Input Row 0: `. . . . X X X X X . . . G .` (Indices: 0-3 are ., 4-8 are X, 9-12 are ., 13 is G, 14 is .)
        *   Output Row 0: `. . . . X X X X X X . . . .` (Indices: 0-3 are ., 4-9 are X, 10-14 are .)
        *   Wait, the dam moved? Or expanded?
        *   Input dam is at cols 4,5,6,7,8.
        *   Output dam is at cols 4,5,6,7,8,9.
        *   The `G` at col 13 is gone.
        *   The dam expanded to the right by 1 cell?
        *   Let's check Row 2.
        *   Input Row 2: `. . . G X X X X X . . G . .`
            *   Left side: `G` at index 3.
            *   Dam: `X` at 4,5,6,7,8.
            *   Right side: `G` at index 10.
        *   Output Row 2: `. . . X X X X X X X . . . .`
            *   Left side: `X` at index 3.
            *   Dam: `X` at 4,5,6,7,8,9.
            *   Right side: `.` at 10.
        *   Wait, the dam expanded to the *left* as well?
        *   Input dam width: 5 cells (4-8).
        *   Output dam width: 7 cells (3-9).
        *   It seems the dam expanded by 1 cell to the left (absorbing the `G` at 3) and 1 cell to the right (absorbing the `G` at 10).
        *   Wait, the `G` at 10 is at distance 2 from the dam (index 10 vs 8). The `G` at 3 is at distance 1 from the dam (index 3 vs 4).
        *   Let's re-read the rule: "absorbing one raindrop's worth of thickness for each drop pressing from that side."
        *   Maybe it's not about distance, but just count?
        *   Let's look at Ro

... [25979 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.91)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 244: "Picture frames preserve the wood but reveal the wall behind ... [5 chars truncated]" k=2 alts: 0/0 4347f46a

Training Examples

Example 1

Input

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Output

Example 2

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Output

Example 3

Input

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Output

Literal Description

See: The input grid contains one or more solid filled rectangles of various colors placed on a black background. Each rectangle is a contiguous block of identically-colored cells forming an axis-aligned rectangle. The rectangles do not overlap and are separated from each other and from the grid edges by black cells.

Do: For each solid colored rectangle in the grid, hollow it out by keeping only its 1-cell-wide border and replacing all interior cells with black. Specifically: preserve the top row, bottom row, leftmost column, and rightmost column of the rectangle, and set every cell that is not on one of these four edges to black.

Grid: The grid dimensions remain unchanged from input to output. The background is black (.). Rectangles vary in size and color but are always at least 3 cells in both dimensions, ensuring there is an interior to hollow out.

Figurative Descriptions (1 variants)

"Picture frames preserve the wood but reveal the wall behind them."

qwen3.6-35b: k=2

See: Colorful canvases hang on a dark gallery wall, each one a solid painted panel — no image, just pure pigment filling every inch of the frame.

Do: The curator removes the canvas from each frame, leaving only the wooden border behind. Where thick paint once covered everything, now you see straight through to the dark wall. The frame remains intact — sturdy on all four sides — but the heart of each piece has been opened up, as if the painting were just a window that forgot it could be transparent.

Grid: The gallery wall stays the same size. The dark wall (.) shows through wherever a canvas has been cleared. Every frame is built from the same color as its original canvas, and each piece is large enough that there's something behind the frame to reveal.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (25342 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   `.` (black): The background or "dark wall".
    *   Colored characters (R, G, B, Y, M, A, etc.): Represent "canvases" or "paintings" hanging on the wall. They form rectangular blocks of solid color.
    *   The "frame": The outer boundary of these colored blocks.

*   **AFFORDANCES (Capabilities/Actions):**
    *   Canvases are solid blocks of color.
    *   The transformation involves "removing the canvas" from the "frame".
    *   The "frame" remains intact.
    *   The "heart" (interior) is opened up, revealing the "dark wall" (`.`).
    *   The frame color matches the original canvas color.

*   **TRANSFORMATION RULE:**
    *   Identify contiguous rectangular regions of a single color (excluding the background `.`).
    *   For each such region, keep the outer boundary pixels (the frame) as they are.
    *   Change the inner pixels (the heart) to the background color `.`.
    *   Essentially, hollow out the solid colored rectangles.

Let's verify this rule with the training examples.

**Example 1 Analysis:**
Input:
```
. . . . . . .
. R R R R R .
. R R R R R .
. R R R R R .
. R R R R R .
. . . . . . .
. . . . . . .
. . . . . . .
```
There is a 4x5 block of 'R's (rows 1-4, cols 1-5, 0-indexed).
Wait, let's look at coordinates.
Row 1: `. R R R R R .` (indices 1 to 5)
Row 2: `. R R R R R .`
Row 3: `. R R R R R .`
Row 4: `. R R R R R .`
It's a 4 rows x 5 columns block of R.
Output:
```
. . . . . . .
. R R R R R .
. R . . . R .
. R . . . R .
. R R R R R .
. . . . . . .
. . . . . . .
. . . . . . .
```
The outer border of the R block is kept. The inner 2x3 area becomes `.`.
This matches the "hollow out" rule.

**Example 2 Analysis:**
Input contains multiple colored blocks.
1.  **Azure (A) block:**
    Rows 1-3, Cols 1-4.
    Row 1: `. A A A A .`
    Row 2: `. A A A A .`
    Row 3: `. A A A A .`
    Wait, looking at input:
    Row 1: `. A A A A . . .`
    Row 2: `. A A A A . . .`
    Row 3: `. A A A A . G G G G G G G . . .`
    Actually, let's trace carefully.
    Input Grid:
    Row 0: `.`...
    Row 1: `. A A A A . . .` (A's at cols 1,2,3,4)
    Row 2: `. A A A A . . .` (A's at cols 1,2,3,4)
    Row 3: `. A A A A . G G G G G G G . . .` (A's at cols 1,2,3,4)
    Wait, row 3 has A's? Yes.
    So A block is 3 rows high (1,2,3) and 4 cols wide (1,2,3,4).
    Output for A block:
    Row 1: `. A A A A .` (Top border kept)
    Row 2: `. A . . A .` (Inner hollowed)
    Row 3: `. A A A A .` (Bottom border kept)
    Wait, looking at Example 2 Output:
    Row 1: `. A A A A .`
    Row 2: `. A . . A .`
    Row 3: `. A A A A .`
    Yes, it's hollowed.

2.  **Green (G) block:**
    Starts Row 3, Col 6.
    Row 3: `... G G G G G G G ...` (Cols 6-12)
    Row 4: `... G G G G G G G ...`
    Row 5: `... G G G G G G G ...`
    Row 6: `... G G G G G G G ...`
    Row 7: `... G G G G G G G ...`
    I

... [22450 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.96)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 246: "A volcano fills its crater and erupts a plume of its unique ... [30 chars truncated]" k=2 alts: 0/0 444801d8

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

Input

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Output

Literal Description

See: The input grid contains one or more U-shaped containers made of blue (B) cells. Each container is a rectangular outline (5 columns wide) with a gap of one or more cells in the top wall — specifically, the interior cells of the top row are missing, leaving only the two corner cells. Inside each container, exactly one non-black, non-blue colored cell (the signal color) is placed somewhere among otherwise black interior cells. The rest of the grid is black background.

Do: For each blue U-shaped container: (1) Identify the signal color — the single non-black, non-blue cell inside the container. (2) Fill every black cell in the interior of the container with the signal color. (3) Fill the gap cells in the top wall of the container (the interior positions of the top row, between the two blue corner cells) with the signal color, closing the opening. (4) In the row immediately above the container (just outside the now-closed top wall), place a full horizontal stripe of the signal color spanning the same column range as the container's full width. All other cells in the grid remain unchanged.

Grid: The grid is 10 rows by 10 columns with a black (.) background. Each U-shaped container occupies a 5-column-wide rectangular region: the bottom row and two side columns are fully blue, the top row has blue only at the two ends (corners), and the interior is 3 columns wide. Containers do not overlap and are axis-aligned. The output grid has the same dimensions as the input.

Figurative Descriptions (1 variants)

"A volcano fills its crater and erupts a plume of its unique lava color into the sky above."

qwen3.6-35b: k=2

See: Blue volcanic craters sit on the black landscape, each with a broken rim — the mountaintop has crumbled open on one side, leaving a gap in the caldera wall. Deep inside each crater, a single glowing ember of colored magma hints at what lies dormant beneath the surface.

Do: Each volcano awakens. The magma surges upward, flooding every dark hollow inside the crater with its molten color. The lava seals the broken rim shut, fusing the gap closed. But the eruption doesn't stop there — a plume of that same radiant color bursts above the sealed peak, painting the sky directly over the volcano in a banner as wide as the mountain itself.

Grid: The landscape is a 10-by-10 expanse of black night. Each volcano is a blue-walled basin five columns across — sturdy walls on three sides, but the top edge is fractured, with only the corner stones remaining. The ember sits somewhere in the three-column-wide hollow within. After the eruption, the row just above each volcano bears the colorful plume, while the sealed crater glows uniformly from within.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (28316 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Input Landscape:** 10x10 grid of black dots (`.`).
*   **Volcano Structure:**
    *   Blue walls (`B`).
    *   5 columns wide.
    *   "Sturdy walls on three sides" (Left, Right, Bottom).
    *   "Top edge is fractured, with only the corner stones remaining." This implies the top row of the 5x3 structure (or similar) is missing the middle parts, leaving corners. Let's look at the examples to confirm the shape.
    *   "Deep inside each crater, a single glowing ember of colored magma hints at what lies dormant beneath the surface." This means there is a colored pixel (`R`, `G`, `Y`, etc.) inside the blue walls.
*   **Transformation (Eruption):**
    *   "Magma surges upward, flooding every dark hollow inside the crater with its molten color." -> The interior of the blue walls (where `.` was) gets filled with the color of the ember.
    *   "The lava seals the broken rim shut, fusing the gap closed." -> The top edge of the blue walls (which was open/fractured) gets filled with the magma color? Or maybe the blue walls stay, but the gap is filled? Let's check the examples.
    *   "A plume of that same radiant color bursts above the sealed peak, painting the sky directly over the volcano in a banner as wide as the mountain itself." -> A row of the magma color appears *above* the volcano structure.

**2. Analyze Training Examples to refine the rules:**

**Example 1:**
*   **Input:**
    *   Volcano 1 (Red ember `R`):
        *   Rows 2-5 (0-indexed? Let's count).
        *   Row 2: `. B B . B B . . . .` -> Wait, looking at the input grid.
        *   Row 0: `.`
        *   Row 1: `.`
        *   Row 2: `. B B . B B . . . .` -> This looks like two separate structures or a wide one?
        *   Let's look at the shape.
        *   Row 2: `B B` at cols 1,2 and `B B` at cols 4,5. Gap at 3.
        *   Row 3: `B . R . B` at cols 1,2,3,4,5. Wait, `B . R . B`.
        *   Row 4: `B . . . B` at cols 1,2,3,4,5.
        *   Row 5: `B B B B B` at cols 1,2,3,4,5.
        *   This looks like a 5-wide structure.
        *   Top row (Row 2) has `B B` at left, `B B` at right. The middle is `.`. Wait, the description says "top edge is fractured, with only the corner stones remaining".
        *   Let's check the columns.
        *   Col 1: B, B, B, B (Rows 2,3,4,5).
        *   Col 2: B, ., ., B (Rows 2,3,4,5).
        *   Col 3: ., R, ., B (Rows 2,3,4,5). Wait, Row 2 Col 3 is `.`.
        *   Col 4: B, ., ., B (Rows 2,3,4,5).
        *   Col 5: B, B, B, B (Rows 2,3,4,5).
        *   Actually, looking at Row 2: `. B B . B B . . . .`. Indices: 0=., 1=B, 2=B, 3=., 4=B, 5=B.
        *   Row 3: `. B . R . B . . . .`. Indices: 1=B, 2=., 3=R, 4=., 5=B.
        *   Row 4: `. B . . . B . . . .`. Indices: 1=B, 2=., 3=., 4=., 5=B.
        *   Row 5: `. B B B B B . . . .`. Indices: 1=B, 2=B, 3=B, 4=

... [25382 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.78)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 270: "The green jewel is a hall of mirrors, and the red dancer see ... [32 chars truncated]" k=2 alts: 9/15 4938f0c2

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Literal Description

See: The input grid contains exactly two objects on a black background: (1) a green 2×2 block, and (2) a red shape made of connected red cells. The red shape is adjacent to the green block, positioned on one side (or in one quadrant) relative to the green center. The green block acts as a central pivot point.

Do: Find the center of the green 2×2 block (the point where its four cells meet). Reflect the entire red shape to produce four-fold symmetry around this center point: (1) mirror the red shape horizontally across the vertical axis through the green center, (2) mirror the red shape vertically across the horizontal axis through the green center, and (3) mirror it diagonally (equivalently, apply both horizontal and vertical reflections). For each original red cell at position (r, c), compute the three reflected positions using the green center (cr, cc): horizontally reflected to (r, 2·cc − c − 1), vertically reflected to (2·cr − r − 1, c), and doubly reflected to (2·cr − r − 1, 2·cc − c − 1). Place red cells at all reflected positions. Keep the green block unchanged. If a reflected copy already exists (the input already has symmetry in some direction), the output is unchanged in that region.

Grid: The grid dimensions match the input exactly (variable size). The background is black (.). The green 2×2 block remains in place. The output grid contains the original red shape plus up to three reflected copies, forming four-fold (bilateral + rotational) symmetry around the green block's center.

Figurative Descriptions (16 variants)

"The green jewel is a hall of mirrors, and the red dancer sees her reflections on every wall."

qwen3.6-35b: k=2

See: A red dancer strikes a pose near a small green jewel sitting on a dark stage. The jewel has four perfectly polished faces — it is a tiny mirror box at the heart of the world.

Do: The green jewel awakens and casts the dancer's image outward in every direction it can reflect — left and right, up and down, and corner to corner. Wherever the dancer stands, her reflections appear on the opposite sides of the jewel, as if she is performing inside a kaleidoscope. The jewel itself never moves — it only watches and reflects. If a reflection would land where the dancer (or another reflection) already stands, nothing changes — mirrors don't argue over who arrived first.

Grid: The dark stage stays the same size. The green jewel remains fixed at its position, glowing quietly. The red dancer now appears to be surrounded by her own reflections, forming a symmetrical constellation that honors the jewel as its center. Every quadrant around the jewel tells the same story, just viewed from a different mirror.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (33288 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST:**
    *   **The Dancer:** Represented by the color Red (R). It's a shape or pattern of red pixels.
    *   **The Jewel:** Represented by the color Green (G). It's a 2x2 block of green pixels. It acts as the center of reflection.
    *   **The Stage:** The background, represented by black (.) or empty space.
    *   **Reflections:** Copies of the Dancer (Red) appearing in other quadrants relative to the Jewel.

*   **AFFORDANCES:**
    *   **The Jewel (G):** It is the pivot point. It stays fixed. It defines the axes of symmetry. Since it's a 2x2 block, the center of symmetry is the intersection of the grid lines between the four green pixels.
    *   **The Dancer (R):** It is the source pattern. It gets reflected across the horizontal and vertical axes defined by the Jewel.
    *   **Reflections:** The rule implies 4-way symmetry (quadrants) centered on the Jewel.

*   **TRANSFORMATION RULE:**
    *   Identify the center of the Green Jewel (G). Since it's a 2x2 block, the center is the point between the four G's.
    *   Identify the Red Dancer (R) pixels.
    *   Reflect the Red pixels across the horizontal axis passing through the center of the G block.
    *   Reflect the Red pixels across the vertical axis passing through the center of the G block.
    *   Reflect the Red pixels across both axes (diagonal reflection relative to the center point).
    *   Essentially, create a 4-way symmetric pattern centered on the G block.
    *   If a reflection lands on an existing Red pixel, it stays Red. If it lands on a Green pixel, it stays Green (Jewel never moves). If it lands on empty space, it becomes Red.
    *   Wait, let's look at the examples to confirm the exact mechanics.

**2. Analyzing Training Examples**

*   **Example 1:**
    *   **Input:**
        *   Red shape: A sort of 'L' or '7' shape or just a cluster.
            Row 0: . R R . . . . . . .
            Row 1: . R . R . . . . . .
            Row 2: . . R R . . . . . .
            Row 3: . . . . G G . . . .
            Row 4: . . . . G G . . . .
        *   Green Jewel: 2x2 block at (3,4), (3,5), (4,4), (4,5).
        *   Center of Jewel: Between row 3/4 and col 4/5. Let's call the center coordinates (3.5, 4.5).
    *   **Output:**
        *   The Red shape is now in all 4 quadrants around the center.
        *   Top-Left (Original): Rows 0-2, Cols 0-3.
        *   Top-Right: Rows 0-2, Cols 6-9.
        *   Bottom-Left: Rows 5-7, Cols 0-3.
        *   Bottom-Right: Rows 5-7, Cols 6-9.
    *   **Symmetry Check:**
        *   Original R at (0,1). Center (3.5, 4.5).
            *   Horizontal reflection (across y=3.5): y' = 3.5 + (3.5 - 0) = 7. x' = 1. -> (7,1). Output has R at (7,1)? Let's check.
                Output Row 7: . R R . . . . R R . -> Yes, (7,1) is R.
            *   Vertical reflection (across x=4.5): x' = 4.5 +

... [30474 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.04)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 277: "Geological strata reveal the age of the earth when read in s ... [7 chars truncated]" k=1 alts: 0/0 4be741c5

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input grid contains several distinct color regions arranged as vertical bands or stripes running from left to right across the grid. Each band spans the full height of the grid, though the boundary between adjacent bands is jagged and irregular rather than a straight vertical line. The colors do not overlap — every cell belongs to exactly one band, and the bands tile the entire grid.

Do: Identify each distinct color present in the grid. Determine the spatial ordering of these color bands from left to right by observing which color dominates the leftmost columns, which comes next, and so on. Output a single row listing each color exactly once, in left-to-right spatial order. If the bands run top to bottom instead of left to right, list them in top-to-bottom order and output a single column instead.

Grid: The output grid is a single row (if bands are arranged left-to-right) or a single column (if bands are arranged top-to-bottom), with one cell per distinct color band. The number of cells equals the number of distinct colors in the input.

Figurative Descriptions (1 variants)

"Geological strata reveal the age of the earth when read in sequence"

qwen3.6-35b: k=1

See: The grid is a cross-section of ancient rock, where each color is a geological layer — sediment deposited in a different era. The boundaries between layers are not clean cuts but the ragged, eroded edges where one epoch gave way to the next. The stone tells its own history in the order the layers were laid down.

Do: Read the rock like a geologist: identify each distinct stratum and record the ages in the order they were deposited — from the oldest exposed edge to the youngest. Each era appears only once in the fossil record you compile.

Grid: The fossil record is a single core sample — one cell per era, arranged in the order the layers appear across the rock face.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (38938 chars)

The user wants me to solve a grid transformation puzzle.

**1. Analyze the Input and Output format:**
- Input: A 2D grid of characters representing colors.
- Output: A 1D grid (or list) of characters representing colors.
- Color Key: `.`=black, `B`=blue, `R`=red, `G`=green, `Y`=yellow, `X`=grey, `M`=magenta, `O`=orange, `A`=azure, `W`=maroon.

**2. Analyze the Metaphorical Description:**
- "Grid is a cross-section of ancient rock... each color is a geological layer".
- "Boundaries... ragged, eroded edges".
- "Read the rock like a geologist: identify each distinct stratum and record the ages in the order they were deposited — from the oldest exposed edge to the youngest."
- "Each era appears only once in the fossil record you compile."
- "The fossil record is a single core sample — one cell per era, arranged in the order the layers appear across the rock face."

**3. Analyze the Training Example:**
Input:
```
R R R R R R R
R R R R R R R
R R R R R R R
R A A A R R A
A A A A A A A
A A A A A A A
A A A X X A A
X A X X X X X
X X X X X X X
```
Output:
```
R
A
X
```

**4. Conceptual Digestion:**

*   **CAST (Roles):**
    *   The grid contains regions of uniform color.
    *   Colors represent "strata" or "eras".
    *   The output is a sequence of these colors.

*   **AFFORDANCES (Properties/Actions):**
    *   Colors are adjacent to each other.
    *   There is a spatial arrangement.
    *   The description mentions "oldest exposed edge to the youngest".
    *   In geology, usually, the oldest layers are at the bottom and youngest at the top (Law of Superposition). However, the description says "order they were deposited" and "oldest exposed edge to the youngest". Let's look at the example to deduce the specific ordering logic.

*   **TRANSFORMATION RULE:**
    *   Let's look at the input grid of Example 1.
    *   Top rows are mostly 'R' (Red).
    *   Middle rows are mostly 'A' (Azure).
    *   Bottom rows are mostly 'X' (Grey).
    *   The output is `R`, `A`, `X`.
    *   This corresponds to the order from Top to Bottom.
    *   Let's check the "oldest exposed edge" phrasing. If the rock is a cross-section, usually the bottom is older. But the output is R -> A -> X. R is at the top, X is at the bottom.
    *   Wait, the text says "record the ages in the order they were deposited — from the oldest exposed edge to the youngest".
    *   If R is at the top and X is at the bottom, and the output is R, A, X, then R is considered the "oldest" in the output sequence? Or is the output just listing the layers from top to bottom?
    *   Let's re-read carefully: "record the ages in the order they were deposited — from the oldest exposed edge to the youngest."
    *   If the output is R, A, X, and R is at the top, maybe the "exposed edge" is the top? Or maybe the description is metaphorical and just means "list the distinct colors found in the grid in a specific order".
    *   Let's look at the spatial distribution.
        *   R 

... [36172 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 278: "A compass needle summons its companion — the red weath ... [70 chars truncated]" k=4 alts: 0/0 4c177718

Training Examples

Example 1

Input

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Output

Example 2

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Output

Example 3

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Output

Example 4

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Output

Literal Description

See: The input is a 15x15 grid with a black background, divided into two sections by a horizontal grey (X) line spanning the full width at row 5. The top section (rows 0-4) contains exactly three non-black shapes arranged side by side, each fitting within a 3x3 bounding box occupying rows 1-3: one blue shape, one red shape, and one shape of a third color (e.g., orange, yellow, magenta, green). The red shape always resembles an arrow or T-shape — it is either wide at the top and narrow at the bottom (pointing down), or narrow at the top and wide at the bottom (pointing up). The bottom section (rows 6-14) contains a single blue shape that is identical in form to the blue shape in the top section, placed somewhere within the 9-row area.

Do: 1. Identify the three shapes in the top section: the blue shape, the red shape, and the companion shape (the third color). Note the 3x3 pixel pattern of each. 2. Identify the blue shape in the bottom section. Confirm it matches the top blue shape. Record its bounding box position (rows and columns) within the bottom section (rows 6-14, treated as a 9-row output grid, rows 0-8). 3. Determine the red shape's orientation: if the wider/heavier end is at the top (e.g., top row has 3 filled cells, bottom rows have 1), it points DOWN; if the wider end is at the bottom, it points UP. 4. Create a 9x15 output grid filled with black. 5. Place the blue shape at its exact position from the bottom section (same rows and columns relative to the 9-row grid). 6. Place the companion shape (using its original pixel pattern from the top section) at the same columns as the blue shape. If the red arrow points DOWN, place the companion shape immediately below the blue shape (its top row touches blue's bottom row + 1). If the red arrow points UP, place the companion shape immediately above the blue shape (its bottom row touches blue's top row - 1). 7. The companion shape's column alignment matches the blue shape's bounding box columns in the bottom section, not its original columns from the top section.

Grid: Input: 15 rows x 15 columns. A horizontal grey divider spans row 5. Top half (rows 0-4) is a legend area with three 3x3 shapes in rows 1-3. Bottom half (rows 6-14) is a query area with one blue shape. Output: 9 rows x 15 columns (same dimensions as the bottom section). Background is black (.). The output contains exactly two shapes stacked vertically and touching: the blue shape and the companion-color shape.

Figurative Descriptions (1 variants)

"A compass needle summons its companion — the red weathervane on the roof tells which direction the wind blows them together."

qwen3.6-35b: k=4

See: A grey horizon line divides the world in two. Above it, a rooftop display shows three figures standing side by side: a blue traveler, a red weathervane, and a colorful companion waiting to be called. The weathervane is asymmetric — its heavy end sags in one direction, pointing either up toward the sky or down toward the earth. Below the horizon, in the open field, a lone blue traveler stands waiting, identical to the one on the rooftop.

Do: The blue traveler in the field calls out to its companion from the rooftop. The companion leaps down from the display and lands next to the traveler, but which side it lands on depends on the weathervane. If the weathervane's heavy end points downward, the companion lands just below the traveler, like a shadow falling at their feet. If the heavy end points upward, the companion descends from above, landing on the traveler's head like a hat. The rooftop, the horizon, and the weathervane all vanish — only the reunited pair remains in the open field, pressed together with no gap between them.

Grid: The rooftop is a narrow band above a grey horizon. Three small figures perch there in a row, each fitting in a small square frame. The open field below is a larger empty expanse — nine rows of darkness. The output shows only this field, now occupied by two figures stacked flush against each other: the blue traveler anchored at its original position, and its colorful companion aligned to the same columns, placed above or below according to the weathervane's command.

qwen3.6-35b — MARC valid, solved with 4 examples

Input

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Prediction

vs

Expected

Reasoning (36768 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**

*   **Visuals:**
    *   "Grey horizon line": A row of 'X's (grey) dividing the grid.
    *   "Rooftop display": Area above the horizon.
    *   "Three figures standing side by side":
        1.  "Blue traveler" (B)
        2.  "Red weathervane" (R)
        3.  "Colorful companion" (G, Y, M, O, etc. - anything not B or R).
    *   "Weathervane is asymmetric": The shape of the 'R' block indicates direction.
    *   "Open field": Area below the horizon.
    *   "Lone blue traveler": A 'B' figure in the field.
*   **Action:**
    *   The blue traveler in the field calls the companion from the rooftop.
    *   The companion moves from the rooftop to the field.
    *   **Direction of movement:** Determined by the "weathervane" (the 'R' shape).
        *   "Heavy end points downward" -> Companion lands *below* the traveler (stacked vertically).
        *   "Heavy end points upward" -> Companion lands *above* the traveler (stacked vertically).
    *   **Result:**
        *   Rooftop, horizon, weathervane vanish.
        *   Only the field remains.
        *   The field contains the original blue traveler and the moved companion.
        *   They are "stacked flush against each other" (adjacent vertically).
        *   The companion aligns to the same columns as the traveler.

**2. Analyze the Grid Details:**

*   **Input Grid Structure:**
    *   Top section: Rooftop. Contains B, R, and a third color (let's call it C).
    *   Middle: Horizon line (X).
    *   Bottom section: Field. Contains a B figure.
*   **Output Grid Structure:**
    *   Same dimensions as input? Or just the field part?
    *   Looking at examples:
        *   Example 1 Input: 15 rows. Output: 9 rows. Wait, let's check dimensions.
        *   Input Ex 1: 15 rows, 15 cols.
        *   Output Ex 1: 9 rows, 15 cols.
        *   Wait, the description says "The output shows only this field". The field is the area below the horizon.
        *   In Ex 1, the horizon is at row index 5 (0-indexed). Rows 0-4 are rooftop. Row 5 is horizon. Rows 6-14 are field.
        *   Wait, let's count rows in Ex 1 Input.
            1.  . . . . . . . . . . . . . . .
            2.  . . B B . . R R R . . O . . .
            3.  . . . B . . . R . . O . O . .
            4.  . . . B B . . R . . . O . . .
            5.  . . . . . . . . . . . . . . .
            6.  X X X X X X X X X X X X X X X  <-- Horizon
            7.  . . . . . . . . . . . . . . .
            8.  . . . . . . . . . . . . . . .
            9.  . . . . . . . . . . . . . . .
            10. . . . . . . . . . . . . . . .
            11. . . . . . . . . . . . . . . .
            12. . . . . . . . . . . . . . . .
            13. . . . . . . . . . . . . . . .
            14. . . . . . . . . . . . . . . .
            15. . . . . . . . . . . . . . . .
            Wait, counting 

... [34039 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.01)

Prediction

Expected

Figurative + 4 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 290: "Two armies join forces under a shared banner" k=1 alts: 7/15 506d28a5

Training Examples

Example 1

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Output

Example 2

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Example 3

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Output

Example 4

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Output

Literal Description

See: The input grid consists of two equally-sized rectangular grids stacked vertically, separated by a single horizontal row of yellow (Y) cells that acts as a divider. The top grid contains red (R) cells and black (.) cells. The bottom grid contains blue (B) cells and black (.) cells.

Do: Remove the yellow divider row to isolate the top grid and bottom grid. Create an output grid of the same dimensions as either half. For each cell position, if the top grid has red (R) at that position OR the bottom grid has blue (B) at that position (or both), set the output cell to green (G). If neither grid has a colored cell at that position (both are black), set the output cell to black (.). This is a logical OR operation across the two grids.

Grid: The input grid has dimensions (2n+1) rows by m columns, where the middle row is entirely yellow. The output grid has dimensions n rows by m columns. In the examples, n=4 and m=5, producing a 9×5 input and a 4×5 output.

Figurative Descriptions (16 variants)

"Two armies join forces under a shared banner"

qwen3.6-35b: k=1

See: A golden river runs across the middle of the battlefield, dividing two kingdoms. Above the river, the Red Army has pitched its tents on certain squares. Below the river, the Blue Army holds its own positions. The rest of the land lies empty and dark.

Do: The war is over — the golden river dries up, and the two kingdoms merge into one. Wherever either army had claimed ground, the united banner of green now flies. Only the squares that neither army ever touched remain barren darkness. Every soldier, red or blue, becomes green in the new alliance.

Grid: The golden river is a single row splitting the world in half. The united kingdom is exactly the size of one half. Every plot of land answers one question: did anyone fight here? If so, it blooms green.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (29409 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Input and Output Grids from Training Examples:**

*   **Example 1 Input:**
    ```
    . . . . .
    . R R R .
    . R . . .
    R R R . R
    Y Y Y Y Y
    B B . . B
    B B . B B
    B . B . B
    . B . B B
    ```
    Dimensions: 9 rows, 5 columns.

*   **Example 1 Output:**
    ```
    G G . . G
    G G G G G
    G G G . G
    G G G G G
    ```
    Dimensions: 4 rows, 5 columns.

*   **Observations on Example 1:**
    *   The input has a row of 'Y' (yellow) at index 4 (0-indexed). This row acts as a divider.
    *   Above the 'Y' row (rows 0-3), there are 'R' (red) characters.
    *   Below the 'Y' row (rows 5-8), there are 'B' (blue) characters.
    *   The output grid has 4 rows. This corresponds to the number of rows *above* the yellow river (or below, since both halves have 4 rows).
    *   The output contains 'G' (green) and '.' (black).
    *   Let's map the positions.
        *   Input Row 0: `. . . . .` -> Output Row 0: `G G . . G`? Wait, let's look closer.
        *   Input Row 1: `. R R R .` -> Output Row 1: `G G G G G`?
        *   Input Row 2: `. R . . .` -> Output Row 2: `G G G . G`?
        *   Input Row 3: `R R R . R` -> Output Row 3: `G G G G G`?
    *   Wait, the mapping isn't a direct copy. Let's look at the "union" logic described in the text.
    *   Text: "Above the river, the Red Army has pitched its tents... Below the river, the Blue Army holds its own positions... Wherever either army had claimed ground, the united banner of green now flies."
    *   Text: "The united kingdom is exactly the size of one half."
    *   Text: "The golden river is a single row splitting the world in half."

    Let's re-examine Example 1 Input structure.
    Rows 0-3: Top half (Red Army).
    Row 4: River (Yellow).
    Rows 5-8: Bottom half (Blue Army).

    Top half content (Red Army):
    Row 0: `.` `.` `.` `.` `.`
    Row 1: `.` `R` `R` `R` `.`
    Row 2: `.` `R` `.` `.` `.`
    Row 3: `R` `R` `R` `.` `R`

    Bottom half content (Blue Army):
    Row 5: `B` `B` `.` `.` `B`
    Row 6: `B` `B` `.` `B` `B`
    Row 7: `B` `.` `B` `.` `B`
    Row 8: `.` `B` `.` `B` `B`

    Output grid size: 4x5.
    Output content:
    Row 0: `G` `G` `.` `.` `G`
    Row 1: `G` `G` `G` `G` `G`
    Row 2: `G` `G` `G` `.` `G`
    Row 3: `G` `G` `G` `G` `G`

    Let's check the logic: "Wherever either army had claimed ground, the united banner of green now flies."
    This implies a superposition or union of the two armies.
    However, the output is a single grid of size 4x5. The input has two halves of size 4x5.
    Does the output correspond to the top half, bottom half, or a combination?
    The text says "The united kingdom is exactly the size of one half."
    And "Wherever either army had claimed ground...".
    This suggests we take the top half grid and the bottom half grid, and perform a logical OR operation 

... [27156 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.75)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 302: "Breathing squares exhale inward, and the smallest take their ... [25 chars truncated]" k=1 alts: 0/0 522fdd07

Training Examples

Example 1

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Output

Example 2

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Example 3

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Example 4

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Output

Literal Description

See: The input is a 16x16 grid with an orange (O) background. On this background are several colored squares, each with an odd side length (1, 3, 5, 7, or 9). Each square is a solid block of a single non-orange color (which may include black/dot). The squares do not overlap each other.

Do: For each colored square in the input: 1. Identify its side length and its center cell (the center of the bounding box). 2. Shrink the square by reducing its side length by 2 (removing one pixel from each side), keeping it centered on the same cell. So a 7x7 becomes 5x5, a 5x5 becomes 3x3, a 3x3 becomes 1x1. 3. If the square is already 1x1, it wraps around and becomes 9x9, still centered on the same cell. The cycle is: 9 → 7 → 5 → 3 → 1 → 9 → 7 → ... 4. Draw the new square at its new size, centered on the original center position, using the same color. 5. Fill all remaining cells with orange (O).

Grid: The grid is 16x16. The background color is orange (O). All colored shapes are axis-aligned solid squares with odd side lengths drawn from the set {1, 3, 5, 7, 9}. The output grid has the same dimensions and background color as the input.

Figurative Descriptions (1 variants)

"Breathing squares exhale inward, and the smallest take their deepest breath back out."

qwen3.6-35b: k=1

See: An orange desert stretches in all directions. Scattered across the sand are colored oases — solid, square pools of water in vivid hues. Some are vast lakes, others modest ponds, and a few are mere puddles — single drops of color. Each sits perfectly still, centered on its own hidden wellspring beneath the sand.

Do: With each tick of the desert clock, every oasis exhales — its waters recede one step inward from every shore, shrinking toward its heart. A great lake contracts into a smaller one, a pond into a puddle. But when a puddle — already just a single drop — tries to shrink further, it cannot disappear; instead, it inhales deeply and swells back to the largest size the desert allows, erupting outward from its wellspring. The cycle of breathing continues: exhale, exhale, exhale, until the smallest breath triggers the deepest inhale. Each oasis stays anchored to its hidden spring beneath the sand, never drifting.

Grid: The desert is a 16×16 expanse of orange sand. Each oasis is a perfectly square pool with sides of odd length, colored in a single vivid hue — even black water counts. After one breath cycle, the desert refills around each resized oasis, and every pool remains centered on the same buried spring it has always known.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (30252 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Background:** The "desert" is represented by the color 'O' (orange). It fills the empty space.
    *   **Objects:** "Oases" are solid square blocks of a single color (B, G, Y, M, W, etc., or even black '.').
    *   **Properties of Oases:**
        *   They are perfectly square.
        *   They have odd side lengths (1, 3, 5, etc.).
        *   They are centered on a "wellspring" (center point).
        *   They are static in position (anchored).

*   **AFFORDANCES (Actions/Changes):**
    *   **Breathing Cycle:**
        *   **Exhale:** The oasis shrinks by 1 step from every shore. This means the side length decreases by 2 (1 from left, 1 from right, 1 from top, 1 from bottom).
        *   **Inhale:** If an oasis is a "puddle" (size 1x1) and tries to shrink, it cannot go to 0. Instead, it "swells back to the largest size the desert allows". Wait, "largest size the desert allows"? Or does it revert to its original size? Let's check the description carefully. "swells back to the largest size the desert allows". This phrasing is slightly ambiguous. Does it mean the size of the bounding box of the grid? Or the size it was before shrinking? Or a specific max size?
        *   Let's look at the training examples to deduce the rule.

*   **TRANSFORMATION RULE (Input -> Output):**
    *   Let's analyze Example 1.
    *   **Input Grid:** 16x16.
    *   **Oases identified:**
        1.  **Yellow (Y):** Top right.
            *   Rows 0-2, Cols 13-15.
            *   Size: 3x3.
            *   Center: (1, 14).
        2.  **Green (G):** Top left-ish.
            *   Rows 1-7, Cols 1-7.
            *   Size: 7x7.
            *   Center: (4, 4).
        3.  **Magenta (M):** Middle right.
            *   Rows 5-7, Cols 11-13.
            *   Size: 3x3.
            *   Center: (6, 12).
        4.  **White (W):** Bottom right.
            *   Rows 9-11, Cols 13-15.
            *   Size: 3x3.
            *   Center: (10, 14).
        5.  **Blue (B):** Bottom left.
            *   Rows 11-15, Cols 3-7.
            *   Size: 5x5.
            *   Center: (13, 5).
    *   **Output Grid Analysis:**
        *   **Yellow (Y):**
            *   Input: 3x3 block at top right.
            *   Output: A single 'Y' at (1, 14). Wait, looking at the output grid:
                *   Row 1: ... O Y O
                *   Row 2: ... O O O
                *   Wait, let's look closer at the output grid provided.
                *   Row 0: All O.
                *   Row 1: ... O O O O O O O O O O O O O O Y O. Wait, the Y is at index 14?
                *   Let's re-read the output grid text carefully.
                *   Row 0: O O O O O O O O O O O O O O O O (All O)
                *   Row 1: O O O O O O O O O O O O O O Y O. Wait, index 14 is Y.
                *   Row 2: O O G G G G G O O O O O O O O O.

... [27405 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

No grid

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 319: "Russian nesting dolls are packed away, each one's importance ... [24 chars truncated]" k=3 alts: 7/15 5587a8d0

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Literal Description

See: The input grid has an orange (O) background containing several distinct non-orange colored shapes, each made up of a different number of cells. Each color appears exactly once as a distinct group of cells scattered across the grid. The key feature of each shape is simply how many cells it occupies — its position and arrangement in the input do not matter.

Do: 1. Identify all distinct non-orange colors in the input and count the number of cells each color occupies. 2. Rank the colors from most cells (largest) to fewest cells (smallest). 3. Let n be the number of distinct colors. The output grid is (2n−1) × (2n−1). 4. Build the output as concentric rectangular rings, each one cell wide, nesting inward: the largest color forms the outermost ring, the second-largest forms the next ring inward, and so on, with the smallest color filling the single center cell. 5. If two colors have the same cell count, their relative order may be ambiguous; otherwise, strict descending cell count determines ring order from outside to inside.

Grid: The output grid is always a square of side length (2n−1), where n is the number of distinct non-orange colors in the input. There is no background color in the output — every cell belongs to one of the concentric rings. The grid is symmetric about both axes and both diagonals.

Figurative Descriptions (16 variants)

"Russian nesting dolls are packed away, each one's importance measured by its weight."

qwen3.6-35b: k=3

See: Scattered across an orange workshop table lie the disassembled pieces of a set of nesting dolls — each painted a different color, some larger and heavier than others. The dolls have tumbled out of order; their sizes are all you need to know, not where they landed.

Do: The dollmaker gathers the pieces and reassembles the set. The heaviest doll becomes the outermost shell, the next heaviest nestles inside it, and so on, each one cradled snugly within the last, until the tiniest doll — light as a single breath — sits alone at the very heart.

Grid: The finished nesting doll, viewed from above, is a perfect square window into concentric colored shells. Each shell is exactly one layer thick, and the whole assembly grows symmetrically outward from the tiny center doll. The workshop table is gone — every inch of the view belongs to a doll.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

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Expected

Reasoning (27008 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Input:** "Scattered across an orange workshop table lie the disassembled pieces of a set of nesting dolls — each painted a different color, some larger and heavier than others. The dolls have tumbled out of order; their sizes are all you need to know, not where they landed."
    *   *Interpretation:* The input grid contains a background color (Orange 'O') and various other colored shapes/pieces scattered around. The background is the "workshop table". The pieces are the non-orange elements.
*   **Action:** "The dollmaker gathers the pieces and reassembles the set. The heaviest doll becomes the outermost shell, the next heaviest nestles inside it, and so on, each one cradled snugly within the last, until the tiniest doll — light as a single breath — sits alone at the very heart."
    *   *Interpretation:* The pieces need to be arranged into concentric squares (shells) centered in the grid. The arrangement is based on "heaviness" or size.
*   **Output:** "The finished nesting doll, viewed from above, is a perfect square window into concentric colored shells. Each shell is exactly one layer thick, and the whole assembly grows symmetrically outward from the tiny center doll. The workshop table is gone — every inch of the view belongs to a doll."
    *   *Interpretation:* The output is a square grid. It consists of concentric square rings (shells) of different colors. The center is a single cell (or a small block). The background 'O' is removed. The size of the output grid seems to depend on the number of distinct pieces or the total count of non-background pixels? Or maybe the number of distinct colors? Let's look at the examples.

**2. Analyze Training Examples:**

**Example 1:**
*   **Input:**
    ```
    O O O O O O
    O O O Y Y O
    O O O Y Y O
    M O O O O O
    M M O O O O
    O O O O O O
    ```
    *   Background: 'O' (Orange).
    *   Pieces:
        *   'Y' (Yellow): 4 pixels (2x2 block).
        *   'M' (Magenta): 3 pixels (L-shape or similar).
    *   Wait, let's count pixels.
        *   Y: 4 pixels.
        *   M: 3 pixels.
    *   Output:
        ```
        Y Y Y
        Y M Y
        Y Y Y
        ```
    *   Output size: 3x3.
    *   Structure:
        *   Outer shell: 'Y' (Yellow).
        *   Inner core: 'M' (Magenta).
    *   Wait, the output has 'Y' on the border and 'M' in the center.
    *   Let's check the "heaviness" logic.
        *   Y count = 4.
        *   M count = 3.
        *   Heavier = larger count? If so, Y is heavier than M.
        *   Rule: Heaviest -> Outermost.
        *   Y (4) is outer. M (3) is inner.
        *   Output grid size: 3x3.
        *   Why 3x3?
        *   Maybe the number of distinct colors determines the number of shells? There are 2 colors (Y, M). A 3x3 grid has 2 shells (outer ring of 8, center of 

... [24584 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.01)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 352: "Three auditions behind curtains, but each actor only wins on ... [7 chars truncated]" k=1 alts: 0/0 5ecac7f7

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input grid consists of three 5-column panels separated by single columns of magenta (M). Each panel is a 5×5 subgrid containing exactly three non-background colors arranged in vertical regions: a left color occupying the leftmost columns, a middle color occupying the central column(s), and a right color occupying the rightmost columns. The background color is orange (O).

Do: 1. Split the input into three 5×5 panels by removing the magenta separator columns. Label them Panel 1 (leftmost), Panel 2 (middle), and Panel 3 (rightmost). 2. In Panel 1, identify the three non-background colors and determine which one forms the leftmost vertical region. Extract the positions of that color. 3. In Panel 2, identify the three non-background colors and determine which one forms the middle vertical region. Extract the positions of that color. 4. In Panel 3, identify the three non-background colors and determine which one forms the rightmost vertical region. Extract the positions of that color. 5. Create a 5×5 output grid filled with the background color (O). 6. Place the extracted left-region color from Panel 1 at its positions, the middle-region color from Panel 2 at its positions, and the right-region color from Panel 3 at its positions onto the output grid.

Grid: The input grid is 5 rows by 17 columns: three 5×5 panels separated by two single-column magenta (M) dividers. The output grid is 5×5. The background color is orange (O). Each panel's non-background cells are organized into three contiguous vertical regions (left, middle, right).

Figurative Descriptions (1 variants)

"Three auditions behind curtains, but each actor only wins one role."

qwen3.6-35b: k=1

See: Three stage rooms sit side by side, divided by magenta curtains. In each room, three troupes of colored actors rehearse, arranged in columns — one troupe holds the left side, one commands the center, and one owns the right. The orange floorboards fill every space not claimed by a performer.

Do: A director is casting a play with three roles: the left voice, the heart, and the right hand. She watches the first room and picks only the troupe standing at stage left. From the second room, she picks only the troupe holding center stage. From the third, only those at stage right. The curtains fall, the unchosen actors leave, and the three chosen troupes step onto a single shared stage, each taking the positions where they originally stood.

Grid: The theater is five rows tall and seventeen columns wide — three five-column stages separated by magenta curtain columns. The final shared stage is a single five-by-five floor of orange, onto which the three winning troupes place themselves exactly where they rehearsed.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (29297 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Input Grid Structure:**
The input grid is 5 rows by 17 columns.
The description says: "The theater is five rows tall and seventeen columns wide — three five-column stages separated by magenta curtain columns."
Let's verify this structure.
Columns 0-4: Stage 1 (5 cols)
Column 5: Curtain (Magenta 'M')
Columns 6-10: Stage 2 (5 cols)
Column 11: Curtain (Magenta 'M')
Columns 12-16: Stage 3 (5 cols)

Let's check the test input grid provided:
Row 0: `Y Y W W O M A A O O O M R R O O O`
Row 1: `Y O W W O M O A O O O M O R O W W`
Row 2: `Y Y O O R M A A O W W M R R X O W`
Row 3: `O Y O O R M A O R O W M O R O W W`
Row 4: `Y Y O O R M A A O W W M R R O O O`

Let's parse the columns:
Cols 0-4:
R0: Y Y W W O
R1: Y O W W O
R2: Y Y O O R
R3: O Y O O R
R4: Y Y O O R
This is Stage 1.

Col 5: M (Magenta) - Curtain 1.

Cols 6-10:
R0: A A O O O
R1: O A O O O
R2: A A O W W
R3: A O R O W
R4: A A O W W
This is Stage 2.

Col 11: M (Magenta) - Curtain 2.

Cols 12-16:
R0: R R O O O
R1: O R O W W
R2: R R X O W
R3: O R O W W
R4: R R O O O
This is Stage 3.

**2. Analyze the Metaphorical Description:**
*   **Three stage rooms:** The three 5x5 blocks identified above.
*   **Divided by magenta curtains:** The 'M' columns.
*   **Three troupes of colored actors rehearse, arranged in columns:** Inside each stage (5x5 block), there are actors. The description says "arranged in columns — one troupe holds the left side, one commands the center, and one owns the right."
    *   Wait, the description says "In each room, three troupes of colored actors rehearse, arranged in columns".
    *   Let's look at the training examples to understand what a "troupe" is.
    *   The grid is 5x5 per stage.
    *   "One troupe holds the left side" -> Columns 0, 1, 2? Or maybe specific columns?
    *   "One commands the center" -> Column 2?
    *   "One owns the right" -> Columns 3, 4, 5?
    *   Actually, let's look at the "Director casting a play" part.
    *   "She watches the first room and picks only the troupe standing at stage left."
    *   "From the second room, she picks only the troupe holding center stage."
    *   "From the third, only those at stage right."
    *   "The curtains fall, the unchosen actors leave, and the three chosen troupes step onto a single shared stage, each taking the positions where they originally stood."
    *   "The final shared stage is a single five-by-five floor of orange, onto which the three winning troupes place themselves exactly where they rehearsed."

    Wait, the output grid in Example 1 is 5x5.
    Input grid in Example 1 is 5x17.
    Output grid is 5x5.
    The output grid is described as "a single five-by-five floor of orange".
    Wait, looking at Example 1 Output:
    `O O A W O`
    `O O A W O`
    `R R A W W`
    `O O A O W`
    `O O A O W`
    It contains colors O, A, W, R. It is not all orang

... [26465 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.40)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 369: "Yellow suns illuminate flowers in a field of weeds — t ... [43 chars truncated]" k=1 alts: 0/0 642d658d

Training Examples

Example 1

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Output

Example 2

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Example 3

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Output

Literal Description

See: The grid is filled predominantly with a single background color. Scattered throughout the grid are various non-background colored cells, most of which are noise. The key structures are plus-shaped (cross-shaped) patterns centered on yellow (Y) cells. Each plus pattern consists of a Y cell at the center with its four orthogonal neighbors (up, down, left, right) all sharing the same non-background, non-yellow color. These arm colors vary across different crosses — for example, one cross might have green arms, another might have red arms, another blue, etc.

Do: 1. Identify the background color — the color that fills the vast majority of the grid. 2. Locate every yellow (Y) cell in the grid. 3. For each Y cell, examine its four orthogonal neighbors (up, down, left, right). If all four neighbors share the same color, and that color is neither the background color nor yellow, then this Y cell is the center of a valid plus-shaped cross. Record the arm color of that cross. 4. Count how many crosses share each arm color. 5. The arm color that appears most frequently across all crosses is the output. Return a 1x1 grid containing that single color.

Grid: The input grid is rectangular, typically around 20-27 rows and 22-24 columns, filled mostly with a single background color. The output is always a 1x1 grid containing a single color. Colors use the standard ARC palette (0-9), represented as single characters: . (black), B (blue), R (red), G (green), Y (yellow), X (grey), M (magenta), O (orange), A (azure), W (maroon). Yellow always serves as the center marker of cross patterns and is never the output.

Figurative Descriptions (1 variants)

"Yellow suns illuminate flowers in a field of weeds — the most common bloom wins the garden prize."

qwen3.6-35b: k=1

See: A vast field overgrown with a single type of weed stretches in every direction. Hidden among the weeds are tiny yellow suns, each radiating light in four directions. Some suns have managed to grow perfect flowers around them — four matching petals reaching up, down, left, and right, all the same vivid color against the drab background. Other colored specks are just scattered debris, weeds pretending to matter. Only the suns with four true, matching petals are real flowers.

Do: Walk through the field and find every yellow sun. Check whether each sun has bloomed — does it wear a crown of four identical petals in its cardinal directions, a color distinct from the weeds and from sunlight itself? Ignore suns that failed to bloom symmetrically. Among the true flowers, tally which petal color appears most often across the entire field. The dominant bloom is the season's champion — pluck one petal and present it.

Grid: The field is a large rectangular plot, roughly twenty-some rows and columns, choked with one dominant weed color. Yellow suns dot the landscape, and the petals around them come in various vivid hues. The prize you present is a single petal — a 1×1 swatch of the winning color. Yellow is always the sun, never the prize.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (24828 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Scene:** A field with a dominant "weed" color.
*   **Elements:**
    *   **Weeds:** The background color.
    *   **Suns:** Yellow ('Y') pixels.
    *   **Flowers:** A sun ('Y') surrounded by four petals in cardinal directions (Up, Down, Left, Right).
    *   **Petals:** Pixels adjacent to a sun.
    *   **Debris:** Other colored pixels not part of a valid flower.
*   **Task:**
    1.  Identify the "weed" color (dominant background).
    2.  Find all "suns" (Yellow 'Y' pixels).
    3.  Check if a sun has bloomed: It must have 4 matching petals in cardinal directions (Up, Down, Left, Right).
    4.  The petals must be a specific color (not 'Y', not the weed color).
    5.  Count the frequency of petal colors among valid flowers.
    6.  Identify the most frequent petal color (the "champion").
    7.  Output a single pixel representing that winning color.

**2. Analyze the Training Example:**
*   **Input Grid:**
    *   Background seems to be 'R' (Red). Let's check.
    *   There are 'Y' pixels.
    *   Let's look for 'Y' pixels and check their neighbors.
    *   Row 4 (0-indexed? Let's count lines):
        *   Line 5: `R A M R R . G Y G R R R R . R R R R B . R O` -> 'Y' at index 7. Neighbors: Left='R', Right='G', Up='R' (from line 4), Down='R' (from line 6). Not a flower.
        *   Line 6: `R R R R R . R G R R R R R R . R R B Y B R R` -> 'Y' at index 16. Neighbors: Left='B', Right='B', Up='R', Down='R'. Not a flower.
        *   Line 10: `R R R G Y G R R R G R R A R R R R R R R R R` -> 'Y' at index 4. Neighbors: Left='G', Right='G', Up='R' (line 9), Down='R' (line 11). Wait, line 9 is `R B . R G R . R . R . R . . R R R R . R B .`. Up is 'R'. Line 11 is `. R . R G R . R R B . R R R . R . . . R G .`. Down is 'R'. Not a flower.
        *   Line 13: `. . . R O R . R . . . . M Y M R . R . R . .` -> 'Y' at index 11. Neighbors: Left='.', Right='M', Up='R' (line 12), Down='R' (line 14). Not a flower.
        *   Line 17: `. . . R R A Y A . R . R . . R R . O Y O . .` -> 'Y' at index 6. Neighbors: Left='A', Right='A', Up='R' (line 16), Down='R' (line 18). Not a flower.
        *   Line 17: 'Y' at index 14. Neighbors: Left='O', Right='O', Up='R' (line 16), Down='R' (line 18). Not a flower.
    *   Wait, let's look closer at the example output. The output is `G`.
    *   This implies there is a valid flower with 'G' petals.
    *   Let's re-examine the grid for 'Y' surrounded by 4 'G's.
    *   Row 4 (index 4): `R A M R R . G Y G R R R R . R R R R B . R O` -> 'Y' at col 7. Left='G', Right='G'. Up (row 3): `R R R G Y G R R R G R R A R R R R R R R R R`. Wait, row 3 has 'Y' at col 4. Row 4 has 'Y' at col 7.
    *   Let's check Row 3 (index 3): `R R R G Y G R R R G R R A R R R R R R R R R`. 'Y' at col 4. Left='G', Right='G'. Up (row 2): `. . . R R R . R . R . R . . R R . B . R R

... [21949 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 421: "A vampire stands before a mirror that reveals not its reflec ... [48 chars truncated]" k=1 alts: 0/0 6f473927

Training Examples

Example 1

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Output

Example 2

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Example 3

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Example 4

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Output

Literal Description

See: The input grid contains a pattern made of red (R) cells on a black (.) background. The red cells form an arbitrary shape within the grid.

Do: 1. Take the input grid as-is — this becomes the left half of the output. 2. Create a horizontally mirrored copy of the input by reversing each row. 3. In this mirrored copy, replace every red (R) cell with black (.) and every black (.) cell with azure (A). 4. Concatenate the two halves side by side: the original input on the left, the color-swapped mirror on the right.

Grid: The output grid has the same number of rows as the input and exactly twice the number of columns. The left half is an exact copy of the input. The right half is the horizontal mirror of the input with colors inverted: black becomes azure and red becomes black. The background color is black (.).

Figurative Descriptions (1 variants)

"A vampire stands before a mirror that reveals not its reflection, but the negative space where it should be."

qwen3.6-35b: k=1

See: A figure made of red embers stands in a dark room, facing a wall-sized mirror.

Do: The vampire cannot see itself — but the mirror reveals everything the vampire is *not*. Where the creature stands, the mirror shows only darkness. Where empty space surrounds it, the mirror glows azure, filling in the void like a ghost-image. The vampire and its anti-reflection stand side by side, the original on the left, the haunted mirror on the right.

Grid: The mirror doubles the world horizontally. The left side is the room as it is — embers and darkness unchanged. The right side is the mirror's vision: a reversed world where the vampire's red form casts no reflection (black) and the surrounding darkness lights up in azure. Together they form a diptych of presence and absence.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (28490 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Input:** A grid representing a "room" with a "figure made of red embers" (Red 'R') standing in "darkness" (Black '.').
*   **Transformation:**
    *   The grid is doubled horizontally.
    *   **Left side:** The original input grid remains unchanged.
    *   **Right side:** This is the "mirror's vision".
        *   The mirror is "reversed".
        *   The "vampire" (Red 'R') casts no reflection, so where 'R' was, the mirror shows "darkness" (Black '.').
        *   The "surrounding darkness" (Black '.') lights up in "azure" (Azure 'A').
    *   **Result:** The output grid is the concatenation of the original grid and the transformed grid side-by-side.

**2. Analyze the Training Examples:**
*   **Example 1 Input:**
    ```
    . R .
    . R R
    . . R
    ```
    Dimensions: 3 rows, 3 columns.
    Colors: '.' (black), 'R' (red).

*   **Example 1 Output:**
    ```
    . R . A . A
    . R R . . A
    . . R . A A
    ```
    Dimensions: 3 rows, 6 columns.
    Let's break down the columns.
    Left half (cols 0-2):
    Row 0: `. R .` -> Matches input row 0.
    Row 1: `. R R` -> Matches input row 1.
    Row 2: `. . R` -> Matches input row 2.
    So, Left side = Input.

    Right half (cols 3-5):
    Row 0: `A . A`
    Row 1: `. . A`
    Row 2: `. A A`

    Let's check the transformation rule on the input to see if it matches the right half.
    Input Row 0: `. R .`
    Reverse it: `. R .`
    Apply color swap: '.' -> 'A', 'R' -> '.'.
    Result: `A . A`. Matches output right half.

    Input Row 1: `. R R`
    Reverse it: `R R .`
    Apply color swap: 'R' -> '.', '.' -> 'A'.
    Result: `. . A`. Matches output right half.

    Input Row 2: `. . R`
    Reverse it: `R . .`
    Apply color swap: 'R' -> '.', '.' -> 'A'.
    Result: `. A A`. Matches output right half.

    **Rule Confirmation:**
    1.  Take the input grid.
    2.  Create a new grid that is the same height but double the width.
    3.  The left half is an exact copy of the input.
    4.  The right half is generated by taking the input grid, reversing the order of columns (horizontal flip), and swapping colors: '.' becomes 'A' (azure), and 'R' becomes '.' (black). Note: The description says "Where the creature stands, the mirror shows only darkness" (R -> .) and "Where empty space surrounds it, the mirror glows azure" (. -> A).

**3. Analyze the Test Input:**
*   **Input Grid:**
    ```
    . . . . . .
    . . . . . R
    . . . . R .
    . . . R R R
    . . . . R R
    . R R R . .
    . . . R R R
    . . . . . R
    . . . . R R
    . . . . R R
    . . . . . .
    . . . . . .
    ```
    Dimensions: 12 rows, 6 columns.
    Colors present: '.' (black), 'R' (red).

**4. Apply the Transformation Rule:**

*   **Step 1: Left Half**
    Copy the input grid exactly.
    Rows 0-11, Cols 0-5.

*   **S

... [25985 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.01)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 422: "A kingdom builds its castle walls to protect the darkness wi ... [5 chars truncated]" k=2 alts: 6/15 6f8cd79b

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Example 4

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Output

Literal Description

See: The input is a rectangular grid filled entirely with black (.) cells. The grid can be any width and height.

Do: Color every cell that lies on the border of the grid azure (A). A border cell is any cell in the first row, last row, first column, or last column. Leave all interior cells black (.).

Grid: The output grid has the same dimensions as the input grid. The background is black, with a 1-cell-thick azure frame around the entire perimeter.

Figurative Descriptions (16 variants)

"A kingdom builds its castle walls to protect the darkness within."

qwen3.6-35b: k=2

See: A quiet kingdom of shadow stretches across the land — nothing but still, dark earth as far as the eye can see.

Do: The kingdom raises azure fortress walls along every exposed edge, one stone thick. The sentinels stand guard only where the land meets the outside world. The interior remains untouched — a sheltered courtyard of darkness the walls were built to protect.

Grid: The kingdom keeps its original shape. Azure stone rises wherever the realm touches the frontier, forming an unbroken perimeter. The dark heart within sleeps undisturbed.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (24590 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Input and Output format:**
- Input grids are composed of characters representing colors.
- `.` represents black.
- `A` represents azure.
- The grids are rectangular arrays of characters.

**2. Analyze the Metaphorical Description:**
- "A quiet kingdom of shadow stretches across the land — nothing but still, dark earth as far as the eye can see." -> The input grid is filled with `.` (black).
- "The kingdom raises azure fortress walls along every exposed edge, one stone thick." -> The output grid should have `A` (azure) characters forming a border around the grid.
- "The sentinels stand guard only where the land meets the outside world." -> The border is on the perimeter.
- "The interior remains untouched — a sheltered courtyard of darkness the walls were built to protect." -> The inner cells remain `.` (black).
- "The kingdom keeps its original shape. Azure stone rises wherever the realm touches the frontier, forming an unbroken perimeter. The dark heart within sleeps undisturbed." -> Confirms the border is `A` and the inside is `.`.

**3. Analyze Training Examples:**

*Example 1:*
Input: 5x4 grid of `.`
Output: 5x4 grid with `A` on the border and `.` inside.
Row 0: A A A A
Row 1: A . . A
Row 2: A . . A
Row 3: A . . A
Row 4: A A A A
This matches the description perfectly.

*Example 2:*
Input: 4x3 grid of `.`
Output: 4x3 grid with `A` on the border and `.` inside.
Row 0: A A A
Row 1: A . A
Row 2: A . A
Row 3: A A A
This also matches.

**4. Analyze the Test Input:**
Input grid:
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .

Dimensions:
Rows: 7
Columns: 6

**5. Apply the Transformation Rule:**
- The input is a 7x6 grid filled with `.`.
- The rule is to replace the outermost layer of cells (perimeter) with `A` (azure).
- The inner cells remain `.` (black).

Let's construct the output grid row by row.
Dimensions: 7 rows, 6 columns.

Row 0 (Top edge): All cells are on the edge.
Output: A A A A A A

Row 1 (Inner row): First and last cells are on the edge. Middle cells are interior.
Columns indices: 0, 1, 2, 3, 4, 5
Col 0: Edge -> A
Col 1: Interior -> .
Col 2: Interior -> .
Col 3: Interior -> .
Col 4: Interior -> .
Col 5: Edge -> A
Output: A . . . . A

Row 2: Same as Row 1.
Output: A . . . . A

Row 3: Same as Row 1.
Output: A . . . . A

Row 4: Same as Row 1.
Output: A . . . . A

Row 5: Same as Row 1.
Output: A . . . . A

Row 6 (Bottom edge): All cells are on the edge.
Output: A A A A A A

**6. Verification:**
Input size: 7 rows x 6 cols.
Output size: 7 rows x 6 cols.
Border is `A`.
Interior is `.`.
Interior dimensions: (7-2) rows x (6-2) cols = 5 rows x 4 cols.
Let's check the rows I generated.
Row 0: 6 A's. Correct.
Row 1: A, 4 dots, A. Total 6 chars. Correct.
Row 2: A, 4 dots, A. Correct.
Row 3: A, 4 dots, A. Correct.
Row 4: A, 4 dots, A. Co

... [21734 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.02)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 430: "Rockets on a launchpad ignite according to their fuel type." k=4 alts: 6/15 72a961c9

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Example 4

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Output

Literal Description

See: The input grid contains a single horizontal bar made of blue (B) cells spanning one full row, with one or more non-blue colored marker cells (such as azure A or red R) embedded at specific positions within that bar. The rest of the grid is black (.) empty space. The bar can appear at any row in the grid.

Do: For each non-blue marker cell in the horizontal bar, grow a vertical column upward from that marker's position. The column's height (including the marker copy at the top) depends on the marker's color: azure (A) produces a column of height 3 (the top cell is A, followed by 2 blue B cells below it, connecting down to the bar), and red (R) produces a column of height 4 (the top cell is R, followed by 3 blue B cells below it, connecting down to the bar). The marker cell in the original bar remains unchanged. All other cells remain black.

Grid: The grid dimensions match the input exactly and do not change. The background is black (.). The horizontal bar occupies exactly one row. Columns grow strictly upward from the bar; no cells are modified below the bar or beyond the grid boundaries.

Figurative Descriptions (16 variants)

"Rockets on a launchpad ignite according to their fuel type."

qwen3.6-35b: k=4

See: A launchpad stretches across the darkness — a solid blue runway with special rocket engines embedded in it, each glowing a distinct color (azure or red) to signal what kind of fuel they carry.

Do: When launch is triggered, each colored engine fires a plume straight up into the night sky. The plume is a column of blue exhaust capped by a bright flare matching the engine's color. Red rockets burn hotter and their plumes reach higher than azure ones. The engines themselves stay bolted to the launchpad.

Grid: The night sky stays dark except where exhaust trails rise. The launchpad remains fixed in its row. Plumes only fire upward — nothing falls below the runway, and no rocket escapes the edge of the sky.

qwen3.6-35b — MARC valid, solved with 4 examples

Input

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Prediction

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Expected

Reasoning (34939 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Launchpad:** A horizontal row of cells containing 'B' (blue) and potentially other colors ('A' for azure, 'R' for red). In the examples, this row is usually at the bottom or near the bottom, but looking closely at the inputs, it's a specific row containing 'B's. Wait, let's look at the inputs.
        *   Ex 1: Row 3 (0-indexed) is `B A B B B B`.
        *   Ex 2: Row 5 is `B B B R B B B`.
        *   Ex 3: Row 7 is `B A B B B A B R B`.
        *   Ex 4: Row 9 is `B B R B B B A B B B`.
        *   Test Input: Row 6 is `B R B A B B B A B R B`.
    *   **Engines:** The non-blue characters ('A' for azure, 'R' for red) embedded in the 'B' row.
    *   **Night Sky:** The '.' (black) cells above the launchpad.
    *   **Plumes/Exhaust:** Columns of color rising from the engines.
    *   **Flares:** The top-most cell of the plume, matching the engine's color.

*   **AFFORDANCES (Capabilities/Properties):**
    *   **Engines:** They are fixed in the launchpad row. They emit plumes upwards.
    *   **Plumes:**
        *   Color: Blue ('B') for the body of the plume.
        *   Top: A 'flare' matching the engine's color ('A' or 'R').
        *   Direction: Upwards (decreasing row index).
        *   Height:
            *   "Red rockets burn hotter and their plumes reach higher than azure ones."
            *   Let's quantify this.
            *   Ex 1: Engine 'A' at (3, 1). Plume goes up to row 0? No, output shows 'A' at (0, 1) and 'B's below it. Wait, let's check coordinates.
                *   Input Ex 1: Row 3 is `B A B B B B`. Grid height is 10.
                *   Output Ex 1:
                    *   Col 1 (where 'A' is): Row 0 is 'A', Row 1 is 'B', Row 2 is 'B'. Row 3 is 'A' (engine).
                    *   Col 0, 2, 3, 4, 5 are 'B' (engine). No plume? Wait.
                    *   Let's re-read the description carefully. "A solid blue runway with special rocket engines embedded in it... Red rockets burn hotter and their plumes reach higher than azure ones."
                    *   In Ex 1, the engines are 'A' (azure) and 'B' (blue). Wait, 'B' is the runway color. Are 'B's engines? Or just the runway?
                    *   Description says: "solid blue runway with special rocket engines embedded in it, each glowing a distinct color (azure or red)".
                    *   So 'B' is the runway. 'A' and 'R' are the engines.
                    *   In Ex 1, there is an 'A' at (3, 1). The output has a plume above it.
                    *   What about the 'B's? In Ex 1, the 'B's at (3, 0), (3, 2), etc., do *not* have plumes.
                    *   Wait, looking at Ex 1 output:
                        *   Col 0: `.` `.` `.` `B` ... (No plume)
                        *   Col 1: `A` `B` `B` `A` ... (Plume from 'A')
                        *   Col 2: `.` `.` `.` `B` ... (No plum

... [32077 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.86)

Prediction

Expected

Figurative + 4 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 436: "A painting hung on a dark gallery wall faces a mirror." k=1 alts: 0/0 7468f01a

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input grid has a black (.) background containing a single rectangular region filled with a dominant color and a secondary color forming a pattern within it. The rectangle is embedded somewhere in the larger black grid.

Do: Extract the rectangular region from the black background. Then flip it horizontally (mirror it left-to-right), so that the first column becomes the last column, the second column becomes the second-to-last, and so on. The resulting flipped rectangle is the output.

Grid: The input is a grid of variable size with a black (.) background. The embedded rectangle can appear at any position and have any dimensions. The output grid has the same dimensions as the extracted rectangle, with no black border.

Figurative Descriptions (1 variants)

"A painting hung on a dark gallery wall faces a mirror."

qwen3.6-35b: k=1

See: A dark gallery wall stretches in every direction. Somewhere on this wall hangs a single small painting — a canvas of one dominant hue with brushstrokes of a contrasting accent color forming a motif within it.

Do: Lift the painting off the wall and hold it before a mirror. The reflection you see — where left becomes right and right becomes left — is the true artwork. Discard the empty wall entirely; only the mirror's image matters.

Grid: The gallery wall is the black (.) expanse. The painting is the colored rectangle hiding within it, and it can hang anywhere and be any size. The output is the reflection alone — the painting as the mirror reveals it, with no wall remaining.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (25139 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion:**

*   **CAST:**
    *   **Background (Gallery Wall):** Represented by `.` (black). This is the empty space surrounding the object of interest.
    *   **Object (Painting):** A rectangular subgrid containing colored characters (B, A, etc.). This is the "canvas" with a "motif".
    *   **Mirror:** An abstract concept representing a horizontal flip (left becomes right, right becomes left).

*   **AFFORDANCES:**
    *   The background `.` is just filler. It needs to be removed.
    *   The colored rectangle (painting) needs to be extracted from the background.
    *   The extracted rectangle needs to be reflected horizontally.

*   **TRANSFORMATION RULE:**
    1.  **Locate the Painting:** Find the bounding box of all non-`.` characters in the input grid.
    2.  **Extract:** Crop the grid to this bounding box.
    3.  **Reflect:** Flip the extracted grid horizontally (reverse the order of characters in each row).
    4.  **Output:** Print the resulting grid.

**2. Analyzing the Test Input:**

Input Grid:
```
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
. . . B B B B A B B B . . . . . .
. . . B B B B B A A B . . . . . .
. . . B B B B B B B B . . . . . .
. . . A A A B B B B B . . . . . .
. . . B B B B B B B B . . . . . .
. . . B B A A A B B B . . . . . .
. . . B B B B B B B B . . . . . .
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
```

**Step 1: Locate the Painting (Bounding Box)**
I need to find the minimum and maximum row and column indices that contain non-`.` characters.

*   **Rows:**
    *   Rows 0-2 are all `.`.
    *   Row 3 has `B`s and `A`s. Indices: 3, 4, 5, 6, 7, 8, 9, 10, 11. (Wait, let's count carefully).
    *   Let's check the columns.
    *   Row 3: `. . . B B B B A B B B . . . . . .`
        *   Indices: 0, 1, 2 are `.`.
        *   Index 3 is `B`.
        *   Index 4 is `B`.
        *   Index 5 is `B`.
        *   Index 6 is `B`.
        *   Index 7 is `A`.
        *   Index 8 is `B`.
        *   Index 9 is `B`.
        *   Index 10 is `B`.
        *   Index 11 is `.`.
        *   So columns range from 3 to 10.
    *   Let's check other rows to confirm the bounding box.
    *   Row 4: `. . . B B B B B A A B . . . . . .` -> Starts at 3, ends at 10.
    *   Row 5: `. . . B B B B B B B B . . . . . .` -> Starts at 3, ends at 10.
    *   Row 6: `. . . A A A B B B B B . . . . . .` -> Starts at 3, ends at 10.
    *   Row 7: `. . . B B B B B B B B . . . . . .` -> Starts at 3, ends at 10.
    *   Row 8: `. . . B B A A A B B B . . . . . .` -> Starts at 3, ends at 10.
    *   Row 9: `. . . B B B B B B B B . . . . . .` -> Starts at 3, ends at 10.
    *   Rows 10-16 are all `.`.

    So, the boundi

... [22436 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 440: "Saplings at the riverbank grow to full trees, but full-grown ... [54 chars truncated]" k=2 alts: 0/0 758abdf0

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Literal Description

See: The input grid has a background of orange (O) cells. One entire edge (a full row or column) is filled with black (.) cells, forming a border wall. Adjacent to this border, within the first two layers of cells perpendicular to it, there are azure (A) cells scattered among the orange. Some positions have a single A cell (only in the layer immediately next to the border), while other positions have a double A (A cells in both the first and second layers from the border). The rest of the grid is entirely orange.

Do: 1. Identify the border edge: the complete row or column of black (.) cells. 2. For each line perpendicular to the border, examine the two cells closest to the border (depth 1 and depth 2). 3. If a line has a single azure (A) at depth 1 only: extend it by also placing an A at depth 2, creating a double-A. 4. If a line has azure (A) at both depth 1 and depth 2 (a double-A): remove both A cells (replace with orange O), then place black (.) cells at the two positions farthest from the border in that line (i.e., at the maximum depth and maximum depth minus one). 5. All other cells remain unchanged.

Grid: Rectangular grid of arbitrary dimensions. One complete edge (row or column) consists of black (.) cells serving as a fixed border wall. The background color is orange (O). Azure (A) is the only signal color and appears only in the two layers adjacent to the border. The border edge and grid dimensions are preserved in the output.

Figurative Descriptions (1 variants)

"Saplings at the riverbank grow to full trees, but full-grown trees uproot and cast their shadows on the far shore."

qwen3.6-35b: k=2

See: An orange meadow stretches out from a dark riverbank. Along the bank's edge, azure saplings have taken root — some are young shoots rising just one row deep, others have grown into full trees extending two rows into the meadow. The rest of the field is empty orange grassland.

Do: Nature follows its cycle along the river. Young saplings (single azure) are still growing — they send their roots one layer deeper, becoming full trees. But full-grown trees (double azure) have completed their life cycle at the bank: they release their hold on the soil, vanishing from the riverside entirely. As they fall, their shadows are cast across the entire meadow, landing as dark marks on the two cells at the farthest opposite shore.

Grid: A rectangular meadow of orange grass bordered on one side by a dark river (a complete row or column of black). Azure saplings appear only in the two layers of soil nearest the riverbank. The river is permanent and the meadow dimensions never change.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (35317 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**

*   **Visuals:**
    *   "Orange meadow" -> Grid filled with 'O' (orange).
    *   "Dark riverbank" -> A row or column of '.' (black).
    *   "Azure saplings" -> 'A' (azure) cells.
    *   "Young shoots" -> Single 'A' (1 row deep from river).
    *   "Full trees" -> Double 'A' (2 rows deep from river).
    *   "Empty orange grassland" -> 'O' cells.
*   **Transformation Rules:**
    *   "Nature follows its cycle along the river."
    *   "Young saplings (single azure) ... send their roots one layer deeper, becoming full trees." -> A single 'A' adjacent to the river (or just one 'A' in the sequence) becomes a double 'A' (two 'A's stacked vertically or horizontally depending on orientation). Wait, let's look at the examples to understand the geometry.
    *   "Full-grown trees (double azure) ... release their hold on the soil, vanishing from the riverside entirely." -> A double 'A' (two 'A's) disappears from the river side.
    *   "As they fall, their shadows are cast across the entire meadow, landing as dark marks on the two cells at the farthest opposite shore." -> When a double 'A' disappears, 'X' (grey) or '.' (black) marks appear at the far end? The description says "dark marks". The color key says '.' is black. The description says "shadows ... landing as dark marks". In the examples, I see '.' appearing. Let's check the color key again. '.' is black. So shadows are black dots.
    *   "Grid details: A rectangular meadow of orange grass bordered on one side by a dark river (a complete row or column of black)." -> The river is a line of '.'.
    *   "Azure saplings appear only in the two layers of soil nearest the riverbank." -> 'A's are only found in rows/cols adjacent to the river.

**2. Analyze Training Examples:**

**Example 1:**
*   **Input Grid:**
    *   Size: 16 rows x 8 columns.
    *   River: Column 0 is all '.' (black). Wait, looking at the input:
        ```
        . O O O O O O O
        . O O O O O O O
        ...
        ```
        Yes, Column 0 is all dots. So the river is on the left.
    *   Meadow: Columns 1-7 are 'O' (orange).
    *   Saplings ('A'):
        *   Row 3: `. A A O ...` -> Two 'A's at (3,1) and (3,2). This is a "full tree" (double azure) because it's 2 cells deep? Or is it 2 cells wide?
        *   Row 5: `. A O O ...` -> One 'A' at (5,1). "Young sapling".
        *   Row 7: `. A O O ...` -> One 'A' at (7,1). "Young sapling".
        *   Row 10: `. A O O ...` -> One 'A' at (10,1). "Young sapling".
        *   Row 12: `. A A O ...` -> Two 'A's at (12,1) and (12,2). "Full tree".
        *   Row 15: `. A O O ...` -> One 'A' at (15,1). "Young sapling".
    *   Wait, the description says "two layers of soil nearest the riverbank". The river is at col 0. The layers are col 1 and col 2.
    *   Let's re-re

... [32509 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.23)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 445: "Two shores share a common reflection in a golden lake." k=2 alts: 0/0 770cc55f

Training Examples

Example 1

Input

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Output

Example 2

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Output

Example 3

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Output

Example 4

Input

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Output

Literal Description

See: The grid is divided into two halves by a horizontal red (R) line that spans the full width. Above and below this red divider, there are two patterns of the same non-red, non-black color (e.g., blue, magenta, green, or orange) located at the top edge and bottom edge of the grid. One pattern sits in the first row (top edge) and the other in the last row (bottom edge). The rows between each colored pattern and the red line are empty (all black). Each colored pattern occupies a specific set of columns.

Do: 1. Identify the horizontal red line that spans the full grid width; this is the divider. 2. Identify the colored pattern in the top row (row 0) and note which columns it occupies. 3. Identify the colored pattern in the bottom row (last row) and note which columns it occupies. 4. Compute the intersection of these two sets of columns — the columns where both patterns have a colored cell. 5. Determine which pattern is larger (occupies more columns). 6. In the half of the grid containing the larger pattern, fill all empty rows between that pattern and the red divider with yellow (Y) in exactly the intersection columns. The other half remains unchanged. All other cells remain black.

Grid: The grid has a variable width and an odd number of conceptual sections: a top region, a single-row red divider, and a bottom region. The top and bottom regions have equal height. The background is black (.). The red divider always spans the full width. The grid dimensions vary but the structure is always: colored row, several empty rows, red divider row, several empty rows, colored row.

Figurative Descriptions (1 variants)

"Two shores share a common reflection in a golden lake."

qwen3.6-35b: k=2

See: A red bridge stretches across the world, dividing it into an upper shore and a lower shore. On each shore, a colored settlement clings to the water's edge — one along the top rim, one along the bottom. The settlements are the same color, like sister cities separated by the bridge. Between each settlement and the bridge, the land lies dark and empty.

Do: The two sister cities gaze across the bridge at each other, and where their footprints overlap — the columns they both inhabit — a golden reflection blooms. But only the smaller city has the power to cast this reflection: the golden light floods the empty land between the *larger* city and the bridge, filling exactly the shared columns with yellow. The smaller city's side remains dark, as if the reflection only appears where there is more shore to illuminate.

Grid: The world is split by a red bridge into two equal dark plains. Each plain has a colored settlement pressed against its outer edge, with empty darkness stretching inward toward the bridge. The bridge always runs the full width, an unbroken red horizon. The golden reflection, when it appears, fills the empty rows like a lake rising between the larger settlement and the bridge.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (34054 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Input Grid and Metaphor:**

*   **Grid Structure:** The grids seem to be rectangular.
    *   Example 1: 13 rows, 5 columns.
    *   Example 2: 13 rows, 5 columns.
    *   Test Input: 11 rows, 5 columns. Wait, let me check the dimensions.
    *   Test Input:
        Row 0: O O O O O
        Row 1: . . . . .
        Row 2: . . . . .
        Row 3: . . . . .
        Row 4: . . . . .
        Row 5: R R R R R
        Row 6: . . . . .
        Row 7: . . . . .
        Row 8: . . . . .
        Row 9: . . . . .
        Row 10: . O O . .
    *   Wait, the test input has 11 rows. The examples have 13 rows. Let's re-read the test input carefully.
    *   Test Input:
        O O O O O
        . . . . .
        . . . . .
        . . . . .
        . . . . .
        R R R R R
        . . . . .
        . . . . .
        . . . . .
        . . . . .
        . O O . .
    *   Count: 1, 2, 3, 4, 5, 6 (R row), 7, 8, 9, 10, 11. Yes, 11 rows.
    *   Wait, looking at the examples, the red bridge is in the middle.
    *   Example 1: 13 rows. Bridge at row 6 (0-indexed). 6 rows above, 6 rows below.
    *   Example 2: 13 rows. Bridge at row 6.
    *   Test Input: 11 rows. Bridge at row 5. 5 rows above, 5 rows below.
    *   Okay, the grid size might vary, but the structure is consistent: Top plain, Red Bridge, Bottom plain.

*   **Metaphorical Description Breakdown:**
    *   "Red bridge stretches across the world": A horizontal line of 'R's dividing the grid.
    *   "Upper shore and lower shore": The rows above and below the bridge.
    *   "Colored settlement clings to the water's edge": A block of colored pixels (not black '.') at the outer edge of the shore.
        *   Top settlement: At the top row (row 0).
        *   Bottom settlement: At the bottom row (last row).
    *   "Settlements are the same color": In the examples, the top and bottom settlements are the same color (Blue in Ex 1, Magenta in Ex 2).
    *   "Empty darkness stretching inward toward the bridge": Rows between the settlement and the bridge are filled with '.'.
    *   "Golden reflection blooms... columns they both inhabit": Intersection of columns occupied by top and bottom settlements.
    *   "Only the smaller city has the power to cast this reflection": Compare the size (number of pixels or width?) of the two settlements.
    *   "Golden light floods the empty land between the *larger* city and the bridge": The yellow pixels ('Y') appear in the rows between the *larger* settlement and the bridge, specifically in the columns where the settlements overlap.
    *   "The smaller city's side remains dark": No yellow pixels on the side of the smaller settlement.

**2. Analyze Training Examples:**

*   **Example 1:**
    *   **Input:**
        *   Top settlement: Row 0, cols 1-2 are 'B' (Blue). Width = 2.
        *   Bridge: Row 6, cols 0-4 are 'R'.
        *   Bottom 

... [31096 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.16)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 449: "A dam holds back a flood that fills everything below it." k=2 alts: 2/15 782b5218

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

Input

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Output

Literal Description

See: The input grid contains cells of three types: red (R) cells that form a diagonal or irregular boundary/separator line, a dominant non-red color (blue, grey, azure, or maroon depending on the puzzle instance) scattered throughout the grid on both sides of the red boundary, and black/empty (.) cells also scattered on both sides. The red cells divide each column into an 'above' region and a 'below' region.

Do: 1. Identify all red (R) cells in the grid. These remain fixed in place throughout the transformation. 2. Identify the non-red, non-black color present in the grid (e.g., blue, grey, azure, maroon) — this is the fill color. 3. For each column independently, find the red cell(s). Every non-red cell ABOVE the topmost red cell in that column becomes black (.). Every non-red cell BELOW the bottommost red cell in that column becomes the fill color. 4. Red cells stay exactly where they are. The result is that the region above the red boundary is cleared to empty/black, the red boundary is preserved, and the region below the red boundary is filled solid with the fill color.

Grid: The grid is square (10x10 in all examples). It uses a black (.) background with exactly two other colors: red (R) serving as a fixed boundary, and one other color serving as fill material. The red cells form a connected or near-connected band that spans the full width of the grid, separating it into an upper and lower region.

Figurative Descriptions (16 variants)

"A dam holds back a flood that fills everything below it."

qwen3.6-35b: k=2

See: A red dam stretches across the landscape, sometimes straight, sometimes staggered like a staircase. Above and below the dam, colored sediment and empty air pockets are scattered randomly — the remnants of a world before the flood.

Do: When the floodwaters rise, the dam holds firm. Everything above the dam is swept clean — scoured to empty sky. Everything below the dam is submerged: the water fills every pocket, every gap, drowning the space in a uniform layer of sediment. The dam itself, red and unyielding, stays exactly where it was built.

Grid: The world is a 10×10 valley. The red dam cuts across it column by column, and the colored sediment is the same substance everywhere — it just needs the flood to press it into place. Above: clear sky. Below: solid earth. The dam: immovable.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (37559 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion:**

*   **CAST (Roles):**
    *   **Red cells (R):** These represent the "dam". The description says "A red dam stretches across the landscape... cuts across it column by column". Looking at the examples, the red cells form a horizontal line (or a jagged line that acts as a barrier) separating the grid into an upper part and a lower part.
    *   **Other colored cells (B, X, W, etc.):** These represent "colored sediment" or "substance".
    *   **Empty cells (.):** These represent "empty air pockets" or "empty sky".
    *   **The Grid:** A 10x10 grid.

*   **AFFORDANCES (Capabilities/Actions):**
    *   **The Dam (R):** It is "unyielding" and "stays exactly where it was built". It acts as a boundary.
    *   **Above the Dam:** "Swept clean — scoured to empty sky". This means any cell above the dam becomes `.` (black/empty).
    *   **Below the Dam:** "Submerged... water fills every pocket... drowning the space in a uniform layer of sediment". This implies that the area below the dam gets filled with a specific color. Wait, let's look closer at the examples.
    *   **The Sediment:** The description says "colored sediment... is the same substance everywhere". In Example 1, the input has Blue (B) cells. The output below the dam is all Blue (B). In Example 2, the input has Grey (X) cells. The output below the dam is all Grey (X).
    *   **Wait, is it just filling with the color present below?** Or is it filling with a specific color?
        *   Example 1 Input: Has Blue (B) cells below the red line. Output below is all Blue.
        *   Example 2 Input: Has Grey (X) cells below the red line. Output below is all Grey.
        *   Let's check the colors above the dam.
        *   Example 1 Input: Has Blue (B) cells above. Output above is all `.`.
        *   Example 2 Input: Has Grey (X) cells above. Output above is all `.`.
    *   **The Dam itself:** Stays Red (R).

*   **TRANSFORMATION RULE:**
    1.  Identify the "Dam": The row(s) containing Red (R) cells. In the examples, the red cells form a continuous horizontal barrier, though sometimes with gaps or specific shapes? Let's check the coordinates.
        *   Example 1: Row 3 (0-indexed) is `R R R R R R R R R R`. It's a solid line.
        *   Example 2: Row 3 is `R . X X R . X . R X`. Row 4 is `X R . R . R . R . R`. Row 5 is `. . R X X X R . X .`.
        *   Wait, the description says "The red dam cuts across it column by column". This might mean it's a vertical line? Or maybe it means it spans the width? "Stretches across the landscape" usually implies horizontal. "Cuts across it column by column" is a bit ambiguous. Let's look at the structure.
        *   In Example 1, the red line is at index 3. Rows 0, 1, 2 are above. Rows 4, 5, 6, 7, 8, 9 are below.
        *   In Example 2, the red cells are scattered.
            *   Row 3: `R . X X R . X 

... [34892 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.02)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 454: "A compass rose unfurls from a single petal, each cardinal di ... [47 chars truncated]" k=1 alts: 15/15 7953d61e

Training Examples

Example 1

Input

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Output

Example 2

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Output

Example 3

Input

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Output

Example 4

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Output

Example 5

Input

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Output

Literal Description

See: A 4×4 grid of colored cells. The grid is treated as a single rigid tile that can be rotated.

Do: Create an 8×8 output by tiling four rotated copies of the 4×4 input into a 2×2 arrangement of quadrants: (1) Top-left quadrant: the original input, unchanged. (2) Top-right quadrant: the input rotated 90° counter-clockwise (equivalently, transpose then reverse each column). (3) Bottom-left quadrant: the input rotated 180°. (4) Bottom-right quadrant: the input rotated 90° clockwise (equivalently, transpose then reverse each row).

Grid: The input is always a 4×4 grid. The output is always an 8×8 grid composed of four 4×4 quadrants arranged in a 2×2 layout. There is no background color or border; every cell is determined by the corresponding rotation of the input.

Figurative Descriptions (16 variants)

"A compass rose unfurls from a single petal, each cardinal direction revealing a new face of the same bloom."

qwen3.6-35b: k=1

See: A small mosaic tile — a 4×4 swatch of stained glass — sits at the heart of a cathedral floor, waiting to be echoed outward.

Do: The tile dreams of itself from every direction. It gazes north and sees its own face. It turns its head east, west, and south, and at each glance the reflection has spun — as if the tile were placed on a lazy Susan and photographed at each quarter-turn. These four portraits are pressed together like pages of a folded map, the original anchoring one corner while its dizzied twins fill the remaining three.

Grid: The cathedral floor is exactly four tiles wide and four tiles tall — a 2×2 arrangement of the original swatch and its three rotated echoes. No grout, no gaps: every cell of colored glass belongs to one of the four spinning memories of the original piece.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (30018 chars)

The user wants me to solve a grid transformation puzzle.

**1. Analyze the Input and Output:**
*   **Input:** A 4x4 grid of characters representing colors.
*   **Output:** An 8x8 grid of characters.
*   **Metaphorical Description:**
    *   "A small mosaic tile — a 4×4 swatch... sits at the heart... waiting to be echoed outward."
    *   "The tile dreams of itself from every direction."
    *   "It gazes north and sees its own face." (Original)
    *   "It turns its head east, west, and south, and at each glance the reflection has spun — as if the tile were placed on a lazy Susan and photographed at each quarter-turn." (Rotations)
    *   "These four portraits are pressed together like pages of a folded map, the original anchoring one corner while its dizzied twins fill the remaining three."
    *   "The cathedral floor is exactly four tiles wide and four tiles tall — a 2×2 arrangement of the original swatch and its three rotated echoes."
    *   "No grout, no gaps: every cell of colored glass belongs to one of the four spinning memories of the original piece."

**2. Conceptual Digestion:**

*   **CAST:**
    *   **Input Grid:** A 4x4 matrix of colors. Let's call this $T$ (Tile).
    *   **Output Grid:** An 8x8 matrix.
    *   **Components:** The output is composed of four 4x4 quadrants.

*   **AFFORDANCES:**
    *   The input tile $T$ can be rotated.
    *   Rotations are likely 90 degrees clockwise (or counter-clockwise, need to check).
    *   The quadrants are arranged in a 2x2 layout.

*   **TRANSFORMATION RULE:**
    *   The output is a 2x2 arrangement of 4x4 blocks.
    *   Let the output grid be $O$. $O$ has dimensions $8 \times 8$.
    *   $O$ is divided into four quadrants: Top-Left (TL), Top-Right (TR), Bottom-Left (BL), Bottom-Right (BR).
    *   The description says: "original anchoring one corner while its dizzied twins fill the remaining three."
    *   "Gazes north and sees its own face" -> This implies the original orientation is likely in the top-left or top-right? Or maybe the description implies a specific mapping.
    *   "Turns its head east, west, and south" -> This suggests rotations.
    *   "Lazy Susan... photographed at each quarter-turn" -> 0°, 90°, 180°, 270° rotations.
    *   Let's look at the training example to deduce the exact mapping.

**3. Analyzing Training Example 1:**

*   **Input (4x4):**
    ```
    Y W B A
    A Y B A
    Y A A B
    B B B A
    ```
    Let's label this matrix $T$.
    $T_{0,0} = Y, T_{0,1} = W, T_{0,2} = B, T_{0,3} = A$
    $T_{1,0} = A, T_{1,1} = Y, T_{1,2} = B, T_{1,3} = A$
    $T_{2,0} = Y, T_{2,1} = A, T_{2,2} = A, T_{2,3} = B$
    $T_{3,0} = B, T_{3,1} = B, T_{3,2} = B, T_{3,3} = A$

*   **Output (8x8):**
    ```
    Y W B A A A B A
    A Y B A B B A B
    Y A A B W Y A B
    B B B A Y A Y B
    A B B B B Y A Y
    B A A Y B A Y W
    A B Y A B A B B
    A B W Y A B A A
    ```
    Let's split this into four 4x4 quadrants.
   

... [28507 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.02)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 467: "A comet streaks away from its home planet, leaving a glowing ... [28 chars truncated]" k=3 alts: 3/15 7ddcd7ec

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input grid contains a single 2x2 solid block of a colored cell (non-black) and one or more isolated single cells of the same color positioned diagonally adjacent to corners of the 2x2 block. These single cells act as diagonal arms indicating ray directions extending outward from the block.

Do: Keep the original 2x2 block and all original single cells in place. For each single cell that is diagonally adjacent to a corner of the 2x2 block, identify the diagonal direction pointing away from the block (i.e., the direction from the block's corner to that single cell). Starting from that single cell, continue placing one cell of the same color per row along that diagonal, stepping one row and one column in the same direction each time, until reaching the edge of the grid.

Grid: The grid is 10x10 with a black (.) background. All colored cells share the same single color. The 2x2 block is positioned away from the edges, leaving room for diagonal rays to extend to the grid boundary.

Figurative Descriptions (16 variants)

"A comet streaks away from its home planet, leaving a glowing trail across the night sky."

qwen3.6-35b: k=3

See: In the darkness of space, a small colored planet floats — a solid 2×2 world. Nearby, one or two comets have just launched from its corners, each a single bright spark sitting diagonally adjacent to the planet's surface.

Do: Each comet is hurtling away from the planet. It blazes a trail across the void, dropping one spark of light in every row it crosses, always flying diagonally outward until it crashes into the edge of the universe. The planet itself stays fixed — only the comets move, and they never look back.

Grid: The universe is a 10×10 field of black void. The planet and its comets share one color — they belong to the same star system. The planet drifts far enough from the edges that each comet has runway to streak across the sky before hitting the boundary.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (30824 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **CAST:**
    *   **Planet:** A 2x2 block of colored pixels.
    *   **Comets:** Single pixels of the same color as the planet, located diagonally adjacent to the planet's corners.
    *   **Void:** The rest of the 10x10 grid, filled with black dots (`.`).
    *   **Trails:** The comets leave a trail of colored pixels as they move.

*   **AFFORDANCES:**
    *   **Planet:** Static. It stays in place.
    *   **Comets:** Move diagonally outward from the planet.
    *   **Trails:** Formed by the comet's path. The description says "dropping one spark of light in every row it crosses". Wait, let's look at the examples to clarify "dropping one spark of light in every row it crosses".
    *   Actually, looking at the examples, the comets seem to move diagonally. Let's trace the movement.

*   **TRANSFORMATION RULE:**
    *   Identify the 2x2 planet.
    *   Identify the "comets". The description says "one or two comets have just launched from its corners, each a single bright spark sitting diagonally adjacent to the planet's surface."
    *   Let's check the examples to see where the comets are relative to the planet.
    *   **Example 1:**
        *   Planet: 2x2 block of Y (yellow) at rows 2-3, cols 4-5 (0-indexed: rows 1-2, cols 4-5? No, let's count carefully).
        *   Input grid:
            Row 0: `.`
            Row 1: `.` `.` `.` `.` `.` `.` `Y` `.` `.` `.` -> Y at (1, 6)
            Row 2: `.` `.` `.` `.` `Y` `Y` `.` `.` `.` `.` -> Y at (2, 4), (2, 5)
            Row 3: `.` `.` `.` `.` `Y` `Y` `.` `.` `.` `.` -> Y at (3, 4), (3, 5)
            Row 4: `.` `.` `.` `.` `.` `.` `Y` `.` `.` `.` -> Y at (4, 6)
        *   Wait, the planet is usually a solid 2x2. Here, the Y's are at (2,4), (2,5), (3,4), (3,5). That's a 2x2 block.
        *   The "comets" are at (1,6) and (4,6).
        *   (1,6) is diagonally adjacent to (2,5)? (2,5) is top-right of planet. (1,6) is row-1, col+1. Yes, top-right diagonal.
        *   (4,6) is diagonally adjacent to (3,5)? (3,5) is bottom-right of planet. (4,6) is row+1, col+1. Yes, bottom-right diagonal.
        *   Wait, the description says "one or two comets". Here we have two.
        *   Output grid:
            Row 0: `.` `.` `.` `.` `.` `.` `.` `Y` `.` `.` -> Y at (0, 7)
            Row 1: `.` `.` `.` `.` `.` `.` `Y` `.` `.` `.` -> Y at (1, 6) (Original comet position)
            Row 2: `.` `.` `.` `.` `Y` `Y` `.` `.` `.` `.` -> Planet
            Row 3: `.` `.` `.` `.` `Y` `Y` `.` `.` `.` `.` -> Planet
            Row 4: `.` `.` `.` `.` `.` `.` `Y` `.` `.` `.` -> Y at (4, 6) (Original comet position)
            Row 5: `.` `.` `.` `.` `.` `.` `.` `Y` `.` `.` -> Y at (5, 7)
            Row 6: `.` `.` `.` `.` `.` `.` `.` `.` `Y` `.` -> Y at (6, 8)
            Row 7: `.` `.` `.` `.` `.` `.` `.` `.` `.` `Y` -> Y at (7, 9)
        *   Let's analyze the movement.
        *   Comet 1 at (

... [28101 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.96)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 477: "A butterfly unfolds its wings from a single scale pattern." k=2 alts: 0/0 7fe24cdd

Training Examples

Example 1

Input

→

Output

Example 2

Input

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Output

Example 3

Input

→

Output

Literal Description

See: The input is a 3×3 grid containing colored cells. This grid serves as a single tile that will be used to construct a larger composite image through rotation.

Do: Create a 6×6 output grid by arranging four rotated copies of the 3×3 input tile in a 2×2 layout. Place the original (0°) tile in the top-left quadrant. Rotate the input 90° clockwise and place it in the top-right quadrant. Rotate the input 270° clockwise (equivalently 90° counter-clockwise) and place it in the bottom-left quadrant. Rotate the input 180° and place it in the bottom-right quadrant. To rotate 90° clockwise: the first column of the original (read bottom to top) becomes the first row of the rotated version.

Grid: The input grid is always 3×3. The output grid is always 6×6, composed of a 2×2 arrangement of 3×3 quadrants. There is no background color convention; all cell colors from the input are preserved through rotation.

Figurative Descriptions (1 variants)

"A butterfly unfolds its wings from a single scale pattern."

qwen3.6-35b: k=2

See: The input is a tiny swatch of a butterfly's wing — a 3×3 fragment of living stained glass, each cell a colored scale carrying the blueprint of the whole creature.

Do: The butterfly opens its wings and you see the full pattern for the first time. The original swatch sits in one corner like a signature, and its reflections spiral outward — each neighboring wing-panel is the same swatch turned as if hinged along the body's axis, so the four quadrants bloom like petals from a center point. The symmetry is rotational, not mirrored: trace the pattern clockwise around the four panels and you'll find the swatch has pirouetted one quarter-turn further in each successive quadrant.

Grid: The wing fragment is always a 3×3 cluster of scales. The full butterfly, fully spread, is a 6×6 mosaic — four wing-panels arranged in a square, each carrying every original color, only reoriented by the body's radial geometry.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

→

Prediction

vs

Expected

Reasoning (26053 chars)

The user wants me to solve a grid transformation puzzle.

**1. Analyze the Input and Output:**
*   **Input:** A 3x3 grid.
*   **Output:** A 6x6 grid.
*   **Metaphor:** A butterfly wing fragment (3x3) expands into a full 6x6 mosaic. The four quadrants are rotations of the original swatch.
*   **Key phrase:** "The symmetry is rotational, not mirrored: trace the pattern clockwise around the four panels and you'll find the swatch has pirouetted one quarter-turn further in each successive quadrant."

**2. Conceptual Digestion:**

*   **CAST:**
    *   Input Grid (3x3): The "swatch" or "signature". Let's call this $S$.
    *   Output Grid (6x6): The "full butterfly". It consists of four 3x3 quadrants. Let's label them Top-Left (TL), Top-Right (TR), Bottom-Left (BL), Bottom-Right (BR).

*   **AFFORDANCES:**
    *   The input grid $S$ is the base pattern.
    *   The output grid is constructed by placing copies of $S$ into the four quadrants.
    *   The copies are rotated.

*   **TRANSFORMATION RULE:**
    *   The description says: "trace the pattern clockwise around the four panels and you'll find the swatch has pirouetted one quarter-turn further in each successive quadrant."
    *   Let's visualize the quadrants in a 6x6 grid.
        *   Top-Left (TL): Rows 0-2, Cols 0-2.
        *   Top-Right (TR): Rows 0-2, Cols 3-5.
        *   Bottom-Left (BL): Rows 3-5, Cols 0-2.
        *   Bottom-Right (BR): Rows 3-5, Cols 3-5.
    *   The description implies a sequence. "Clockwise around the four panels".
    *   Usually, reading order is TL -> TR -> BR -> BL. But "clockwise around the four panels" starting from where?
    *   "The original swatch sits in one corner like a signature". This suggests the first quadrant (TL) is the original, unrotated swatch.
    *   "its reflections spiral outward... each neighboring wing-panel is the same swatch turned as if hinged along the body's axis".
    *   "trace the pattern clockwise around the four panels and you'll find the swatch has pirouetted one quarter-turn further in each successive quadrant."
    *   Let's check the examples to confirm the rotation order and direction.

**3. Analyzing Training Examples:**

**Example 1:**
Input ($S$):
```
G A R
G R R
A X R
```
Output:
```
G A R A G G
G R R X R A
A X R R R R
R R R R X A
A R X R R G
G G A R A G
```

Let's break the output into 3x3 quadrants.
TL (Top-Left):
```
G A R
G R R
A X R
```
This matches the Input $S$ exactly. So, TL = $S$ (0 degrees rotation).

TR (Top-Right):
```
A G G
X R A
R R R
```
Let's see if this is a rotation of $S$.
$S$ is:
```
G A R
G R R
A X R
```
Rotate $S$ 90 degrees clockwise:
Row 0 becomes Col 2 (reversed? No, standard rotation).
(0,0)->(0,2), (0,1)->(1,2), (0,2)->(2,2)
(1,0)->(0,1), (1,1)->(1,1), (1,2)->(2,1)
(2,0)->(0,0), (2,1)->(1,0), (2,2)->(2,0)
Wait, let's just do it visually.
Original:
G A R
G R R
A X R

90 deg CW:
A G G
X R A
R R R
Let's check TR again.
TR is:
A G G
X R A
R R R
Yes! TR is $S$ rot

... [23802 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 500: "A talent show lineup where the shyest performers shuffle to ... [10 chars truncated]" k=3 alts: 2/15 85b81ff1

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Literal Description

See: The grid is 13 rows by 14 columns. Columns 2, 5, 8, and 11 are fixed separator columns filled entirely with black (.). The remaining columns form five 2-column blocks: block 0 (cols 0-1), block 1 (cols 3-4), block 2 (cols 6-7), block 3 (cols 9-10), and block 4 (cols 12-13). Every even row (0, 2, 4, 6, 8, 10, 12) is fully filled with the grid's color in every block. Each odd row (1, 3, 5, 7, 9, 11) has each block in one of two states: 'full' (both cells are the color, e.g. M M) or 'dotted' (first cell is the color, second is black, e.g. M .). This creates a 6-row by 5-column binary matrix where 1 = full and 0 = dotted.

Do: 1. Identify the five 2-column blocks and the six odd rows. 2. For each block (column of the binary matrix), compute its column sum — the number of odd rows where that block is full (1). 3. Sort the five block-columns by their column sum in ascending order (fewest full blocks on the left, most on the right). Ties may be broken by preserving relative input order. 4. Reconstruct the grid: even rows remain fully filled across all blocks, separator columns remain black, and each odd row's block values come from the rearranged column order. The content within each block-column (which specific odd rows are full vs dotted) is preserved — only the left-to-right ordering of the block-columns changes.

Grid: The grid is always 13 rows by 14 columns. A single non-black color is used throughout (blue, orange, magenta, etc.). Columns 2, 5, 8, and 11 are always black separators. The grid has a rigid alternating structure: even rows are uniform, odd rows encode binary block states. The output grid has identical dimensions and structure.

Figurative Descriptions (16 variants)

"A talent show lineup where the shyest performers shuffle to the front."

qwen3.6-35b: k=3

See: A stage is divided into five booths by black curtain dividers. Each booth has six spotlight moments (the odd rows) where performers can either stand tall and fill their booth with color, or shrink back into shadow, leaving a gap. Between these moments, the full chorus line blazes across every booth in unison. Each booth has its own personality — some performers are bold and fill nearly every spotlight, while others are timid, retreating into darkness more often than not.

Do: The stage director watches the dress rehearsal and counts how many times each booth's performer steps into the spotlight versus shrinks away. Then she rearranges the lineup: the shyest performer — the one who hid in shadow most often — is moved to the leftmost booth, and the boldest — the one who filled the most spotlights — takes the rightmost position. Each performer keeps their own unique pattern of courage and shyness; only their position on stage changes. The chorus-line moments remain untouched — everyone still shines together on those beats.

Grid: The stage is always thirteen rows deep and fourteen columns wide, lit in a single color against a black backdrop. Four black curtains hang at regular intervals, carving the stage into five equal booths. The chorus rows blaze uniformly; the solo rows reveal each booth's character — full presence or partial retreat. After the reshuffle, the stage dimensions and curtains remain identical, only the order of booths has changed.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

→

Prediction

vs

Expected

Reasoning (24482 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Input Grid Structure:**
*   **Dimensions:** 13 rows, 14 columns.
*   **Colors:** The background is black (`.`). The main color is Magenta (`M`) in the test input. In training examples, it was Blue (`B`) and Orange (`O`).
*   **Layout:**
    *   There are vertical dividers (black curtains) at specific columns.
    *   Looking at the input: `M M . M M . M M . M M . M M`
    *   The dots `.` appear at indices 2, 5, 8, 11 (0-indexed).
    *   This divides the grid into 5 vertical sections (booths).
    *   Booth 1: Columns 0-1 (width 2)
    *   Booth 2: Columns 3-4 (width 2)
    *   Booth 3: Columns 6-7 (width 2)
    *   Booth 4: Columns 9-10 (width 2)
    *   Booth 5: Columns 12-13 (width 2)
    *   Wait, let's check the column indices carefully.
    *   Row 0: `M M . M M . M M . M M . M M`
    *   Indices:
        *   0: M
        *   1: M
        *   2: . (Curtain)
        *   3: M
        *   4: M
        *   5: . (Curtain)
        *   6: M
        *   7: M
        *   8: . (Curtain)
        *   9: M
        *   10: M
        *   11: . (Curtain)
        *   12: M
        *   13: M
    *   Yes, 5 booths, each 2 columns wide. Separated by 1 column of black dots.
    *   Total width = 2 + 1 + 2 + 1 + 2 + 1 + 2 + 1 + 2 = 14. Correct.

*   **Rows:**
    *   Total 13 rows.
    *   The description mentions "odd rows" (1, 3, 5, 7, 9, 11) as "spotlight moments" where performers stand tall or shrink.
    *   "Even rows" (0, 2, 4, 6, 8, 10, 12) are "chorus line" moments where the full chorus line blazes across.
    *   Let's check the input rows.
    *   Row 0 (Even): `M M . M M . M M . M M . M M` -> All M (except curtains).
    *   Row 1 (Odd): `M . . M M . M . . M M . M .` -> Mixed.
    *   Row 2 (Even): `M M . M M . M M . M M . M M` -> All M.
    *   Row 3 (Odd): `M M . M . . M M . M . . M .` -> Mixed.
    *   ...
    *   Row 12 (Even): `M M . M M . M M . M M . M M` -> All M.
    *   So, even rows are uniform (full color), odd rows have patterns of `M` and `.` inside the booths.

**2. Analyze the Metaphorical Description:**
*   **Booths:** 5 vertical sections.
*   **Spotlight Moments (Odd Rows):** Performers can fill the booth (color) or shrink (black `.`).
*   **Chorus Line (Even Rows):** Full color across all booths.
*   **Personality:** "Bold" (fills spotlights often) vs "Timid" (shrinks often).
*   **Transformation:**
    *   Count how many times each booth's performer steps into the spotlight (is `M`) vs shrinks away (is `.`) in the odd rows.
    *   Actually, the description says "counts how many times each booth's performer steps into the spotlight versus shrinks away".
    *   Then rearranges: "shyest performer ... moved to the leftmost booth, and the boldest ... takes the rightmost position."
    *   "Each performer keeps their own unique pattern of courage and shyness; only their position on stage c

... [21650 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 530: "A photographic negative develops only in the darkroom's shad ... [4 chars truncated]" k=3 alts: 0/0 8e2edd66

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input is a 3×3 grid containing some cells filled with a single non-black color and some black (.) cells. The pattern forms a sparse arrangement of colored and empty positions.

Do: 1. Note the single non-black color used in the input (e.g., blue, orange, maroon). 2. Create the 'inverse' of the input: a 3×3 pattern where every colored cell becomes black (.) and every black cell becomes the color. 3. Construct a 9×9 output as a 3×3 arrangement of 3×3 blocks. For each cell in the original 3×3 input: (a) if the cell is colored, fill the corresponding 3×3 block with all black (.) cells; (b) if the cell is black (.), place the inverse pattern into the corresponding 3×3 block. 4. The block at row r, column c of the 3×3 arrangement occupies output rows 3r to 3r+2 and columns 3c to 3c+2.

Grid: The input is always a 3×3 grid with exactly one non-black color and black (.) as background. The output is always a 9×9 grid using the same single color and black. The output is tiled as a 3×3 arrangement of 3×3 blocks, so its dimensions are exactly 3× the input in each direction.

Figurative Descriptions (1 variants)

"A photographic negative develops only in the darkroom's shadows."

qwen3.6-35b: k=3

See: A small 3×3 snapshot shows scattered gems of color against a dark background — some cells glow with life, others sit in darkness.

Do: Each gem casts a shadow — its own photographic negative, where light and dark trade places. Now imagine the snapshot blown up into a mosaic of nine darkroom panels. Where a gem originally shone, its brilliance blinds the panel into total darkness — nothing develops there. But where darkness originally sat, the negative image quietly develops in that panel, revealing color exactly where the original had none. The bright consume themselves; the empty give birth to reversed echoes.

Grid: The snapshot is a small 3×3 frame with one color of gem against black. The developed mosaic is nine panels arranged 3×3, each panel itself a 3×3 frame — so the full print is three times the snapshot in each direction. Every panel is either blacked out (where a gem stood) or printed with the negative (where shadow was).

qwen3.6-35b — MARC valid, solved with 3 examples

Input

→

Prediction

vs

Expected

Reasoning (31786 chars)

The user wants me to solve a grid transformation puzzle.

**1. Analyze the Input and Output format:**
- Input: A 3x3 grid.
- Output: A 9x9 grid.
- Colors: `.` (black), `B` (blue), `R` (red), `G` (green), `Y` (yellow), `X` (grey), `M` (magenta), `O` (orange), `A` (azure), `W` (maroon).

**2. Analyze the Metaphorical Description:**
- "A small 3×3 snapshot shows scattered gems of color against a dark background".
- "Each gem casts a shadow — its own photographic negative, where light and dark trade places."
- "Snapshot blown up into a mosaic of nine darkroom panels."
- "Where a gem originally shone, its brilliance blinds the panel into total darkness — nothing develops there." -> If input cell is colored (gem), the corresponding 3x3 block in output is all black (`.`).
- "But where darkness originally sat, the negative image quietly develops in that panel, revealing color exactly where the original had none." -> If input cell is black (`.`), the corresponding 3x3 block in output is the "negative" of the input grid.
- "The bright consume themselves; the empty give birth to reversed echoes."

**3. Conceptual Digestion:**

*   **CAST:**
    *   **Input Grid (3x3):** The "snapshot". Contains colored cells (gems) and black cells (darkness).
    *   **Output Grid (9x9):** The "mosaic" or "developed print". It is composed of 9 sub-grids, each 3x3.
    *   **Sub-grids (3x3):** The "panels".

*   **AFFORDANCES:**
    *   **Colored Cell (Gem):** In the input, it represents light/color. In the output, it dictates that the corresponding 3x3 panel becomes completely black (darkness).
    *   **Black Cell (Darkness):** In the input, it represents empty space. In the output, it dictates that the corresponding 3x3 panel becomes a copy of the *negative* of the input grid.

*   **TRANSFORMATION RULE:**
    1.  Divide the 9x9 output grid into a 3x3 arrangement of 3x3 blocks. Let's call the block at row $r$ and column $c$ (where $r, c \in \{0, 1, 2\}$) as $Block(r, c)$.
    2.  Look at the input grid cell at row $r$ and column $c$, let's call it $Input(r, c)$.
    3.  **Case 1: $Input(r, c)$ is a color (not `.`).**
        *   $Block(r, c)$ is filled entirely with `.` (black).
    4.  **Case 2: $Input(r, c)$ is `.` (black).**
        *   $Block(r, c)$ is filled with the "negative" of the input grid.
        *   What is the "negative"? The description says "light and dark trade places".
        *   In the input, `.` is dark, colors are light.
        *   So, in the negative:
            *   Where input was `.` (dark), output block should be colored (light).
            *   Where input was colored (light), output block should be `.` (dark).
        *   Wait, let's re-read carefully: "revealing color exactly where the original had none."
        *   Original had none (was `.`) -> Output block has color.
        *   Original had color -> Output block is black.
        *   But what *color*? The description says "its own photographic negative". Us

... [28994 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.10)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 543: "In a noisy room, the loudest voice shapes the echo on the wa ... [3 chars truncated]" k=2 alts: 15/15 9110e3c5

Training Examples

Example 1

Input

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Output

Example 2

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Output

Example 3

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Output

Example 4

Input

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Output

Example 5

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Output

Example 6

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Output

Example 7

Input

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Output

Literal Description

See: The input is a 7×7 grid containing black (empty) cells and several different colors. One color appears far more frequently than all others — this is the dominant color. The remaining non-black colors (such as W, X, Y, O, A, M) each appear only once or twice, scattered throughout the grid as distractors.

Do: 1. Count the occurrences of each non-black color in the input grid. Identify the dominant color — the one that appears most frequently. 2. Map the dominant color to a fixed 3×3 output pattern using azure (A) on a black background: If the dominant color is R (red), output a horizontal line: row 1 = '. . .', row 2 = 'A A A', row 3 = '. . .'. If the dominant color is G (green), output an inverted-L shape: row 1 = '. A A', row 2 = '. A .', row 3 = '. A .'. If the dominant color is B (blue), output a mirrored shape: row 1 = '. . A', row 2 = 'A A .', row 3 = '. A .'. 3. Output the corresponding 3×3 pattern. The specific positions and arrangement of colors in the input grid do not matter — only which color is most frequent.

Grid: The input grid is always 7×7. The output grid is always 3×3. The output uses only two colors: black (.) for background and azure (A) for the pattern. The output pattern is entirely determined by which non-black color dominates the input grid, not by spatial arrangement.

Figurative Descriptions (16 variants)

"In a noisy room, the loudest voice shapes the echo on the wall."

qwen3.6-35b: k=2

See: A crowded square buzzes with chatter. Most voices are faint — a whisper of maroon here, a murmur of orange there — but one color is practically shouting over everyone else, filling the room with its presence. The rest are just passersby.

Do: Listen to the crowd and find the voice that drowns out all others. That dominant voice doesn't just win the argument — it chooses a signature gesture, a pose struck in azure light on a small dark stage. Each color-voice has rehearsed its own distinctive pose: one stands bold as a horizon line, another rises like a bent elbow, another traces a zigzag path. The loudest voice steps onto the stage and strikes the only pose it knows.

Grid: The crowded square is always seven paces on each side. The stage where the winner performs is a tiny three-by-three platform, lit only in azure against darkness. No matter how chaotic the crowd, only one pose appears — chosen not by where anyone stood, but simply by who was loudest.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

→

Prediction

vs

Expected

Reasoning (32034 chars)

The user wants me to solve a grid transformation puzzle.

**1. Analyze the Input and Output format:**
- Input grids are 7x7.
- Output grids are 3x3.
- Colors are represented by single characters: `.` (black), `B` (blue), `R` (red), `G` (green), `Y` (yellow), `X` (grey), `M` (magenta), `O` (orange), `A` (azure), `W` (maroon).

**2. Analyze the Metaphorical Description:**
- "Crowded square buzzes with chatter": The input grid is a 7x7 grid full of characters.
- "Most voices are faint... but one color is practically shouting over everyone else": There is a dominant color in the input grid.
- "The rest are just passersby": Other colors are irrelevant or background noise.
- "The dominant voice... chooses a signature gesture, a pose struck in azure light on a small dark stage": The output is a 3x3 grid (the stage) filled with `A` (azure) and `.` (black/darkness).
- "Each color-voice has rehearsed its own distinctive pose": Different colors correspond to different patterns (poses) in the 3x3 output grid.
- "The loudest voice steps onto the stage and strikes the only pose it knows": The output grid is determined solely by the dominant color in the input.

**3. Analyze the Training Examples to deduce the "Poses":**

*Example 1:*
Input:
```
B . B . O . .
B B W B . B .
. . B B . R .
. . . . G . B
. Y . B . . B
. . B . R . A
. . B . O G B
```
Let's count the occurrences of each color to find the "loudest voice" (dominant color).
- B (blue):
  - Row 1: 2
  - Row 2: 4
  - Row 3: 2
  - Row 4: 1
  - Row 5: 1
  - Row 6: 1
  - Row 7: 2
  - Total B: 2+4+2+1+1+1+2 = 13.
- O (orange): 2
- W (maroon): 1
- R (red): 2
- G (green): 2
- Y (yellow): 1
- A (azure): 1
- Others (.): many.

Dominant color is **B (blue)**.

Output:
```
. . A
A A .
. A .
```
This is a 3x3 grid. Let's visualize the pattern of `A` (azure) vs `.` (black).
Row 1: `.` `.` `A`
Row 2: `A` `A` `.`
Row 3: `.` `A` `.`
Pattern:
```
0 0 1
1 1 0
0 1 0
```
(where 1 is A, 0 is .)

*Example 2:*
Input:
```
. G . G X G .
. . G G . . .
A . . . . . G
G Y G W G . G
. . W G B G G
. G G G . G .
. . . . . . G
```
Let's count occurrences.
- G (green):
  - Row 1: 3
  - Row 2: 2
  - Row 3: 1
  - Row 4: 4
  - Row 5: 3
  - Row 6: 3
  - Row 7: 1
  - Total G: 3+2+1+4+3+3+1 = 17.
- X (grey): 1
- A (azure): 1
- Y (yellow): 1
- W (maroon): 2
- B (blue): 1
- Others (.): many.

Dominant color is **G (green)**.

Output:
```
. A A
. A .
. A .
```
Pattern of `A` vs `.`:
Row 1: `.` `A` `A`
Row 2: `.` `A` `.`
Row 3: `.` `A` `.`
Pattern:
```
0 1 1
0 1 0
0 1 0
```

**4. Deduce the Mapping from Color to Pose:**
We have two examples.
- Color **B** (Blue) -> Pattern:
  ```
  . . A
  A A .
  . A .
  ```
- Color **G** (Green) -> Pattern:
  ```
  . A A
  . A .
  . A .
  ```

Wait, the description says "Each color-voice has rehearsed its own distinctive pose: one stands bold as a horizon line, another rises like a bent elbow, another traces a zigzag path."
This implies there might be a specific geometric shape associated with each color.


... [29322 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.78)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 561: "Two shields with holes reveal the vulnerable spots where arr ... [19 chars truncated]" k=1 alts: 1/15 94f9d214

Training Examples

Example 1

Input

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Output

Example 2

Input

→

Output

Example 3

Input

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Output

Example 4

Input

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Output

Literal Description

See: The input is a rectangular grid with 8 rows and 4 columns, composed of two 4×4 halves stacked vertically. The top half contains a pattern made of green (G) cells and black (.) cells. The bottom half contains a pattern made of blue (B) cells and black (.) cells.

Do: Split the input grid into two 4×4 halves: the top half (green pattern) and the bottom half (blue pattern). For each cell position in the 4×4 grid, check whether that position is black (absent) in BOTH halves — that is, the cell is '.' in the top half AND '.' in the bottom half. If both are absent, place a red (R) cell at that position in the output. Otherwise, place a black (.) cell. The output is a single 4×4 grid.

Grid: The input grid is 4 columns wide and 8 rows tall, consisting of two equal 4×4 sub-grids stacked vertically. The output grid is 4×4. The background color is black (.).

Figurative Descriptions (16 variants)

"Two shields with holes reveal the vulnerable spots where arrows strike through."

qwen3.6-35b: k=1

See: A warrior carries two shields stacked one behind the other — the front shield is forged from green iron, the rear from blue steel. Each shield has gaps where the metal was never filled in, leaving dark empty spaces.

Do: An archer fires arrows at the paired shields. Where both shields have holes — where neither green iron nor blue steel stands guard — the arrow passes clean through and leaves a red wound on the wall behind. Wherever at least one shield holds firm, the arrow is deflected and the wall stays unmarked.

Grid: The two shields sit one atop the other in the input, each a square slab four units across. The wall behind them, revealed in the output, is the same size as a single shield, dark except where it bleeds red.

qwen3.6-35b — MARC valid, solved with 1 example

Input

→

Prediction

vs

Expected

Reasoning (29747 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Input:** "A warrior carries two shields stacked one behind the other".
    *   "Front shield is forged from green iron" -> Green (G) pixels.
    *   "Rear from blue steel" -> Blue (B) pixels.
    *   "Stacked one behind the other" -> In the input grid, these are likely represented as two separate blocks or layers. The description says "The two shields sit one atop the other in the input". This suggests the input grid contains two distinct 4x4 grids (or similar size) stacked vertically.
    *   "Each shield has gaps where the metal was never filled in, leaving dark empty spaces" -> Black (.) pixels represent holes.
*   **Action:** "An archer fires arrows at the paired shields."
*   **Output:** "The wall behind them... is the same size as a single shield, dark except where it bleeds red."
    *   Output grid size: Same as a single shield (4x4).
    *   "Red wound" -> Red (R) pixels.
    *   "Dark" -> Black (.) pixels.
*   **Logic:**
    *   "Where both shields have holes — where neither green iron nor blue steel stands guard — the arrow passes clean through and leaves a red wound on the wall behind."
        *   Condition: Input Shield 1 has hole (.) AND Input Shield 2 has hole (.).
        *   Result: Output has Red (R).
    *   "Wherever at least one shield holds firm, the arrow is deflected and the wall stays unmarked."
        *   Condition: Input Shield 1 has metal (G) OR Input Shield 2 has metal (B) (or both).
        *   Result: Output has Black (.) (unmarked wall).

**2. Analyze the Grid Details:**
*   Input grid structure: "The two shields sit one atop the other in the input, each a square slab four units across."
    *   This implies the input grid is 8 rows high and 4 columns wide (4x4 + 4x4).
    *   Top 4 rows = Front Shield (Green).
    *   Bottom 4 rows = Rear Shield (Blue).
*   Output grid structure: "The wall behind them... is the same size as a single shield".
    *   Output grid is 4 rows high and 4 columns wide.

**3. Analyze Training Examples:**

*   **Example 1 Input:**
    ```
    . G G .
    . G . G
    . . G .
    G G G G
    B B B B
    B B . .
    B B . .
    . B B .
    ```
    *   Top 4 rows (Green Shield):
        ```
        . G G .
        . G . G
        . . G .
        G G G G
        ```
    *   Bottom 4 rows (Blue Shield):
        ```
        B B B B
        B B . .
        B B . .
        . B B .
        ```
    *   Wait, the description says "Front shield is forged from green iron" and "Rear from blue steel".
    *   Let's check the colors in the input.
    *   Top part has G. Bottom part has B.
    *   Let's align them.
    *   Row 0 (Top): `. G G .` vs Row 4 (Bottom): `B B B B`
    *   Row 1: `. G . G` vs Row 5: `B B . .`
    *   Row 2: `. . G .` vs Row 6: `B B . .`
    *   Row 3: `G G G G` vs Row 7: `. B B .`

    

... [27683 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.06)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 616: "An archer shoots through a field, and the arrow punches a ho ... [22 chars truncated]" k=1 alts: 0/0 9f8de559

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Literal Description

See: The grid has a rectangular orange (O) canvas region surrounded by colored border strips made of non-orange colors (W, X, A). Inside the orange canvas, there is an arrow formed by one red (R) cell and a line of magenta (M) cells. The M cells form the tail/shaft of the arrow, and R is the arrowhead at the tip. The arrow points in a specific direction: from the tail (M cells) through the head (R cell) and onward. Along the border surrounding the orange canvas, there is exactly one cell that differs from its neighboring border cells — a single anomalous cell that breaks the otherwise uniform pattern of its border strip.

Do: 1. Locate the red (R) cell and all magenta (M) cells inside the orange canvas. 2. Determine the arrow's direction: the M cells form a line trailing away from R, so the arrow points from the M tail through R and continuing in the same direction (i.e., away from the M cells). 3. Starting from R, extend a ray in the arrow's pointing direction, stepping one cell at a time through the orange canvas. 4. Continue until the ray reaches the first non-orange border cell. 5. Change that border cell to orange (O). 6. Leave everything else in the grid unchanged.

Grid: The grid is 14 rows by 14 columns. A rectangular region of orange (O) cells forms the interior canvas. This canvas is bounded on all four sides by border strips composed of non-orange colors (combinations of W, X, and A), typically 2-3 cells wide. The border strips are mostly uniform in color along each side, with exactly one cell in one border strip that will become the target of the transformation. The arrow (R + M cells) inside the canvas is always aligned along a cardinal or diagonal direction.

Figurative Descriptions (1 variants)

"An archer shoots through a field, and the arrow punches a hole in the castle wall."

qwen3.6-35b: k=1

See: An open orange field is enclosed by thick castle walls built from colored stone (maroon, grey, azure). Standing in the field is an archer — a red (R) figure — with a trail of magenta (M) banners streaming behind them like a wind sock, showing which way the wind blows. Somewhere along the castle wall, one stone block is a different color from its neighbors — a weak spot in the masonry.

Do: The archer looses an arrow in the direction the wind carries — away from the trailing banners, through the red archer, and onward across the open field. The arrow flies straight until it strikes the castle wall. Where it hits, the stone crumbles and reveals the orange earth beneath — one block of wall becomes part of the field. Nothing else in the kingdom changes.

Grid: The kingdom is a 14×14 realm. The orange field occupies the interior, walled in on all sides by thick borders of colored stone (W, X, A), typically two or three blocks deep. The archer (R) and banners (M) stand in a line within the field, aligned along a straight compass heading or diagonal. The walls are mostly uniform on each side, with one block somewhere that fate has marked for the arrow's impact.

qwen3.6-35b — MARC valid, solved with 1 example

Input

→

Prediction

vs

Expected

Reasoning (28178 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and a test input.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Castle Walls:** Thick borders of colored stone (W=maroon, X=grey, A=azure). They enclose the field.
    *   **Open Field:** The interior area, usually filled with O=orange.
    *   **Archer:** A red (R) figure located inside the field.
    *   **Banners:** Magenta (M) blocks trailing behind the archer, indicating the direction of the wind (and thus the arrow's flight).
    *   **Weak Spot:** A specific stone block in the wall that is different from its neighbors or just the target of the arrow.

*   **AFFORDANCES (Capabilities/Actions):**
    *   **Archer/Banners:** Define a vector/direction. The banners trail *behind* the archer. The arrow flies *away* from the banners, *through* the archer, and in the direction of the arrow's flight.
    *   **Arrow:** Travels in a straight line from the archer's position, in the direction indicated by the banners.
    *   **Walls:** Can be struck by the arrow.
    *   **Weak Spot:** The specific wall block where the arrow hits.

*   **TRANSFORMATION RULE:**
    1.  **Locate the Archer (R) and Banners (M).**
    2.  **Determine Direction:** The banners trail *behind* the archer. The arrow flies *forward* from the archer. So, if the banners are at $(r, c)$ and the archer is at $(r', c')$, the direction is from $(r, c)$ to $(r', c')$ (or rather, the vector pointing away from the banners). Wait, let's re-read carefully: "trailing behind them like a wind sock, showing which way the wind blows... looses an arrow in the direction the wind carries — away from the trailing banners, through the red archer".
        *   If banners are at $B$ and archer is at $A$, the wind blows from $B$ towards $A$? No, "trailing behind" usually means the wind is coming from the direction of the banners. If a sock trails behind, the wind is pushing it. So wind direction is $B \to A$.
        *   "Arrow flies... away from the trailing banners, through the red archer". This confirms the direction is $B \to A$ and continues past $A$.
    3.  **Trace the Path:** Start at the Archer's position $(r_A, c_A)$. Move in the direction defined by the vector from the nearest Banner to the Archer. Continue moving in that direction step by step.
    4.  **Identify Impact:** The arrow travels until it hits a wall block (W, X, or A).
    5.  **Execute Change:** The wall block at the impact point changes color to O (orange), representing the earth beneath.
    6.  **Constraint:** "Nothing else in the kingdom changes."

**2. Analyzing the Test Input**

Let's parse the grid. It's a 14x14 grid.

Row 0: `A A W W A A A A A A A A A A`
Row 1: `A A W W A A A A A A A A A A`
Row 2: `A A W W A A A A A A A A A A`
Row 3: `A A O O O O O O O O O O O W`
Row 4: `A A O O O O O O O O O M O W`
Row 5: `A A O O O O O O O O M O O W`
Row 6: `A A O O O O O O O M O O O W`
Row 7: `A A O O O O O O M O O O O 

... [25393 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 626: "Two rulers hold court along the edges, and where their domai ... [40 chars truncated]" k=1 alts: 0/0 a406ac07

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input is a square grid (10×10) with a black background. The rightmost column contains a sequence of colored segments stacked vertically, where each color occupies one or more consecutive rows. The bottom row contains a sequence of colored segments arranged horizontally, where each color occupies one or more consecutive columns. The rest of the interior cells are black. Each color that appears in the right column also appears in the bottom row, and the bottom-right corner cell belongs to the color that occupies both the last row of the right column and the last column of the bottom row.

Do: 1. Preserve the rightmost column and the bottom row exactly as they are. 2. For each distinct color, determine which consecutive rows it spans in the rightmost column and which consecutive columns it spans in the bottom row. 3. Fill the rectangular region defined by the intersection of those rows and those columns with that color. 4. All other interior cells (those not in any color's row-column intersection, and not in the rightmost column or bottom row) remain black.

Grid: The grid is 10×10. The background color is black (.). The rightmost column (column 9) and the bottom row (row 9) serve as headers that encode color segment positions. The interior region spans rows 0–8 and columns 0–8. The coordinate system is row-major with row 0 at the top and column 0 at the left.

Figurative Descriptions (1 variants)

"Two rulers hold court along the edges, and where their domains overlap, their banners fill the hall."

qwen3.6-35b: k=1

See: A dark banquet hall has two rulers seated along its edges — one enthroned down the right wall, the other stretched across the floor. Each ruler wears a sequence of colored banners representing the lands they govern. The hall itself is empty and dark, waiting to be claimed. The corner seat where both rulers meet belongs to the color that rules both thresholds.

Do: Each color serves both rulers simultaneously. Where a color's vertical reign along the wall overlaps with its horizontal reign along the floor, that color unfurls its banners across the hall, filling the territory where its two claims intersect. Lands not claimed by any color's overlapping authority remain in darkness. The rulers themselves do not move from their edges.

Grid: The hall is a 10×10 stone floor shrouded in darkness (.). The right wall (the eastern throne) and the ground floor (the southern throne) are the two seats of power that remain fixed. The interior of the hall — everything not along those two edges — is where banners may or may not be raised depending on overlapping claims.

qwen3.6-35b — MARC valid, solved with 1 example

Input

→

Prediction

vs

Expected

Reasoning (27473 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Setting:** A 10x10 grid.
*   **Initial State:** "Dark banquet hall" (mostly `.` or black).
*   **Rulers:**
    *   "Enthroned down the right wall": This refers to the last column (column index 9, 0-indexed).
    *   "Stretched across the floor": This refers to the last row (row index 9, 0-indexed).
    *   Wait, let's check the grid details. "The right wall (the eastern throne) and the ground floor (the southern throne) are the two seats of power".
    *   In a standard matrix representation (row, col), the "right wall" is the last column. The "ground floor" (southern) is the last row.
    *   The description says "The rulers themselves do not move from their edges." This implies the input grid already has these rulers defined on the edges.
*   **Banners:** "Each ruler wears a sequence of colored banners representing the lands they govern." This means the colors in the last column and last row represent specific colors.
*   **Intersection:** "The corner seat where both rulers meet belongs to the color that rules both thresholds." This is the bottom-right corner cell (9, 9).
*   **Action:** "Each color serves both rulers simultaneously. Where a color's vertical reign along the wall overlaps with its horizontal reign along the floor, that color unfurls its banners across the hall, filling the territory where its two claims intersect."
    *   This sounds like a projection or intersection logic.
    *   If a color $C$ appears in the right wall (column 9) at row $r$, and the same color $C$ appears in the floor (row 9) at column $c$, then the cell $(r, c)$ in the interior of the grid gets filled with color $C$.
    *   Wait, let's re-read carefully: "Where a color's vertical reign along the wall overlaps with its horizontal reign along the floor, that color unfurls its banners across the hall, filling the territory where its two claims intersect."
    *   "Vertical reign" = presence of color in the right column.
    *   "Horizontal reign" = presence of color in the bottom row.
    *   "Overlaps" = intersection of the row index from the vertical reign and the column index from the horizontal reign.
    *   So, if cell $(r, 9)$ has color $C$ and cell $(9, c)$ has color $C$, then cell $(r, c)$ becomes color $C$.
    *   What about the edges themselves? "The rulers themselves do not move from their edges." This suggests the input edges are preserved in the output.
    *   "Lands not claimed by any color's overlapping authority remain in darkness." So interior cells $(r, c)$ where $r < 9$ and $c < 9$ remain `.` unless the condition is met.

**2. Analyze Training Examples:**

**Example 1:**
Input:
Row 0: `...X` (last char X)
Row 1: `...M` (last char M)
Row 2: `...M` (last char M)
Row 3: `...O` (last char O)
Row 4: `...O` (last char O)
Row 5: `...O` (last char O)
Row 6: `...A` (last char 

... [24857 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.56)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 648: "A still lake reflects the sky, but where the reflection meet ... [34 chars truncated]" k=1 alts: 9/15 a8610ef7

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Literal Description

See: The input grid contains cells of two types: azure (A) cells and black (.) cells. The azure cells form an irregular pattern scattered across the grid, while black cells serve as the background.

Do: For each cell in the grid: (1) If the cell is black (.), leave it unchanged. (2) If the cell is azure (A) at position (row, col), find its vertical mirror position at (H-1-row, col), where H is the grid height. Check what occupies that mirror position in the input grid. If the mirror position also contains azure (A), replace the current cell with red (R). If the mirror position contains black (.), replace the current cell with grey (X).

Grid: The grid is 6 rows by 6 columns. Black (.) is the background color and remains unchanged throughout the transformation. The coordinate system has row 0 at the top. The vertical reflection axis is the horizontal midline of the grid, pairing row r with row H-1-r.

Figurative Descriptions (16 variants)

"A still lake reflects the sky, but where the reflection meets solid ground, it turns to stone."

qwen3.6-35b: k=1

See: A landscape of azure figures stands on a dark stage. Some areas are empty darkness, others are occupied by azure presences — scattered unevenly, as if a crowd milling about before a performance.

Do: A great lake lies along the horizon, perfectly still. Each azure figure gazes down into the water to find its reflection on the opposite shore. If the figure sees a twin gazing back — another azure soul standing at the mirrored spot — both blush red with recognition. But if the figure peers into the water and finds only empty darkness where a twin should be, it turns grey with loneliness, hardening to stone. The dark empty spaces, having no one to cast a reflection, remain untouched.

Grid: The stage is six steps wide and six steps tall. The lake's surface runs horizontally through the middle, so each figure on the upper shore has a counterpart position on the lower shore, and vice versa. The darkness is merely empty ground — it plays no part in the reflection and stays as it is.

qwen3.6-35b — MARC valid, solved with 1 example

Input

→

Prediction

vs

Expected

Reasoning (27246 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**

*   **Grid details:** 6x6 grid.
*   **Colors involved:**
    *   `.` (black/darkness) - Empty ground.
    *   `A` (azure) - Azure figures.
    *   `R` (red) - Blushing figures (twin found).
    *   `X` (grey) - Lonely figures (no twin).
*   **The "Lake":** Runs horizontally through the middle.
    *   Since the grid is 6x6, the middle is between row 2 and row 3 (0-indexed) or between row 3 and 4 (1-indexed).
    *   Let's check the indices. Rows 0, 1, 2, 3, 4, 5.
    *   "Horizontally through the middle" usually implies a reflection across a horizontal axis.
    *   If the lake is the mirror, row 0 reflects to row 5, row 1 to row 4, row 2 to row 3.
    *   Wait, the text says "each figure on the upper shore has a counterpart position on the lower shore".
    *   Let's verify the reflection logic.
    *   Row 0 <-> Row 5
    *   Row 1 <-> Row 4
    *   Row 2 <-> Row 3
    *   This is a vertical flip (reflection across the horizontal midline).

*   **The Rule:**
    *   Input contains `A` (azure) and `.` (black).
    *   For every `A` at position $(r, c)$:
        *   Find its reflection position $(r', c)$.
        *   If the reflection position $(r', c)$ also contains an `A` in the input grid:
            *   Both figures turn `R` (red).
        *   If the reflection position $(r', c)$ contains `.` (or anything else, but likely just `.` based on description):
            *   The figure at $(r, c)$ turns `X` (grey).
    *   What about the figures at the reflection position?
        *   "If the figure sees a twin... both blush red".
        *   "If the figure peers... and finds only empty darkness... it turns grey".
        *   This implies a symmetric check. If $A$ at $(r, c)$ sees $A$ at $(r', c)$, both become $R$. If $A$ at $(r, c)$ sees `.` at $(r', c)$, it becomes $X$.
        *   What if $(r', c)$ is `.`? Then the figure at $(r, c)$ becomes $X$.
        *   What if $(r', c)$ is `A`? Then both become $R$.
    *   What about `.` cells? "The dark empty spaces... remain untouched." So `.` stays `.`.

**2. Analyze Training Examples:**

*   **Example 1 Input:**
    ```
    . A . A A A
    A A A A A .
    A . A . A .
    . A A A . A
    A A . A A .
    A A . . . A
    ```
    Grid size: 6x6.
    Rows:
    0: `. A . A A A`
    1: `A A A A A .`
    2: `A . A . A .`
    3: `. A A A . A`
    4: `A A . A A .`
    5: `A A . . . A`

*   **Example 1 Output:**
    ```
    . R . X X R
    R R X R R .
    X . R . X .
    . X R X . X
    R R . R R .
    X R . . . R
    ```

    Let's check the reflection logic.
    Reflection pairs: (0,5), (1,4), (2,3).

    **Row 0 vs Row 5:**
    *   Col 0: Input(0,0)=`.`, Input(5,0)=`A`.
        *   (0,0) is `.`, stays `.`.
        *   (5,0) is `A`. Reflection is (0,0) which is `.`. So (5,0) sees darkness. Becomes `X`.
        *   Output(5,0) is `X`

... [24864 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.31)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 662: "An archaeologist restores the largest damaged section of a m ... [12 chars truncated]" k=2 alts: 0/0 abbfd121

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input grid is filled with a repeating tile pattern that covers the entire background. Overlaid on this pattern are two or three solid-colored rectangles, each filled uniformly with a single color that is distinct from the colors used in the tiling pattern. These rectangles occlude (hide) portions of the underlying repeating pattern. The rectangles vary in size.

Do: 1. Identify all solid-colored rectangles in the grid — contiguous rectangular regions filled with a single color that does not belong to the underlying repeating tile pattern. 2. Determine the size (area) of each rectangle. 3. Select the largest rectangle by area. 4. Reconstruct the repeating tile pattern that would exist underneath that rectangle by extending the surrounding pattern into the occluded region. The tile pattern repeats predictably, so infer the correct values from the visible portions of the pattern adjacent to the rectangle. 5. Output only the reconstructed patch — the grid region corresponding to the largest rectangle, filled with the restored tiling pattern.

Grid: The output grid has the same dimensions as the largest solid-colored rectangle found in the input. It contains only the colors used in the repeating background tile pattern — the solid overlay color does not appear in the output. The output represents the hidden portion of the tiling pattern that was masked by the rectangle.

Figurative Descriptions (1 variants)

"An archaeologist restores the largest damaged section of a mosaic floor."

qwen3.6-35b: k=2

See: An ancient mosaic floor stretches across a grand hall, its tiles repeating in an elegant, rhythmic pattern. But vandals have splashed buckets of paint over parts of the mosaic — two or three ugly stains of solid color now blot out sections of the original artwork beneath. Each stain is a different color and a different size, but all are rectangular, as if tarps were laid down and painted over.

Do: You are the archaeologist called in to restore the mosaic. Survey the damage and find the largest paint stain — the one that hides the most of the original floor. Ignore the smaller stains; they're someone else's assignment. Carefully chip away the paint from that largest stain, using the surviving mosaic around its edges as your guide. The mosaic's rhythm is predictable — its melody repeats — so you can reconstruct every hidden tile by listening to the pattern still singing at the borders. Lift out only your restored section and present it.

Grid: Your restoration is exactly the size of the largest stain you removed. Every tile matches the mosaic's original palette — no trace of the vandal's paint remains. You are holding up just the recovered fragment, proof of what was always underneath.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

→

Prediction

vs

Expected

Reasoning (22682 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **CAST:**
    *   **Background Pattern:** A repeating mosaic pattern. It seems to be a grid of characters.
    *   **Stains:** Rectangular blocks of solid color (different from the background pattern) covering parts of the mosaic.
    *   **Target:** The "largest paint stain" (the one covering the most area).
    *   **Output:** The restored section of the mosaic that was hidden under the largest stain.

*   **AFFORDANCES:**
    *   **Background Pattern:** It has a rhythm or periodicity. I can infer the hidden tiles by looking at the surrounding tiles.
    *   **Stains:** They are rectangular. I need to identify their coordinates and dimensions.
    *   **Restoration:** I need to reconstruct the pattern inside the largest stain's bounding box.

*   **TRANSFORMATION RULE:**
    1.  Identify the repeating background pattern.
    2.  Identify all rectangular regions of solid color that disrupt the pattern (stains).
    3.  Determine the size (area) of each stain.
    4.  Select the stain with the largest area.
    5.  Extract the subgrid corresponding to the coordinates of this largest stain.
    6.  Reconstruct the content of this subgrid based on the periodicity of the background pattern observed in the rest of the grid.
    7.  Output this reconstructed subgrid.

**2. Analyzing the Test Input**

Let's look at the input grid provided.

Input Grid Dimensions:
Let's count rows and columns.
Row 1: `A M O A M O A M O A M O A M O A M O A M O A` (22 chars)
Row 2: `M O A M O A M O A M O A M O A M O A M O A M` (22 chars)
...
It looks like a 22x22 grid. Let's verify.
Rows:
1.  `A M O A M O A M O A M O A M O A M O A M O A`
2.  `M O A M O A M O A M O A M O A M O A M O A M`
3.  `O G G G G G O A M O A M O A M O A M O A M O`
4.  `A G G G G G A M O A M O A M O A M O A M O A`
5.  `M G G G G G M O A M O Y Y Y Y Y Y Y Y Y A M`
6.  `O G G G G G O A M O A Y Y Y Y Y Y Y Y Y M O`
7.  `A G G G G G A M O A M Y Y Y Y Y Y Y Y Y O A`
8.  `M G G G G G M O A M O Y Y Y Y Y Y Y Y Y A M`
9.  `O A M O A M O A M O A Y Y Y Y Y Y Y Y Y M O`
10. `A M O A M O A M O A M Y Y Y Y Y Y Y Y Y O A`
11. `M O A M O A M O A M O Y Y Y Y Y Y Y Y Y A M`
12. `O A M O A M O A M O A Y Y Y Y Y Y Y Y Y M O`
13. `A M O A M O A M O A M O A M O A M O A M O A`
14. `M O A M O A M O A M O A M O A M O A M O A M`
15. `O A W W W W W W W W W M O A M O A M O A M O`
16. `A M W W W W W W W W W O A M O A M O A M O A`
17. `M O W W W W W W W W W A M O A M O A M O A M`
18. `O A W W W W W W W W W M O A M O A M O A M O`
19. `A M W W W W W W W W W O A M O A M O A M O A`
20. `M O W W W W W W W W W A M O A M O A M O A M`
21. `O A W W W W W W W W W M O A M O A M O A M O`
22. `A M O A M O A M O A M O A M O A M O A M O A`
23. `M O A M O A M O A M O A M O A M O A M O A M`

Wait, let me recount the rows carefully.
1. `A M O A M O A M O A M O A M O A M O A M O A`
2. `M O A M O A M O A M O A M O A M O A M O A M`
3. `O G G G G G O A M O A M O

... [19733 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.03)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 683: "A spy encrypts messages using a codebook, and you must decod ... [38 chars truncated]" k=1 alts: 0/0 b0722778

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Literal Description

See: The input grid is organized into horizontal bands of two rows each, separated by rows of dots. Within each band, there are three 2×2 sub-grids arranged left to right: Block A (columns 0–1), Block B (columns 3–4), and Block C (columns 7–8), separated by dot columns. Each 2×2 sub-grid contains cells colored with up to two distinct colors.

Do: For each band, determine the combined transformation that converts Block A into Block B. This transformation has two components: (1) a spatial operation — one of identity, horizontal flip, vertical flip, 90° clockwise rotation, 90° counter-clockwise rotation, or 180° rotation; and (2) an optional color remapping — a consistent substitution of colors (e.g., every green becomes azure, every orange becomes green). To find the correct transformation: try each of the possible spatial operations on Block A, and for each, check whether there is a consistent one-to-one color substitution that makes the spatially transformed Block A equal Block B. Exactly one combination of spatial operation and color mapping will work. Once identified, apply that same spatial operation to Block C, then apply the same color substitution to the result. This produces the output block for that band. Stack all output blocks vertically in order, separated by rows of two dots, to form the complete output grid.

Grid: The input grid is 9 columns wide. Columns 2, 5, and 6 are always dots, serving as separators between the three 2×2 sub-grids. The number of rows equals 3×N−1 where N is the number of bands (each band is 2 rows, with single dot-separator rows between them). The output grid is 2 columns wide and has the same number of rows as the input (same band structure with dot-row separators preserved). The dot (.) represents black and is used only as a separator, never as a meaningful cell color within the 2×2 sub-grids.

Figurative Descriptions (1 variants)

"A spy encrypts messages using a codebook, and you must decode a new message using the same cipher."

qwen3.6-35b: k=1

See: The grid is a series of encrypted transmissions, each on its own frequency band separated by static. Within each band, three sealed envelopes sit side by side: the original message, the encrypted version, and a new message awaiting encryption. Each envelope contains a tiny 2×2 mosaic of colored seals.

Do: For each band, the spymaster has transformed the first envelope into the second using a secret cipher — she may have rotated, flipped, or turned the mosaic, and she may have swapped the ink colors according to a private codebook (red ink becomes blue, blue becomes green, etc.). Your job is to crack the cipher by comparing the original to the encrypted version: figure out how she rearranged the tiles and which colors she substituted. Once you've broken her code, apply the same rotation and the same ink substitutions to the third envelope. That decoded result is your intelligence report for that band. Stack all your decoded reports top to bottom, with static lines preserved between them.

Grid: Each frequency band holds three tiny 2×2 mosaics — the plaintext, the ciphertext, and the target — separated by dead channels of static (dot columns). Bands are stacked vertically with single rows of static between them. Your decoded output is a single column of 2×2 mosaics, one per band, preserving the static separators. The static itself is never part of the message — it's just the silence between transmissions.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (29255 chars)

The user wants me to solve a grid transformation puzzle.

**1. Understand the Goal:**
I need to analyze a set of training examples to deduce a transformation rule. Then, I need to apply this rule to a test input grid to produce an output grid.

**2. Analyze the Input/Output Structure:**
*   **Input Grid:** A large grid containing multiple "bands".
    *   Each band consists of three 2x2 mosaics (envelopes) separated by columns of dots (static).
    *   The bands are separated by rows of dots (static).
    *   The input grid seems to be 9x9 based on the examples, but let's check dimensions.
    *   Example 1 Input:
        ```
        R Y . Y R . . A M
        Y Y . Y Y . . A A
        . . . . . . . . .
        B B . R B . . X X
        R R . R B . . Y Y
        . . . . . . . . .
        G O . A G . . G G
        G G . A A . . G O
        ```
        Dimensions: 8 rows, 9 columns.
        Wait, let's count carefully.
        Row 1: R Y . Y R . . A M (9 chars)
        Row 2: Y Y . Y Y . . A A (9 chars)
        Row 3: . . . . . . . . . (9 chars)
        Row 4: B B . R B . . X X (9 chars)
        Row 5: R R . R B . . Y Y (9 chars)
        Row 6: . . . . . . . . . (9 chars)
        Row 7: G O . A G . . G G (9 chars)
        Row 8: G G . A A . . G O (9 chars)
        Total 8 rows.
    *   Structure:
        *   Band 1: Rows 1-2.
            *   Mosaic 1 (Plaintext): Top-left 2x2.
            *   Separator: Column 3 (dots).
            *   Mosaic 2 (Ciphertext): Top-middle 2x2.
            *   Separator: Columns 5-6 (dots).
            *   Mosaic 3 (Target): Top-right 2x2.
        *   Separator Row: Row 3 (all dots).
        *   Band 2: Rows 4-5.
            *   Mosaic 1: Rows 4-5, Cols 1-2.
            *   Separator: Col 3.
            *   Mosaic 2: Rows 4-5, Cols 4-5.
            *   Separator: Cols 6-7.
            *   Mosaic 3: Rows 4-5, Cols 8-9.
        *   Separator Row: Row 6 (all dots).
        *   Band 3: Rows 7-8.
            *   Mosaic 1: Rows 7-8, Cols 1-2.
            *   Separator: Col 3.
            *   Mosaic 2: Rows 7-8, Cols 4-5.
            *   Separator: Cols 6-7.
            *   Mosaic 3: Rows 7-8, Cols 8-9.

*   **Output Grid:**
    *   Example 1 Output:
        ```
        M A
        A A
        . .
        Y X
        Y X
        . .
        A A
        A G
        ```
        Dimensions: 8 rows, 2 columns.
        Wait, the output description says: "Stack all your decoded reports top to bottom, with static lines preserved between them."
        The decoded report for a band is a 2x2 mosaic.
        So, for 3 bands, we expect 3 * 2 = 6 rows of data.
        Plus separator rows?
        The output has 8 rows.
        Rows 1-2: Decoded Band 1.
        Row 3: Separator (static).
        Rows 4-5: Decoded Band 2.
        Row 6: Separator (static).
        Rows 7-8: Decoded Band 3.
        This matches the structure. The output is a single column of 2x2 mosaics? No, the output is 2 columns wide.
        Wait, "Stack all your decoded

... [26870 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.25)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 705: "Two jousting knights lower their lances and charge, meeting ... [44 chars truncated]" k=3 alts: 1/15 b7249182

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input grid contains exactly two colored pixels on a black background. These two pixels share either the same row or the same column, forming an axis between them. They are separated by some distance D (measured cell-to-cell).

Do: 1. Identify the two colored pixels and the axis (row or column) they share. Call them P1 and P2, where P1 is closer to the top or left edge. Let D be the distance between them along the shared axis. 2. Each pixel grows into an open-ended cross shape directed toward the other pixel: a. From P1, extend an arm along the shared axis toward P2, covering (D-3)/2 cells beyond P1 (not counting P1 itself). Call the endpoint of this arm the crossbar position. b. At the crossbar position, draw a perpendicular crossbar centered on the axis, extending 2 cells in each perpendicular direction (5 cells total including the axis cell). c. From the two ends of the crossbar, extend 1 additional cell toward P2 along the shared axis. These form corner pieces. 3. Repeat symmetrically for P2: extend an arm from P2 toward P1 for (D-3)/2 cells, draw a perpendicular 5-cell crossbar at the arm's end, and extend the crossbar endpoints 1 cell toward P1. 4. This leaves a 2-cell gap between the two shapes along the shared axis. The corner extensions from each crossbar face each other across this gap. 5. Each shape is drawn in the color of its originating pixel. The original pixel positions remain colored as part of their respective arms.

Grid: The grid dimensions match the input exactly. The background is black (.). The two colored pixels are always aligned on the same row or same column, with enough surrounding space for the cross shapes to be drawn without clipping the grid edges.

Figurative Descriptions (16 variants)

"Two jousting knights lower their lances and charge, meeting shield-to-shield in the middle of the field."

qwen3.6-35b: k=3

See: Two lone knights of different colors stand on a dark tournament field, facing each other across a shared lane — either the same row or the same column.

Do: Each knight charges toward the other, dragging their lance along the shared lane. Halfway to meeting, each knight plants a shield — a broad crossbar perpendicular to their charge — and the edges of the shield curl forward like pauldrons reaching toward the opponent. The two knights never collide; they halt with a narrow no-man's-land between their shields, close enough to lock eyes through the gap. Each knight's trail, shield, and pauldrons are forged in that knight's own heraldic color.

Grid: The tournament field keeps its original dimensions. The dark grass remains untouched except where each knight has carved a colored path. The two knights always share the same row or column, and the field is wide enough that no shield or lance stroke flies off the edge.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (36143 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Knights:** Two distinct colored cells in the input grid. They are the "actors".
    *   **Field:** The background grid, mostly empty (black `.`).
    *   **Lane:** The row or column connecting the two knights.
    *   **Lance/Trail:** The path drawn by the knights moving towards each other.
    *   **Shield:** A crossbar perpendicular to the movement direction.
    *   **Pauldrons:** The edges of the shield curling forward.
    *   **No-man's-land:** The gap between the shields.

*   **AFFORDANCES (Capabilities):**
    *   Knights move towards each other along a shared row or column.
    *   They leave a trail (their color) behind them.
    *   They stop before colliding.
    *   They plant a shield (a line of their color) perpendicular to their movement.
    *   The shield has "pauldrons" (extensions) reaching towards the opponent.

*   **TRANSFORMATION RULE (Mapping):**
    *   **Identify Knights:** Find the two non-background cells. Let's call them $K_1$ (color $C_1$) and $K_2$ (color $C_2$).
    *   **Determine Orientation:** Check if they share a row or a column.
        *   If row: Horizontal movement.
        *   If column: Vertical movement.
    *   **Movement & Trail:**
        *   The knights move towards each other.
        *   They leave a trail of their color along the path.
        *   Looking at Example 1:
            *   Input: G at (6, 2) [0-indexed row 6, col 2], B at (6, 12). Wait, let's count carefully.
            *   Input grid size: 11 rows, 13 columns.
            *   Row 6 (7th row): `. G . . . . . . . . . . B`
            *   G is at index 1 (2nd char). B is at index 12 (13th char).
            *   Wait, the string is `. G . . . . . . . . . . B`.
            *   Indices: 0=., 1=G, 2=., 3=., 4=., 5=., 6=., 7=., 8=., 9=., 10=., 11=., 12=B.
            *   So G is at (6, 1), B is at (6, 12).
            *   Output:
                *   Row 4: `... G G B B ...` -> G's at 5,6. B's at 7,8.
                *   Row 5: `... G . . B ...` -> G at 5. B at 8.
                *   Row 6: `G G G G G G . . B B B B B` -> G's at 0-5. B's at 8-12.
                *   Row 7: `... G . . B ...` -> G at 5. B at 8.
                *   Row 8: `... G G B B ...` -> G's at 5,6. B's at 7,8.
            *   Wait, the knights are at (6,1) and (6,12).
            *   The output shows a structure centered around the middle.
            *   Let's check the distance. Distance between 1 and 12 is 11 steps.
            *   Midpoint is roughly 6.5.
            *   The output shows a gap between the shields.
            *   Let's look at the "Shield" shape.
            *   Knight G is on the left. Knight B is on the right.
            *   Knight G moves Right. Knight B moves Left.
            *   Trail: G leaves a trail from (6,1) to the left? No, G is at 1. The trail 

... [33288 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.48)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 716: "A cathedral's stained glass window has been vandalized with ... [94 chars truncated]" k=1 alts: 0/0 b8825c91

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Literal Description

See: The input is a square grid (e.g., 16×16) that exhibits near-perfect 4-fold mirror symmetry — it is symmetric both horizontally (left-right) and vertically (top-bottom), meaning cell(r,c) should equal cell(r, N-1-c), cell(N-1-r, c), and cell(N-1-r, N-1-c) where N is the grid size. However, one or more rectangular patches of yellow (Y) cells have been placed over parts of the grid, breaking the symmetry. These Y patches act as damage or corruption markers, obscuring the true values underneath. All non-Y cells are consistent with the 4-fold symmetry.

Do: For each cell in the grid that contains a Y value, replace it with the correct value by looking up its symmetric counterpart. For a grid of size N×N, cell(r,c) has three mirror partners: cell(r, N-1-c), cell(N-1-r, c), and cell(N-1-r, N-1-c). At least one of these partners will be a non-Y cell holding the true value. Copy that non-Y value into the Y cell. Leave all non-Y cells unchanged. The result is a fully 4-fold symmetric grid with no Y cells remaining.

Grid: The grid is always square (N×N, e.g., 16×16). It uses colors 0-9 (black, blue, red, green, yellow, grey, magenta, orange, azure, maroon). The grid has 4-fold mirror symmetry with the horizontal and vertical axes of symmetry passing through the center. Yellow (Y) is reserved exclusively as the corruption marker and does not appear in the true underlying pattern.

Figurative Descriptions (1 variants)

"A cathedral's stained glass window has been vandalized with yellow paint, but the window's perfect reflections in a still pool below reveal what was lost."

qwen3.6-35b: k=1

See: A grand stained-glass mandala hangs in the nave of a cathedral, its colored panes arranged so that every quarter mirrors every other — look left to see the right, look up to see down, a kaleidoscope frozen in glass. But a vandal has splashed ugly yellow paint across one corner, blotting out the true colors beneath. The paint is crude and obvious — yellow screams against the harmony of the surviving design.

Do: The restorer consults the reflections. Every painted-over pane has a twin — a sibling pane mirrored across the cathedral's central cross-beams. Where yellow paint covers a pane, the restorer peers across the axis to find an untouched twin still showing its true color, then restores the vandalized pane to match. The yellow paint is scraped away and the original hue is returned, until the mandala is whole again and every quarter sings in perfect chorus with the others.

Grid: The mandala is a square arrangement of colored glass panes. Two invisible cross-beams divide it through its exact center — one horizontal, one vertical — creating four quadrants that are perfect reflections of each other. Yellow is not a true color of the design; it is only the vandal's paint. Every other color belongs to the sacred pattern beneath.

qwen3.6-35b — MARC valid, solved with 1 example

Input

→

Prediction

vs

Expected

Reasoning (27425 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **CAST:**
    *   **Grid:** A square grid of characters representing colored glass panes.
    *   **Colors:** Various colors (W, G, R, A, O, B, M, X, etc.) representing the "sacred pattern".
    *   **Yellow (Y):** Represents "vandal's paint" covering the true colors.
    *   **Quadrants:** The grid is divided into four quadrants by a horizontal and a vertical axis passing through the center.
    *   **Reflections:** The quadrants are mirror images of each other. Specifically, the description says "look left to see the right, look up to see down". This implies symmetry. Let's look closer at the description: "every quarter mirrors every other".
    *   **Restorer:** The agent that fixes the grid.

*   **AFFORDANCES:**
    *   **Yellow (Y):** Can be replaced. It's an error state.
    *   **Other Colors:** Represent the "true color" of a pane.
    *   **Symmetry:** The grid has 4-fold symmetry (or at least reflectional symmetry across both axes). If a cell $(r, c)$ has a color $C$, then its reflections across the center lines should also have color $C$, unless covered by yellow.
    *   **Restoration:** If a cell contains 'Y', look at its symmetric counterparts. If a counterpart is not 'Y', use that color to replace 'Y'.

*   **TRANSFORMATION RULE:**
    *   The grid is a square of size $N \times N$.
    *   There is a center point. Since the grid size in the examples is 16x16, the center is between indices 7 and 8 (0-indexed).
    *   The grid exhibits symmetry. Let's verify the type of symmetry.
        *   "look left to see the right" -> Horizontal reflection (Left/Right).
        *   "look up to see down" -> Vertical reflection (Up/Down).
        *   "every quarter mirrors every other" -> This usually implies 4-way symmetry.
    *   Let's check the training examples to confirm the symmetry type.
    *   **Example 1 Analysis:**
        *   Input size: 16x16.
        *   Let's check the top-left quadrant vs top-right.
        *   Row 0: `W G W W R A O A` (Left) vs `A O A R W W G W` (Right).
            *   Left: W G W W R A O A
            *   Right: A O A R W W G W
            *   Reverse of Left: A O A R W W G W. Matches Right. So, horizontal symmetry (Left mirrors Right).
        *   Row 0 vs Row 15 (Bottom).
            *   Row 0: `W G W W R A O A A O A R W W G W`
            *   Row 15: `W G W W R A O A A O A R W W G W`
            *   They are identical. Wait, "look up to see down" usually means vertical reflection. If Row 0 is identical to Row 15, that's vertical reflection if the axis is horizontal. But usually, reflection means $Row[i] == Row[N-1-i]$. Here $Row[0] == Row[15]$.
            *   Let's check Row 1 vs Row 14.
            *   Row 1: `G W W G A A A X X A A A G W W G`
            *   Row 14: `G W Y Y Y Y A X X A A A G W W G` (Input) -> Output: `G W W G A A A X X A A A G W W G`.
            *   Yes, Row 1 matches Row 14.
        

... [24605 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 731: "A lock only turns when the right key fits perfectly into its ... [9 chars truncated]" k=3 alts: 10/15 bbb1b8b6

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Example 5

Input

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Output

Example 6

Input

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Output

Example 7

Input

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Output

Literal Description

See: The input is a 4-row by 9-column grid. A vertical column of grey (X) cells at column index 4 divides the grid into two 4×4 sub-grids: a left grid and a right grid. The left grid contains a pattern of blue (B) cells and black (.) cells. The right grid contains a pattern of a single non-black color (such as red, magenta, orange, or green) and black (.) cells.

Do: 1. Split the input along the grey (X) column to extract the left 4×4 grid and the right 4×4 grid. 2. Identify all positions that are black (.) in the left grid — these are the 'empty slots.' 3. Identify all positions occupied by the colored (non-black) cells in the right grid. 4. Compare the two sets of positions. If they are exactly equal (same positions, same count), replace every black cell in the left grid with the color from the right grid and output the result. 5. If the positions do NOT exactly match, output the left grid unchanged.

Grid: The input grid is always 4 rows by 9 columns. Column 4 is always grey (X) and serves as a separator. The output grid is always 4×4. The left sub-grid uses only blue (B) and black (.), and the right sub-grid uses only one non-black, non-blue color and black (.). The output grid uses at most two colors: blue and either black or the color from the right grid.

Figurative Descriptions (16 variants)

"A lock only turns when the right key fits perfectly into its grooves."

qwen3.6-35b: k=3

See: A grey wall divides two rooms. On the left, a blue vault door has gaps cut into it — empty keyholes waiting. On the right, a colored key floats in darkness, its teeth shaped from a single vivid color.

Do: Slide the key into the lock. If every tooth fits perfectly into every keyhole — no extra teeth, no empty holes left over — the key merges with the vault door, filling each gap with its color. If the key doesn't match the lock, the vault stays sealed and unchanged, its empty keyholes still dark.

Grid: The grey wall always stands in the center, separating lock from key. The vault door is always built from blue steel and dark gaps. The key is always carved from a single color. What emerges is either a door transformed — blue and the key's color fused together — or the same cold, unturned lock.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

→

Prediction

vs

Expected

Reasoning (32246 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Visuals:** A grey wall (X) divides two rooms.
    *   Left room: Blue vault door (B) with gaps (empty keyholes).
    *   Right room: A colored key (single vivid color) floating.
*   **Action:** Slide the key into the lock.
*   **Condition:** If every tooth fits perfectly into every keyhole (no extra teeth, no empty holes), the key merges with the door.
    *   Result: The gaps (empty keyholes) are filled with the key's color.
*   **Failure Condition:** If the key doesn't match (extra teeth or empty holes), the vault stays sealed (unchanged).
*   **Grid Details:**
    *   Grey wall (X) is in the center.
    *   Vault door is Blue (B) with dark gaps (likely `.` or empty space, but looking at examples, the gaps are represented by `.` inside the B structure).
    *   Key is a single color.

**2. Analyze Training Examples:**

*   **Example 1:**
    *   Input:
        ```
        B B B B X . . . .
        B . . B X . M M .
        B . . B X . M M .
        B B B B X . . . .
        ```
    *   Structure:
        *   Left side (4x4): A blue square frame `B B B B` / `B . . B` / `B . . B` / `B B B B`. The inner part is `.` (black/dark).
        *   Divider: `X` column.
        *   Right side (4x3): A block of Magenta `M`. Specifically, `M M` in rows 2 and 3.
    *   Output:
        ```
        B B B B
        B M M B
        B M M B
        B B B B
        ```
    *   Observation: The key (M) fits into the gaps (.) of the lock. The output is the left side (the lock) where the `.` cells have been replaced by `M`. The right side and the wall are removed.
    *   Wait, let's look closer at the "fit".
        *   Lock gaps: (1,1), (1,2), (2,1), (2,2) (0-indexed relative to the 4x4 block). Actually, looking at the input:
            Row 0: B B B B
            Row 1: B . . B
            Row 2: B . . B
            Row 3: B B B B
            The gaps are at (1,1), (1,2), (2,1), (2,2).
        *   Key shape:
            Row 0: . . . (empty)
            Row 1: . M M
            Row 2: . M M
            Row 3: . . .
            Wait, the input grid is 4 rows x 9 columns.
            Left block: 4x4. Right block: 4x4 (since X is at index 4, indices 5-8 are 4 cols).
            Let's re-read the input grid for Ex 1 carefully.
            `B B B B X . . . .` -> Row 0. Left: B B B B. Wall: X. Right: . . . .
            `B . . B X . M M .` -> Row 1. Left: B . . B. Wall: X. Right: . M M .
            `B . . B X . M M .` -> Row 2. Left: B . . B. Wall: X. Right: . M M .
            `B B B B X . . . .` -> Row 3. Left: B B B B. Wall: X. Right: . . . .
            
            The "Key" is the non-black/non-blue/non-wall part on the right?
            The key is Magenta (M). It occupies positions (1, 6), (1, 7), (2, 6), (2, 7) in the full grid.
            Relative to the right block (cols 5-8), it's 

... [29405 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 733: "Two distant shores reflected in a shrinking lake, merging as ... [23 chars truncated]" k=1 alts: 1/15 bc1d5164

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Example 5

Input

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Output

Literal Description

See: The input is a 5-row by 7-column grid with a single non-black color. Colored cells appear only in the two leftmost columns (0 and 1) and the two rightmost columns (5 and 6). The middle three columns (2, 3, 4) are always black. The grid has a vertical axis of symmetry in its structure: the left pair of columns (0–1) and the right pair (5–6) encode two overlapping copies of a 3-column pattern, sharing their inner columns (1 and 5). Row 2 (the middle row) is always entirely black, creating a similar horizontal split: rows 0, 1 and rows 3, 4 encode two overlapping copies of a 3-row pattern sharing their inner rows (1–3).

Do: Produce a 3×3 output grid by combining the left and right column pairs and compressing the five rows into three, using an OR-merge (a cell is colored if either of its source cells is colored, otherwise black): 1. Output column 0 comes from input column 0. 2. Output column 1 is the OR-merge of input column 1 and input column 5 (colored if either is colored). 3. Output column 2 comes from input column 6. For rows: 1. Output row 0 comes from input row 0. 2. Output row 1 is the OR-merge of input rows 1, 2, and 3 (colored if any of those rows has a colored cell in that column). 3. Output row 2 comes from input row 4. Apply both column and row mappings simultaneously to determine each of the 9 output cells.

Grid: The input grid is always 5 rows by 7 columns. The background is black (.). Exactly one non-black color is used per puzzle. Columns 2, 3, and 4 are always entirely black, serving as a separator between the left column pair (0–1) and the right column pair (5–6). The output grid is always 3 rows by 3 columns, using the same single color on a black background.

Figurative Descriptions (16 variants)

"Two distant shores reflected in a shrinking lake, merging as the water drains away."

qwen3.6-35b: k=1

See: A wide landscape stretches across seven columns, but the heart of it—three columns in the center—is nothing but still, dark water. Life clings only to the narrow shores on the far left and far right, two columns wide on each side. A similar emptiness runs through the middle row, a quiet channel dividing north from south. The colored marks are like campfires lit on these shores, mirrored signals calling to each other across the void.

Do: The dark water evaporates and the land folds inward like a closing book. The left shore and the right shore slide together until they overlap, their inner edges merging into a single shared column. Where either shore had a campfire burning, the merged land keeps the flame—darkness only wins where both sides were dark. The same folding happens vertically: the northern and southern banks collapse toward the center channel, and wherever any of those middle rows carried a signal, the fire persists in the compressed land.

Grid: The wide world is five rows by seven columns, with a single color of campfire against the black night. The three central columns are always empty water. After the fold, only a small three-by-three island remains—the essence of both shores unified, fires combined, darkness only where silence reigned on every side.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (31878 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Input and Output Grids (Training Examples):**

*   **Input Grid Size:** 5 rows x 7 columns.
*   **Output Grid Size:** 3 rows x 3 columns.
*   **Color Key:** `.` is black (empty), `B` is blue, `R` is red, `G` is green, `Y` is yellow, `X` is grey, `M` is magenta, `O` is orange, `A` is azure, `W` is maroon.

**Example 1 Analysis:**
Input:
```
Y . . . . . Y
. . . . . . .
. . . . . . .
. . . . . . .
Y . . . . Y Y
```
Output:
```
Y . Y
. . .
Y Y Y
```

Let's look at the structure described in the text.
"The wide landscape stretches across seven columns... three columns in the center... is nothing but still, dark water."
Columns 0, 1, 2, 3, 4, 5, 6.
Center columns are 2, 3, 4? Or 1, 2, 3?
Text says: "Life clings only to the narrow shores on the far left and far right, two columns wide on each side."
If width is 7, and center is 3 columns, then 7 - 3 = 4 columns left. 4 / 2 = 2 columns per side.
So, Left Shore = Columns 0, 1. Center Water = Columns 2, 3, 4. Right Shore = Columns 5, 6.
Let's check the input grid for Example 1.
Row 0: `Y . . . . . Y` -> Col 0 is Y, Col 1 is ., Col 5 is ., Col 6 is Y.
Row 4: `Y . . . . Y Y` -> Col 0 is Y, Col 1 is ., Col 5 is Y, Col 6 is Y.
Rows 1, 2, 3 are all empty.

Wait, the text says "The three central columns are always empty water."
In Example 1 input:
Row 0: `Y . . . . . Y` -> Cols 2,3,4 are `.`. Correct.
Row 4: `Y . . . . Y Y` -> Cols 2,3,4 are `.`. Correct.
So the "water" is indeed columns 2, 3, 4.
The "shores" are columns 0, 1 (Left) and 5, 6 (Right).

Text says: "The left shore and the right shore slide together until they overlap, their inner edges merging into a single shared column."
Left Shore: Cols 0, 1.
Right Shore: Cols 5, 6.
Inner edges are Col 1 (Left) and Col 5 (Right).
They merge into a single column.
Wait, "overlap" usually implies superposition.
"Where either shore had a campfire burning, the merged land keeps the flame—darkness only wins where both sides were dark."
This sounds like a logical OR operation. If Left has color or Right has color, result has color. If both are empty, result is empty.

Let's look at the vertical folding.
"A similar emptiness runs through the middle row... dividing north from south."
Height is 5 rows. Middle row is Row 2 (index 2).
Top bank: Rows 0, 1.
Bottom bank: Rows 3, 4.
"Northern and southern banks collapse toward the center channel... wherever any of those middle rows carried a signal, the fire persists in the compressed land."
Wait, "middle rows" (plural) or "middle row" (singular)?
Text: "A similar emptiness runs through the middle row". Singular.
But then: "The same folding happens vertically: the northern and southern banks collapse toward the center channel, and wherever any of those middle rows carried a signal..."
This phrasing is slightly confusing. "Middle rows" might refer to the rows adjacent to the cente

... [28992 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.22)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 755: "The majority party prints its banner wherever it holds a sea ... [2 chars truncated]" k=1 alts: 0/0 c3e719e8

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input is a 3×3 grid containing cells of various colors. One color appears more frequently than all others — this is the dominant color. The positions of cells containing this dominant color form a pattern within the 3×3 grid.

Do: 1. Count the occurrences of each color in the 3×3 input grid and identify the most frequent color (the dominant color). 2. Create a 9×9 output grid filled entirely with black (.) cells, conceptually divided into a 3×3 arrangement of 3×3 blocks. 3. For each cell in the original 3×3 input that contains the dominant color, place a complete copy of the entire input grid into the corresponding 3×3 block of the output. The block at meta-row r, meta-column c corresponds to input cell (r, c). 4. All blocks corresponding to input cells that do NOT contain the dominant color remain filled with black (.).

Grid: The input is always a 3×3 grid with colors from the ARC palette (values 0–9). The output is a 9×9 grid, structured as a 3×3 meta-grid of 3×3 blocks. Each block is either a full copy of the input or an all-black (.) 3×3 block. The background (empty block) color is black (.).

Figurative Descriptions (1 variants)

"The majority party prints its banner wherever it holds a seat."

qwen3.6-35b: k=1

See: A small 3×3 parliament of colored delegates sits in session. One faction holds more seats than any rival — they are the ruling party, and their influence radiates outward.

Do: The ruling party calls for expansion. A grand 9×9 hall is built — a 3×3 arrangement of chambers, each the size of the original parliament. Every seat held by the ruling party becomes a portal: the entire parliament is cloned into the corresponding chamber, delegates and all. Chambers aligned with minority seats remain dark and empty — no representation, no presence. The ruling party reproduces itself everywhere it already exists; the minority vanishes into silence.

Grid: The original parliament is a 3×3 grid of colored delegates. The grand hall is 9×9 — nine chambers in a 3×3 layout. Each chamber is either a faithful reproduction of the full parliament or a darkened, empty room (all black). The darkness is the color of absence.

qwen3.6-35b — MARC valid, solved with 1 example

Input

→

Prediction

vs

Expected

Reasoning (30366 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Input and Output Grids:**

*   **Input Grid:** 3x3
*   **Output Grid:** 9x9

**2. Analyze the Metaphorical Description:**

*   **Input:** "A small 3×3 parliament of colored delegates". This matches the input grid size.
*   **Ruling Party:** "One faction holds more seats than any rival". This implies I need to count the occurrences of each color in the 3x3 input grid to find the most frequent color.
*   **Expansion:** "A grand 9×9 hall is built — a 3×3 arrangement of chambers, each the size of the original parliament." This means the output is a 3x3 grid of 3x3 blocks.
*   **Portal/Cloning:** "Every seat held by the ruling party becomes a portal: the entire parliament is cloned into the corresponding chamber".
    *   If a cell in the input grid contains the "ruling party" color, the corresponding 3x3 block in the output grid should be a copy of the original input grid.
*   **Minority Seats:** "Chambers aligned with minority seats remain dark and empty — no representation, no presence."
    *   If a cell in the input grid contains a color that is *not* the ruling party color, the corresponding 3x3 block in the output grid should be filled with the "darkness" color, which is defined as `.` (black).
*   **Ruling Party Reproduction:** "The ruling party reproduces itself everywhere it already exists". This is consistent with the cloning rule.
*   **Minority Vanishing:** "The minority vanishes into silence". Consistent with filling with `.`.

**3. Analyze the Training Examples:**

*   **Example 1 Input:**
    ```
    A M A
    G G A
    A A A
    ```
    *   Colors: A, M, G.
    *   Counts:
        *   A: 1 (0,0) + 1 (0,2) + 1 (1,2) + 1 (2,0) + 1 (2,1) + 1 (2,2) = 6.
        *   M: 1 (0,1) = 1.
        *   G: 1 (1,0) + 1 (1,1) = 2.
    *   Ruling Party: **A** (Azure).
    *   Minority: M, G.

*   **Example 1 Output:**
    ```
    A M A . . . A M A
    G G A . . . G G A
    A A A . . . A A A
    . . . . . . A M A
    . . . . . . G G A
    . . . . . . A A A
    A M A A M A A M A
    G G A G G A G G A
    A A A A A A A A A
    ```
    Let's check the structure. It's a 3x3 grid of 3x3 blocks.
    *   **Block (0,0)** [Top-Left]: Corresponds to input cell (0,0) which is 'A'. Since 'A' is the ruling party, this block should be the full input grid.
        *   Input grid:
            A M A
            G G A
            A A A
        *   Block (0,0) in output:
            A M A
            G G A
            A A A
        *   Matches.
    *   **Block (0,1)** [Top-Middle]: Corresponds to input cell (0,1) which is 'M'. 'M' is not 'A'. So this block should be all `.`.
        *   Output shows:
            . . .
            . . .
            . . .
        *   Matches.
    *   **Block (0,2)** [Top-Right]: Corresponds to input cell (0,2) which is 'A'. Ruling party. Copy input grid.
        *   Output shows:
   

... [27769 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.01)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 759: "Three neighboring kingdoms trade their national dyes across ... [12 chars truncated]" k=1 alts: 0/0 c4d1a9ae

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Literal Description

See: The input grid has a uniform background color (the most frequent color) with three groups of columns containing signal patterns. Each group is defined by having one distinct non-background color forming a pattern against the background. The groups are separated by columns that contain only the background color (separator columns). For example, Group 1 might occupy columns 0-1 with signal color M on background X, Group 2 columns 3-4 with signal color W on background X, and Group 3 columns 6-7 with signal color A on background X, with columns 2 and 5 serving as separators (all background color).

Do: 1. Identify the background color (the most frequent color in the grid). 2. Identify the separator columns — columns composed entirely of the background color. These divide the grid into three column-groups. 3. Within each group, identify the signal color (the single non-background color present in that group). Call these S1, S2, S3 for Groups 1, 2, 3 respectively. 4. Replace background cells in each group with a cyclic rotation of the other groups' signal colors: in Group 1, replace every background cell with S2 (Group 2's signal color); in Group 2, replace every background cell with S3 (Group 3's signal color); in Group 3, replace every background cell with S1 (Group 1's signal color). 5. Leave all signal-color cells and separator columns unchanged.

Grid: The grid is rectangular (typically 10 rows by 8 columns). It is partitioned into exactly three column-groups by separator columns that contain only the background color. Each group contains exactly one signal color besides the background. The separator columns remain unchanged in the output. The output grid has the same dimensions as the input.

Figurative Descriptions (1 variants)

"Three neighboring kingdoms trade their national dyes across the borders."

qwen3.6-35b: k=1

See: The grid is a continent divided into three kingdoms by rivers of neutral earth. Each kingdom flies a single banner color against the common soil. The rivers (pure earth-colored columns) mark where one realm ends and the next begins.

Do: Each kingdom grows envious of a neighbor's banner and dyes all its bare soil in tribute. The tribute follows a round-robin exchange: the first kingdom paints its earth with the second kingdom's color, the second borrows from the third, and the third from the first — a closed circle of cultural exchange. The banners themselves remain untouched, proud and unchanged. The rivers between them flow on, indifferent to the commerce of color.

Grid: The continent is a rectangular realm split into exactly three kingdoms by one-column-wide rivers of the land's most common color. Each kingdom bears exactly one banner color woven among the earth. After the exchange, every patch of bare earth within a kingdom takes on the hue of the next kingdom's banner, while the banners and rivers stand unchanged.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (31290 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Input and Output Grids (Training Examples)**

Let's look at Example 1.
Input Grid (10x8):
Row 0: Y R Y Y M Y X X
Row 1: R Y Y Y M Y Y X
Row 2: Y R Y Y M Y X X
Row 3: R Y Y M Y Y Y X
Row 4: Y R Y M Y Y X X
Row 5: R Y Y M Y Y Y X
Row 6: Y R Y M Y Y X X
Row 7: R Y Y Y M Y Y X
Row 8: Y R Y Y M Y X X
Row 9: R Y Y Y M Y Y X

Output Grid (10x8):
Row 0: M R Y X M Y X X
Row 1: R M Y X M Y R X
Row 2: M R Y X M Y X X
Row 3: R M Y M X Y R X
Row 4: M R Y M X Y X X
Row 5: R M Y M X Y R X
Row 6: M R Y M X Y X X
Row 7: R M Y X M Y R X
Row 8: M R Y X M Y X X
Row 9: R M Y X M Y R X

**2. Conceptual Digestion**

**1. Identify the CAST:**
*   **Rivers:** The description mentions "rivers of neutral earth" and "one-column-wide rivers of the land's most common color". Looking at the input, column 4 (0-indexed) seems to be a vertical line of 'M's? No, wait.
    Let's check the columns in Input 1.
    Col 0: Y, R, Y, R, Y, R, Y, R, Y, R (Alternating Y/R)
    Col 1: R, Y, R, Y, R, Y, R, Y, R, Y (Alternating R/Y)
    Col 2: Y, Y, Y, Y, Y, Y, Y, Y, Y, Y (All Y)
    Col 3: Y, Y, Y, M, M, M, M, Y, Y, Y (Mixed)
    Col 4: M, M, M, Y, Y, Y, Y, M, M, M (Mixed)
    Col 5: Y, Y, Y, Y, Y, Y, Y, Y, Y, Y (All Y)
    Col 6: X, Y, X, Y, X, Y, X, Y, X, Y (Alternating X/Y)
    Col 7: X, X, X, X, X, X, X, X, X, X (All X)

    Wait, the description says "rivers of neutral earth" and "one-column-wide rivers".
    Let's look at the colors.
    Colors present: Y (yellow), R (red), M (magenta), X (grey).
    The description says "rivers of neutral earth". In the key, X is grey. Grey is often neutral.
    Let's look for columns that are entirely X (grey).
    In Input 1, Col 7 is all X.
    Is there another river? The text says "divided into three kingdoms by rivers". This implies two rivers separating three regions.
    Let's look at the structure again.
    Maybe the rivers are vertical lines of a specific color.
    In Input 1, Col 7 is all X.
    Is there another column of X?
    Col 6 has Xs but also Ys.
    Col 4 has Ms and Ys.
    Col 3 has Ys and Ms.
    Col 2 is all Y.
    Col 5 is all Y.

    Let's re-read the description carefully.
    "The grid is a continent divided into three kingdoms by rivers of neutral earth."
    "The rivers (pure earth-colored columns) mark where one realm ends and the next begins."
    "The rivers between them flow on, indifferent to the commerce of color." -> Rivers are unchanged.

    Let's look at the Output 1.
    Col 7 is still all X.
    Col 6 is X, Y, X, Y, X, Y, X, Y, X, Y. Wait, in output, Col 6 is X, Y, X, Y, X, Y, X, Y, X, Y.
    Wait, let's check Output 1 Col 6.
    Row 0: X
    Row 1: Y
    Row 2: X
    Row 3: Y
    Row 4: X
    Row 5: Y
    Row 6: X
    Row 7: Y
    Row 8: X
    Row 9: Y
    It's alternating.
    Wait, in Input 1, Col 6 was X, Y, X, Y, X, Y, X, Y, X, Y.
    So Col 6 didn't change?
    Let's che

... [28635 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.06)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 790: "A mirror lake reveals which stars have true reflections" k=1 alts: 0/0 ce039d91

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Literal Description

See: The input is a grid with a black (.) background containing grey (X) cells scattered across it. Some grey cells form vertically symmetric pairs — that is, for a given row, a grey cell at column c has a corresponding grey cell at column (width-1-c), mirrored across the vertical center axis of the grid. Other grey cells are isolated, lacking a mirror partner in their row.

Do: For each row, examine every grey (X) cell at column c. Check whether there is also a grey cell at column (width-1-c) in the same row. If both mirror positions contain grey cells, recolor both to blue (B). If a grey cell has no mirror partner in its row, leave it as grey (X). All black background cells remain unchanged.

Grid: The grid is 10x10 with a black (.) background. The vertical axis of symmetry runs between columns 4 and 5 (at position 4.5). Only grey (X) cells appear in the input; the output contains grey (X) and blue (B) cells on the same black background.

Figurative Descriptions (1 variants)

"A mirror lake reveals which stars have true reflections"

qwen3.6-35b: k=1

See: A still lake at night (the black expanse) reflects scattered stars (grey cells). Some stars hang in pairs across the water's center line — each one gazing at its twin on the opposite shore. Other stars shine alone, with no reflection to answer them.

Do: When a star finds its twin reflected perfectly across the lake's center, both ignite with blue fire — recognized, validated, made luminous by their symmetry. Stars that peer into the water and see only darkness remain dim and grey, forever unreflected.

Grid: The lake stretches 10 paces wide and 10 deep. An invisible seam runs down its exact center, the line where reality meets reflection. Only stars (grey) dot the sky at first; after the lake works its magic, the paired ones glow blue while the loners keep their grey solitude.

qwen3.6-35b — MARC valid, solved with 1 example

Input

→

Prediction

vs

Expected

Reasoning (24741 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **CAST:**
    *   **Black (.)**: The background, the "lake".
    *   **Grey (X)**: The "stars" in the sky.
    *   **Blue (B)**: The "blue fire" or "luminous" state of a star.
*   **AFFORDANCES:**
    *   Stars (X) can be paired.
    *   The grid has a center line (vertical axis of symmetry).
    *   Stars can "see" their reflection across this center line.
*   **TRANSFORMATION RULE:**
    *   The grid is 10x10.
    *   The "center line" is the vertical line between column 4 and column 5 (0-indexed: 0,1,2,3 | 4,5,6,7,8,9). Wait, 10 columns means indices 0 to 9. The center is between index 4 and 5.
    *   Let's check the symmetry. If a star is at $(r, c)$, its reflection across the vertical center line would be at $(r, 9-c)$.
    *   If a star exists at $(r, c)$ AND a star exists at $(r, 9-c)$, then *both* stars turn Blue (B).
    *   If a star exists at $(r, c)$ but there is no star at $(r, 9-c)$, it remains Grey (X).
    *   Wait, let's re-read the description carefully. "Some stars hang in pairs across the water's center line — each one gazing at its twin on the opposite shore." "When a star finds its twin reflected perfectly across the lake's center, both ignite with blue fire".
    *   This implies a horizontal reflection? No, "across the water's center line" usually implies a vertical axis if the lake is horizontal, or a horizontal axis if the lake is vertical.
    *   Let's look at the grid dimensions: 10 wide, 10 deep.
    *   "Invisible seam runs down its exact center". If it's a lake, usually the horizon is horizontal. But "down its exact center" suggests a vertical line splitting left and right.
    *   Let's check the training examples to confirm the axis of symmetry.

**2. Analyzing Training Examples**

*   **Example 1 Input:**
    Row 0: `. . . . . X . . . .` -> X at index 5. Reflection index: 9-5 = 4. Is there an X at index 4? No. So X at (0,5) should stay X?
    Output Row 0: `. . . . . X . . . .` -> Yes, it stays X.
    Wait, let's look at Row 1.
    Input Row 1: `. X . . . . . . X X` -> X at 1, 8, 9.
    Reflections:
    - X at 1 -> reflection at 8. Is there an X at 8? Yes.
    - X at 8 -> reflection at 1. Is there an X at 1? Yes.
    - X at 9 -> reflection at 0. Is there an X at 0? No.
    Output Row 1: `. B . . . . . . B X`
    - X at 1 became B.
    - X at 8 became B.
    - X at 9 stayed X.
    This confirms the rule: **Vertical symmetry across the center line.**
    The center line is between column 4 and 5.
    Pairs are $(c, 9-c)$.
    If Input[r][c] == 'X' AND Input[r][9-c] == 'X', then Output[r][c] = 'B' and Output[r][9-c] = 'B'.
    Otherwise, if Input[r][c] == 'X', Output[r][c] = 'X'.
    If Input[r][c] == '.', Output[r][c] = '.'.

    Let's check Row 2.
    Input: `. . . X X X X . . .` -> X at 3, 4, 5, 6.
    Pairs:
    - 3 <-> 6. Both X. -> Both become B.
    - 4 <-> 5. Both X. -> Bo

... [22857 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.62)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 795: "Trees sink their roots into underground water" k=2 alts: 0/0 ce9e57f2

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input grid has a black background with several vertical bars (columns) made of red (R) cells. Each bar is exactly one cell wide and bars are separated by empty columns. The bars have varying heights — they all grow upward from near the bottom of the grid but start at different rows, so some bars are taller than others.

Do: For each vertical bar of red cells, count its height (number of contiguous R cells in that column). Compute floor(height / 2). Recolor that many cells at the bottom of the bar from red (R) to azure (A). The top portion of each bar remains red. For example, a bar of height 7 has its bottom 3 cells turned to azure while the top 4 stay red; a bar of height 2 has its bottom 1 cell turned to azure.

Grid: The grid dimensions vary but the background is always black (.). Vertical red bars occupy specific columns, each one cell wide, separated by at least one empty column. The grid is wide enough to contain all bars with spacing between them.

Figurative Descriptions (1 variants)

"Trees sink their roots into underground water"

qwen3.6-35b: k=2

See: A dark field stands quiet under a night sky. Rising from the earth are slender red saplings of different ages — some tall and ancient, others young and short. Each tree is a single trunk, perfectly straight, growing upward from the ground with no branches.

Do: As each tree matures, its roots push deeper into the water table below. The deeper half of every trunk — the portion hidden beneath the soil line — transforms from woody red to the cool azure of subterranean water. The taller and older the tree, the deeper its roots reach. A sapling barely sprouted has only begun to taste the water; a towering elder is steeped halfway in blue.

Grid: The night sky and open ground are black (.). Each tree trunk is a vertical column of red (R) cells, one cell wide, rooted at the bottom. When the water rises through a trunk, those lower cells become azure (A) while the canopy above stays red.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (29325 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   `.` (black): Background (sky/ground).
    *   `R` (red): Tree trunks. Vertical columns of red cells.
    *   `A` (azure): The transformed state of the lower part of the tree trunks.

*   **AFFORDANCES (Properties/Actions):**
    *   Trees are vertical columns of `R` cells.
    *   Trees are rooted at the bottom of the grid (or at least, the description implies they grow upwards from the bottom).
    *   Trees have a height (number of `R` cells).
    *   Transformation: The lower half of the tree turns into `A` (azure).

*   **TRANSFORMATION RULE:**
    *   Identify each vertical column of `R` cells.
    *   Determine the height of the column (count of `R`s).
    *   Calculate the "water line" or the point where the transformation happens.
    *   The description says: "The deeper half of every trunk... transforms from woody red to the cool azure".
    *   "The taller and older the tree, the deeper its roots reach. A sapling barely sprouted has only begun to taste the water; a towering elder is steeped halfway in blue."
    *   Wait, let's look closer at the examples to confirm the "halfway" rule.

**2. Analyzing Training Examples**

*   **Example 1:**
    *   Input Grid (8 rows, 9 cols):
        Row 0: `.` `.` `.` `.` `.` `.` `.` `.` `.`
        Row 1: `.` `R` `.` `.` `.` `.` `.` `.` `.`
        Row 2: `.` `R` `.` `.` `.` `.` `.` `R` `.`
        Row 3: `.` `R` `.` `R` `.` `.` `.` `R` `.`
        Row 4: `.` `R` `.` `R` `.` `.` `.` `R` `.`
        Row 5: `.` `R` `.` `R` `.` `R` `.` `R` `.`
        Row 6: `.` `R` `.` `R` `.` `R` `.` `R` `.`
        Row 7: `.` `R` `.` `R` `.` `R` `.` `R` `.`
    *   Let's check the columns of `R`s.
        *   Col 1: Rows 1-7. Height = 7.
        *   Col 3: Rows 3-7. Height = 5.
        *   Col 5: Rows 5-7. Height = 3.
        *   Col 7: Rows 2-7. Height = 6.
    *   Output Grid:
        Row 0: `.` `.` `.` `.` `.` `.` `.` `.` `.`
        Row 1: `.` `R` `.` `.` `.` `.` `.` `.` `.`
        Row 2: `.` `R` `.` `.` `.` `.` `.` `R` `.`
        Row 3: `.` `R` `.` `R` `.` `.` `.` `R` `.`
        Row 4: `.` `R` `.` `R` `.` `.` `.` `R` `.`
        Row 5: `. A` `.` `R` `.` `R` `.` `A` `.`  <- Wait, let's look at the output text carefully.
        Output Row 5: `. A . R . R . A .`
        Output Row 6: `. A . A . R . A .`
        Output Row 7: `. A . A . A . A .`

    *   Let's re-examine the columns in the output.
        *   Col 1 (Height 7):
            *   Input R's at rows 1, 2, 3, 4, 5, 6, 7.
            *   Output R's at rows 1, 2, 3, 4.
            *   Output A's at rows 5, 6, 7.
            *   Wait, row 5 is index 5. Total rows 0-7.
            *   Indices: 1, 2, 3, 4 are R. Indices 5, 6, 7 are A.
            *   Count of R's = 4. Count of A's = 3.
            *   Total height = 7.
            *   "Deeper half" -> Bottom half.
            * 

... [26439 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.64)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 797: "A seed crystal grows reflections in a hall of four mirrors." k=2 alts: 0/0 cf5fd0ad

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Literal Description

See: The input is a 3×3 grid with azure (A) as the background color and one or more non-background colored cells placed at various positions.

Do: 1. Compute four rotations of the 3×3 input grid: (a) 180° rotation, (b) 90° clockwise rotation, (c) 90° counter-clockwise rotation, (d) the original unrotated grid. 2. Construct a 12×12 output grid divided into four 6×6 quadrants arranged in a 2×2 layout. 3. Fill the top-left quadrant (rows 0-5, columns 0-5) by tiling the 180° rotation in a 2×2 arrangement (the 3×3 block repeated twice across and twice down). 4. Fill the top-right quadrant (rows 0-5, columns 6-11) by tiling the 90° clockwise rotation in the same 2×2 arrangement. 5. Fill the bottom-left quadrant (rows 6-11, columns 0-5) by tiling the 90° counter-clockwise rotation in a 2×2 arrangement. 6. Fill the bottom-right quadrant (rows 6-11, columns 6-11) by tiling the original input in a 2×2 arrangement.

Grid: The input grid is always 3×3. The output grid is always 12×12, composed of a 2×2 arrangement of quadrants, each quadrant being a 2×2 tiling of a 3×3 block (one of the four rotations of the input). The background color is azure (A).

Figurative Descriptions (1 variants)

"A seed crystal grows reflections in a hall of four mirrors."

qwen3.6-35b: k=2

See: A tiny 3×3 tile floats in an azure void — a seed crystal carrying a few colored impurities frozen in its lattice.

Do: The crystal is placed at the center of a hall where four great mirrors face inward from each corner. Each mirror catches the crystal at a different angle — one flips it completely on its head, one spins it a quarter-turn clockwise, one a quarter-turn the other way, and the last shows it true. Each reflection then echoes, stamping itself twice across and twice down to wallpaper its own quadrant of the hall floor. The top-left corner belongs to the fully inverted reflection, the top-right to the clockwise turn, the bottom-left to the counter-clockwise turn, and the bottom-right to the faithful original.

Grid: The seed is always a 3×3 crystal. The hall floor is a 12×12 mosaic — four quadrants, each paved by its own reflected wallpaper pattern of the seed repeated in a 2×2 patch. Azure is the empty space between impurities.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (27991 chars)

The user wants me to solve a grid transformation puzzle.

**1. Analyze the Input and Output format:**
- Input: A 3x3 grid of characters representing colors.
- Output: A 12x12 grid of characters representing colors.
- Color Key: .=black, B=blue, R=red, G=green, Y=yellow, X=grey, M=magenta, O=orange, A=azure, W=maroon.

**2. Analyze the Metaphorical Description:**
- **Input:** "A tiny 3×3 tile floats in an azure void — a seed crystal carrying a few colored impurities frozen in its lattice." -> This is the 3x3 input grid.
- **Output Structure:** "The hall floor is a 12×12 mosaic — four quadrants, each paved by its own reflected wallpaper pattern of the seed repeated in a 2×2 patch." -> The output is a 12x12 grid. It is divided into four 6x6 quadrants.
- **Quadrants:**
    - Top-Left (TL): "fully inverted reflection" (flips it completely on its head).
    - Top-Right (TR): "spins it a quarter-turn clockwise".
    - Bottom-Left (BL): "quarter-turn the other way" (counter-clockwise).
    - Bottom-Right (BR): "faithful original".
- **Pattern within Quadrants:** "Each reflection then echoes, stamping itself twice across and twice down to wallpaper its own quadrant of the hall floor." -> Each quadrant is a 6x6 area. The "seed" (3x3) is repeated in a 2x2 pattern to fill the 6x6 quadrant.
    - Wait, let's check the dimensions.
    - Input is 3x3.
    - Output is 12x12.
    - 12x12 divided into 4 quadrants means each quadrant is 6x6.
    - If the seed is 3x3, repeating it 2x2 (2 times across, 2 times down) creates a 6x6 block.
    - So, each quadrant is a 6x6 block formed by tiling the transformed 3x3 seed 2 times horizontally and 2 times vertically.

**3. Analyze the Transformations:**
Let the input 3x3 grid be $S$.
$S = \begin{pmatrix} s_{00} & s_{01} & s_{02} \\ s_{10} & s_{11} & s_{12} \\ s_{20} & s_{21} & s_{22} \end{pmatrix}$

- **Top-Right (TR) Quadrant:** "faithful original".
    - The pattern is $S$ repeated 2x2.
    - Top-left of TR quadrant (at grid coords [0,6]) is $s_{00}$.
    - The 6x6 block looks like:
      $S$ $S$
      $S$ $S$
    - Wait, let's verify the order of quadrants.
    - "The top-left corner belongs to the fully inverted reflection" -> TL quadrant.
    - "the top-right to the clockwise turn" -> TR quadrant.
    - "the bottom-left to the counter-clockwise turn" -> BL quadrant.
    - "the bottom-right to the faithful original" -> BR quadrant.

    Let's re-read carefully: "The top-left corner belongs to the fully inverted reflection, the top-right to the clockwise turn, the bottom-left to the counter-clockwise turn, and the bottom-right to the faithful original."
    Wait, usually "top-left" refers to the top-left quadrant of the output grid.
    Let's check the training examples to confirm the mapping.

**4. Analyze Training Examples:**

**Example 1:**
Input:
A O A
O A A
A X B

Let's denote the input grid $I$.
$I = \begin{pmatrix} A & O & A \\ O &

... [25792 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.44)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 817: "A strand of holiday lights where every other bulb switches o ... [9 chars truncated]" k=2 alts: 12/15 d406998b

Training Examples

Example 1

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Output

Example 2

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Example 3

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Example 4

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Output

Literal Description

See: A grid with exactly 3 rows. Each column contains exactly one grey (X) cell; all other cells are black (.). The grey cells trace a zigzag path across the columns.

Do: Determine the index of the last column (width minus 1) and note whether it is even or odd. For every grey (X) cell in the grid, check the parity of its column index. If the column index shares the same parity (even/odd) as the last column index, recolor that cell green (G). Otherwise, leave it as grey (X). All black (.) cells remain unchanged.

Grid: The grid is always exactly 3 rows tall. Width varies but each column contains exactly one non-background cell. The background color is black (.). The only non-background colors are grey (X) in the input, and grey (X) plus green (G) in the output.

Figurative Descriptions (16 variants)

"A strand of holiday lights where every other bulb switches on at dusk"

qwen3.6-35b: k=2

See: A single strand of holiday lights is strung across three hooks, zigzagging up and down. Each vertical post holds exactly one unlit grey bulb; the rest of the strand is dark wire.

Do: As evening falls, the strand checks which side of the street the last post stands on. Bulbs that stand on the same side as that final post flicker to life in green. The others stay dormant and grey, waiting for a different night.

Grid: The strand always spans exactly three hooks tall. The dark wire is black (.), unlit bulbs are grey (X), and bulbs that catch the evening current glow green (G).

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (33396 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Visuals:** A "strand of holiday lights" strung across "three hooks". It zigzags up and down.
*   **Components:**
    *   Vertical posts (hooks) hold exactly one unlit grey bulb (X).
    *   The rest is dark wire (black, .).
    *   The strand spans exactly three hooks tall.
*   **Action:**
    *   Check which side of the street the *last post* stands on.
    *   Bulbs on the *same side* as the final post flicker to life (turn Green, G).
    *   Others stay dormant (Grey, X).
*   **Grid Details:**
    *   Strand height: 3 rows.
    *   Dark wire: . (black)
    *   Unlit bulb: X (grey)
    *   Lit bulb: G (green)

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input Grid (3 rows, 13 columns):
        ```
        . . X . . X . X . . . X .
        X . . . X . X . . X . . X
        . X . X . . . . X . X . .
        ```
    *   Output Grid:
        ```
        . . G . . X . X . . . X .
        G . . . G . G . . X . . G
        . X . X . . . . G . G . .
        ```
    *   Observation:
        *   The input contains 'X's and '.'s.
        *   The output changes some 'X's to 'G's.
        *   Let's look at the positions of 'X's in the input.
            *   Row 0: indices 2, 5, 7, 11
            *   Row 1: indices 0, 4, 6, 9, 12
            *   Row 2: indices 1, 3, 8, 10
        *   Let's look at the positions of 'G's in the output.
            *   Row 0: index 2 (was X)
            *   Row 1: indices 0, 4, 6, 12 (were X)
            *   Row 2: indices 8, 10 (were X)
        *   Wait, the description says "A single strand of holiday lights is strung across three hooks". This implies a connected path.
        *   Let's trace the 'X's.
            *   (0, 2) -> (1, 4) -> (2, 3)? No, (2,3) is X.
            *   Let's look at the zigzag pattern.
            *   Row 0: X at 2.
            *   Row 1: X at 0, 4, 6, 9, 12.
            *   Row 2: X at 1, 3, 8, 10.
        *   This doesn't look like a single connected strand. It looks like multiple disconnected X's.
        *   Let's re-read the description carefully. "A single strand of holiday lights is strung across three hooks, zigzagging up and down."
        *   Maybe the "hooks" are the columns? Or maybe the X's represent the hooks?
        *   "Each vertical post holds exactly one unlit grey bulb". This suggests that in a column, there is exactly one X?
        *   Let's check the columns in Example 1 Input.
            *   Col 0: X at row 1. (1 X)
            *   Col 1: X at row 2. (1 X)
            *   Col 2: X at row 0. (1 X)
            *   Col 3: X at row 2. (1 X)
            *   Col 4: X at row 1. (1 X)
            *   Col 5: X at row 0. (1 X)
            *   Col 6: X at row 1. (1 X)
            *   Col 7: X at row 0. (1 X)
            *   Col 8: X at row 2. (1 X)
            *   Col 9: X at row 1. (1 X)
       

... [30777 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.39)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 856: "A bookshelf sorts volumes by weight, with the lightest books ... [52 chars truncated]" k=3 alts: 0/0 dc2aa30b

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Literal Description

See: The input is an 11×11 grid divided by dot-filled rows and columns into a 3×3 arrangement of nine 3×3 subgrids. Each subgrid contains only red (R) and blue (B) cells. The dot separators appear at row indices 3 and 7 and column indices 3 and 7, creating a tic-tac-toe-like layout of subgrids.

Do: 1. Extract the nine 3×3 subgrids from their positions in the 3×3 arrangement (row 0–2, col 0–2). 2. Count the number of red (R) cells in each subgrid (each subgrid has 9 cells total). 3. Sort the nine subgrids in ascending order by their red-cell count (fewest R first, most R last). 4. Place the sorted subgrids into the output grid in right-to-left, top-to-bottom order. That is, the subgrid with the fewest R cells goes to position (row 0, col 2), the next to (row 0, col 1), then (row 0, col 0), then (row 1, col 2), (row 1, col 1), (row 1, col 0), then (row 2, col 2), (row 2, col 1), and the subgrid with the most R cells goes to (row 2, col 0). 5. Reconstruct the full 11×11 output grid with dot separators in the same positions as the input.

Grid: The grid is 11 rows by 11 columns. Rows 3 and 7 and columns 3 and 7 are filled entirely with dots (.) and serve as separators. The remaining cells form nine 3×3 subgrids arranged in a 3×3 layout. Each cell in a subgrid is either R (red) or B (blue). The dot-separator structure is preserved identically in the output.

Figurative Descriptions (1 variants)

"A bookshelf sorts volumes by weight, with the lightest books placed on the highest shelf, reading right to left."

qwen3.6-35b: k=3

See: A grand wooden cabinet with nine cubbyholes arranged three-by-three, separated by thin strips of bare wood. Each cubbyhole holds a patchwork tile made of red embers and blue ice crystals. Some tiles burn hot with many embers; others are cool, nearly frozen over with blue.

Do: The librarian inspects each tile, weighing how much fire it carries — how intensely red it burns. She then rearranges the collection so that the coolest, most frozen tiles sit in the upper-right corner of the cabinet, and the hottest, most ember-filled tiles sink to the lower-left. She fills the shelves from the top row down, placing each tile from right to left, as if stacking cooling stones on a shelf where heat naturally settles to the bottom-left corner. The wooden dividers stay fixed — only the tiles move between their cubbyholes.

Grid: The cabinet is eleven slats wide and eleven slats tall. Thin strips of bare wood divide it into a three-by-three arrangement of cubbyholes, each holding a three-by-three patchwork of red embers and blue ice. The wooden strips never change — they are the skeleton of the cabinet. Only the nine patchwork tiles are reshuffled among the cubbyholes.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

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Expected

Reasoning (29652 chars)

The user wants me to solve a grid transformation puzzle.

**1. Understand the Goal:**
The goal is to transform an input grid into an output grid based on a specific set of rules described metaphorically and demonstrated through training examples.

**2. Analyze the Input/Output Structure:**
*   **Grid Size:** The description says "eleven slats wide and eleven slats tall". Let's check the examples.
    *   Example 1 Input: 11 rows, 21 columns? No, let's count.
    *   Row 1: `B B R . R B R . R B B` -> 11 characters.
    *   Wait, the text says "eleven slats wide". Let's count the characters in the provided text.
    *   `B B R . R B R . R B B` -> 11 characters.
    *   There are 11 rows.
    *   So the grid is 11x11.
*   **Layout:**
    *   The grid is divided into a 3x3 arrangement of "cubbyholes".
    *   The dividers are rows and columns of dots (`.`).
    *   Looking at the input:
        *   Row 4 is all dots: `. . . . . . . . . . .`
        *   Row 7 is all dots: `. . . . . . . . . . .`
        *   Row 10 is all dots: `. . . . . . . . . . .`
        *   Column 5 (index 4) is dots? Let's check.
        *   Row 1: `B B R . R B R . R B B`. Indices: 0,1,2 are `B B R`. Index 3 is `.`. Index 4 is `R`. Wait.
        *   Let's look at the spacing. `B B R . R B R . R B B`.
        *   Characters: B, space, B, space, R, space, ., space, R, space, B, space, R, space, ., space, R, space, B, space, B.
        *   Actually, the input format in the prompt usually has spaces between characters. Let's assume the string provided is the grid content.
        *   Let's parse Example 1 Input Row 1: `B B R . R B R . R B B`.
        *   If spaces are delimiters, the tokens are `B`, `B`, `R`, `.`, `R`, `B`, `R`, `.`, `R`, `B`, `B`. That's 11 tokens.
        *   So the grid is 11x11.
    *   **Dividers:**
        *   Rows 4, 7, 10 (1-based index) or indices 3, 6, 9 (0-based) are all dots.
        *   Columns 4, 7, 10 (1-based index) or indices 3, 6, 9 (0-based) are dots.
        *   Let's verify.
        *   Row 1: `B B R . R B R . R B B`.
            *   Col 0: B
            *   Col 1: B
            *   Col 2: R
            *   Col 3: . (Divider)
            *   Col 4: R
            *   Col 5: B
            *   Col 6: R
            *   Col 7: . (Divider)
            *   Col 8: R
            *   Col 9: B
            *   Col 10: B
        *   Yes. The grid is composed of 3x3 blocks of 3x3 cells, separated by single rows/cols of dots.
        *   The blocks are at:
            *   Top-Left: Rows 0-2, Cols 0-2
            *   Top-Mid: Rows 0-2, Cols 4-6
            *   Top-Right: Rows 0-2, Cols 8-10
            *   Mid-Left: Rows 4-6, Cols 0-2
            *   Mid-Mid: Rows 4-6, Cols 4-6
            *   Mid-Right: Rows 4-6, Cols 8-10
            *   Bot-Left: Rows 8-10, Cols 0-2
            *   Bot-Mid: Rows 8-10, Cols 4-6
            *   Bot-Right: Rows 8-10, Cols 8-10
        *   The dots at indices 3, 6, 9 are fixed dividers.

**3. Analyze the Metaphorical Descr

... [26868 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.07)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 863: "Kingdoms compete to attract the most wandering fireflies." k=1 alts: 0/0 de1cd16c

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Example 4

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Output

Literal Description

See: The input grid is divided into several rectangular regions, each filled uniformly with a single background color (e.g., blue, red, green, magenta, azure, yellow, black). These regions tile the grid completely with no gaps or overlaps. Scattered within some of these regions are isolated single-cell dots of a single 'foreign' color that differs from all the background colors. The foreign color is the same across all regions.

Do: 1. Identify the foreign color: find the single color that appears as isolated dots within regions but is not the background color of any region. 2. Identify each rectangular region by its background color. 3. Count the number of foreign-colored dots in each region. 4. The output is a 1×1 grid containing the background color of the region that has the most foreign-colored dots.

Grid: The input grid is rectangular and composed of several abutting rectangular sub-regions, each uniformly filled with a distinct background color. The output is always a single 1×1 cell containing one color.

Figurative Descriptions (1 variants)

"Kingdoms compete to attract the most wandering fireflies."

qwen3.6-35b: k=1

See: The land is divided into neighboring kingdoms, each painted in its own proud banner color. Drifting across these kingdoms are tiny fireflies — all glowing the same strange color that belongs to no kingdom. They have landed scattered across the territories, resting like uninvited guests.

Do: The fireflies are drawn to warmth and company. Whichever kingdom has attracted the most fireflies to settle within its borders wins the night — its banner color is raised as the sole victor.

Grid: The world is a patchwork quilt of colored territories stitched edge to edge. The fireflies are lone sparks dotting the fabric. When the contest ends, only the winning kingdom's color remains — a single flag on a single pole.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (33446 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and a training example.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Kingdoms:** Large contiguous blocks of a specific color (excluding the "fireflies").
    *   **Fireflies:** Small, scattered pixels of a specific color (Yellow 'Y' in the example, but let's check the test input). The description says "glowing the same strange color that belongs to no kingdom". In Example 1, the kingdoms are Blue (B), Grey (X), and Magenta (M). The fireflies are Yellow (Y).
    *   **Victor:** The kingdom that has the most fireflies inside its borders.

*   **AFFORDANCES (Capabilities):**
    *   **Kingdoms:** They occupy space. They can "contain" fireflies.
    *   **Fireflies:** They are scattered. They "settle" within a kingdom.
    *   **Transformation:** The grid is reduced to a single color representing the winning kingdom.

*   **TRANSFORMATION RULE:**
    1.  Identify the distinct "Kingdom" colors in the grid. These are the dominant background colors.
    2.  Identify the "Firefly" color. This is the color that appears as scattered single pixels or small groups, distinct from the large blocks. In Example 1, it's 'Y'.
    3.  Count the number of fireflies located within the boundaries of each kingdom.
        *   How to define boundaries? The grid seems to be divided into rectangular regions.
        *   Let's look at Example 1 input structure.
            *   Top-left block: Blue (B).
            *   Top-right block: Grey (X).
            *   Bottom-left block: Black (.)? Wait, looking at the input:
                Rows 0-7: B... and X...
                Rows 8-15: . ... and M...
            *   Actually, let's look closer at Example 1 Input.
                Rows 0-7:
                Cols 0-6: B
                Cols 7-18: X
                Rows 8-15:
                Cols 0-6: . (black)
                Cols 7-18: M
            *   Wait, the fireflies are 'Y'.
            *   Let's count 'Y's in each region.
            *   Region 1 (Blue B): Rows 0-7, Cols 0-6.
                Row 1: B Y B... (1 Y)
                Row 3: B B B Y B... (1 Y)
                Row 5: B B B B B B B X X X X Y X X X X X -> Wait, row 5 has Y at col 11?
                Let's re-examine the grid layout of Example 1.
                Input:
                Row 0: B B B B B B B X X X X X X X X X X (7 B's, 12 X's)
                Row 1: B Y B B B B B X X X X X X X X X X (1 Y in B region, 0 in X)
                Row 2: B B B B B B B X X X X X X X X X X
                Row 3: B B B Y B B B X X X X X X X X X X (1 Y in B region)
                Row 4: B B B B B B B X X X X X X X X X X
                Row 5: B B B B B B B X X X X Y X X X X X (1 Y in X region? Col 11 is in X region)
                Row 6: B B Y B B B B X X X X X X X X X X (1 Y in B region)
                Row 7: B B B B B B B X X X X X X X X X X
                Row 8: . . . . . . . M M M M M M M M M M (7 dots, 12 M's

... [30647 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 875: "A wanted poster leads bounty hunters to fence in the fugitiv ... [2 chars truncated]" k=3 alts: 0/15 e2092e0c

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input is a 15×15 grid containing single-character color codes. In the top-left corner there is a distinctive cross or L-shaped structure made of X cells: the entire fourth row (row 3) is X X X X, and the entire fourth column (column 3) is X for rows 0 through 3. This creates a 4×4 region where row 3 and column 3 are all X, leaving a 3×3 sub-grid of non-X colored cells in rows 0–2, columns 0–2. This 3×3 sub-grid is the 'key pattern.' Somewhere else in the grid, a copy of this exact 3×3 pattern of colors exists at another location.

Do: 1. Extract the 3×3 key pattern from the top-left corner of the grid (rows 0–2, columns 0–2 — the non-X portion of the cross structure). 2. Search the rest of the grid for a 3×3 region that exactly matches this key pattern, cell by cell. 3. Once found, draw a 5×5 rectangular border of X cells centered on that 3×3 region. That is, if the matching 3×3 occupies rows r to r+2 and columns c to c+2, replace the border cells of the 5×5 rectangle spanning rows (r−1) to (r+3) and columns (c−1) to (c+3) with X. Specifically, the top and bottom rows of the 5×5 rectangle become all X, and the leftmost and rightmost columns of the three middle rows become X. The interior 3×3 cells (the matched pattern) remain unchanged. All other cells in the grid remain unchanged.

Grid: The grid is 15×15. It uses the standard ARC color palette (0–9) rendered as single characters: .=black, B=blue, R=red, G=green, Y=yellow, X=grey, M=magenta, O=orange, A=azure, W=maroon. The grid has no uniform background color; cells contain a variety of colors. The top-left 4×4 region always contains the cross template (row 3 all X, column 3 all X for rows 0–3). The output grid has the same dimensions as the input; the only change is the addition of the 5×5 X-border around the located pattern.

Figurative Descriptions (16 variants)

"A wanted poster leads bounty hunters to fence in the fugitive."

qwen3.6-35b: k=3

See: In the top-left corner of the grid, a grey stone wall forms an L-shaped jail—bars running across the fourth row and down the fourth column. Locked behind those bars sits a 3×3 'mugshot' of colored suspects. Somewhere out in the wider grid, those same three-by-three suspects are hiding in plain sight among the crowd, wearing identical colors in the same arrangement.

Do: The sheriff studies the mugshot pinned to the jailhouse wall, then rides out into the grid to hunt for the fugitives. When the matching trio is found—same faces, same positions—the posse erects a grey stone fence around them: a 5×5 perimeter of X-bars that encircles the hideout one cell out in every direction. The fugitives inside remain untouched, but the fence announces they've been caught. Nothing else in the town changes—only the fence is new.

Grid: The town is a 15×15square of colored buildings. Grey (X) is the material of walls, bars, and fences. The jailhouse always occupies the top-left four rows and four columns, with its signature cross of grey bars. Every other color is a civilian going about their day. After the capture, the grid looks the same except for the new rectangular grey fence surrounding the discovered hideout.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (24405 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Grid:** 15x15 square.
    *   **Jailhouse:** Top-left 4x4 area. Contains a "grey stone wall" (X) forming an L-shape. Specifically, the 4th row and 4th column of the grid (indices 3, 0-based) are filled with X's, creating a cross/barrier. Wait, the description says "bars running across the fourth row and down the fourth column". Let's check the input grids.
        *   Row 3 (0-indexed) is `X X X X ...`.
        *   Column 3 (0-indexed) is `X X X X ...`.
        *   Actually, looking at Example 1 input:
            Row 0: `G Y . X ...` -> Col 3 is X.
            Row 1: `. . Y X ...` -> Col 3 is X.
            Row 2: `. A G X ...` -> Col 3 is X.
            Row 3: `X X X X ...` -> Row 3 is all X.
            So yes, the "jail" is defined by the intersection of Row 3 and Column 3 being filled with X's. The top-left 4x4 block is bounded by these.
    *   **Mugshot:** A 3x3 pattern of colored suspects located *behind* the bars. The bars are at Row 3 and Col 3. The area "behind" the bars in the top-left corner would be the 3x3 block at Rows 0-2 and Cols 0-2. Let's verify.
        *   In Example 1, the 3x3 block at (0,0) to (2,2) is:
            `G Y .`
            `. . Y`
            `. A G`
        *   Wait, the description says "Locked behind those bars sits a 3x3 'mugshot'". The bars are at row 3 and col 3. The cells (0,0) to (2,2) are indeed the 3x3 area enclosed by the top/left edges and the bars.
    *   **Fugitives:** A 3x3 pattern of the *same* colors in the *same* arrangement as the mugshot, found somewhere else in the grid.
    *   **Sheriff/Posse:** The logic agent.
    *   **Fence:** A 5x5 perimeter of X's surrounding the found fugitive pattern. The fence is "one cell out in every direction". So if the fugitive 3x3 is at rows $r$ to $r+2$ and cols $c$ to $c+2$, the fence covers rows $r-1$ to $r+3$ and cols $c-1$ to $c+3$, but only the perimeter (border) of this 5x5 area.

*   **AFFORDANCES (Capabilities):**
    *   **Mugshot:** Defines a specific 3x3 pattern of colors.
    *   **Fugitives:** Can be found by scanning the grid for the mugshot pattern.
    *   **Fence:** Can be drawn (overwriting existing cells with X) around the fugitives.

*   **TRANSFORMATION RULE:**
    1.  **Identify the Mugshot Pattern:** Extract the 3x3 grid of colors from the top-left corner (Rows 0-2, Cols 0-2). Note: The bars are at Row 3 and Col 3, so the 3x3 area is strictly inside the top-left 4x4 block.
    2.  **Locate the Fugitives:** Search the entire 15x15 grid for a 3x3 subgrid that matches the Mugshot Pattern exactly.
        *   *Self-Correction/Refinement:* The description says "Somewhere out in the wider grid, those same three-by-three suspects are hiding...". It implies there is exactly one match, or perhaps multiple? The text says "When the matching trio is found...". "Trio" might refer to the group. Usually, in these puzzl

... [21603 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.01)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 879: "Two shields overlap, and light passes only through holes sha ... [12 chars truncated]" k=1 alts: 0/0 e345f17b

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Example 4

Input

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Output

Literal Description

See: The input is a 4×8 grid containing three colors: black (.), magenta (M), and grey (X). The grid naturally divides into a left 4×4 half and a right 4×4 half. The left half contains a pattern of magenta cells on a black background, and the right half contains a pattern of grey cells on a black background. In each half, the black cells represent gaps or empty spaces.

Do: 1. Split the input grid vertically into two equal halves: a left half and a right half, each 4×4. 2. Create an output grid of the same dimensions as each half (4×4), filled with black (.). 3. For each cell position (row, col) in the output grid, check the corresponding cell in the left half and the corresponding cell in the right half. 4. If BOTH the left-half cell and the right-half cell are black (.), place a yellow (Y) in the output at that position. 5. Otherwise, leave the output cell as black (.).

Grid: The input grid is always 4 rows by 8 columns. The output grid is always 4 rows by 4 columns — exactly half the width of the input. The background color of the output is black (.). Yellow (Y) is the only non-background color in the output.

Figurative Descriptions (1 variants)

"Two shields overlap, and light passes only through holes shared by both."

qwen3.6-35b: k=1

See: A fortress wall is built from two shields placed side by side — one forged in magenta, one in grey. Each shield is riddled with gaps where the metal has rusted away, leaving black openings. Together they span the full width of the wall, standing guard over whatever lies behind.

Do: An archer fires arrows of golden light at the wall. Where a magenta shield has solid metal, the light is blocked. Where the grey shield has solid metal, the light is blocked. Only where BOTH shields have holes — where neither offers protection — does the golden light pierce through and strike the ground beyond. Mark those sunlit spots on the ground.

Grid: The fortress wall stretches wide but the ground behind it is only as wide as a single shield. The ground is dark by default — only the golden strikes of light that found passage through both shields leave their mark.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (31021 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Input and Output Grids in Training Examples:**

*   **Example 1 Input:**
    ```
    M . M . . . X X
    . M M M X . X X
    M M . M X . X X
    M M . . X . . .
    ```
    Dimensions: 4 rows, 8 columns.
    Colors present: M (magenta), . (black), X (grey).

*   **Example 1 Output:**
    ```
    . Y . .
    . . . .
    . . . .
    . . Y Y
    ```
    Dimensions: 4 rows, 4 columns.
    Colors present: . (black), Y (yellow).

*   **Observation:**
    *   The input width is 8. The output width is 4.
    *   The input height is 4. The output height is 4.
    *   The input seems to be composed of two halves. Let's split the input columns into two groups of 4.
        *   Left half (Columns 0-3):
            ```
            M . M .
            . M M M
            M M . M
            M M . .
            ```
        *   Right half (Columns 4-7):
            ```
            . . X X
            X . X X
            X . X X
            X . . .
            ```
    *   The metaphor mentions "two shields placed side by side". This aligns with the input being split into two halves.
    *   Left half colors: M (magenta) and . (black).
    *   Right half colors: X (grey) and . (black).
    *   The output contains Y (yellow) and . (black).
    *   The metaphor says: "Where a magenta shield has solid metal, the light is blocked. Where the grey shield has solid metal, the light is blocked. Only where BOTH shields have holes — where neither offers protection — does the golden light pierce through".
    *   "Solid metal" corresponds to the colored pixels (M and X). "Holes" correspond to the black pixels (.).
    *   "Golden light" corresponds to the output color Y (yellow).
    *   So, the rule seems to be: Compare the left half (Magenta shield) and the right half (Grey shield). If a cell in the left half is a hole (.) AND the corresponding cell in the right half is a hole (.), then the output cell is Yellow (Y). Otherwise, it is Black (.).
    *   Wait, let's check the colors.
        *   Left half: M is solid, . is hole.
        *   Right half: X is solid, . is hole.
        *   Intersection: Both are holes (.).
        *   Result: Y.
    *   Let's verify with Example 1 data.

    *   **Row 0:**
        *   Left: `M . M .` -> Holes at indices 1, 3.
        *   Right: `. . X X` -> Holes at indices 0, 1.
        *   Wait, the right half is columns 4, 5, 6, 7.
        *   Row 0 Right: `.` (col 4), `.` (col 5), `X` (col 6), `X` (col 7).
        *   Let's align them.
        *   Left: `M` (0), `.` (1), `M` (2), `.` (3)
        *   Right: `.` (4), `.` (5), `X` (6), `X` (7)
        *   Comparison:
            *   Col 0: Left `M` (Solid), Right `.` (Hole). Result: Blocked. -> `.`
            *   Col 1: Left `.` (Hole), Right `.` (Hole). Result: Pass. -> `Y`
            *   Col 2: Left `M` (Solid), Right `X` (Solid). Resu

... [28387 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.62)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 880: "A mirror stands in a hall, and scattered guests on both side ... [26 chars truncated]" k=1 alts: 0/0 e3497940

Training Examples

Example 1

Input

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Output

Example 2

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Output

Example 3

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Output

Literal Description

See: The input grid has a vertical column of grey (X) cells running top to bottom, dividing the grid into a left half and a right half of equal width. Both halves contain scattered colored cells (non-black, non-grey) on a black background. The colored cells appear on either or both sides of the grey divider.

Do: Remove the central grey (X) column entirely. Take the right half of the grid and mirror it horizontally (flip it left-to-right). Then merge the mirrored right half with the left half: for each cell position, if either the left half or the mirrored right half has a non-black color, place that color in the output. If both are black, the output cell is black. The result is a grid with the same number of rows as the input but only as many columns as one half (excluding the grey divider).

Grid: The input grid has an odd number of columns, with the exact center column filled entirely with grey (X). The output grid has the same number of rows as the input and a number of columns equal to half the input width (excluding the center column). The background color is black (.).

Figurative Descriptions (1 variants)

"A mirror stands in a hall, and scattered guests on both sides step through to reunite."

qwen3.6-35b: k=1

See: A tall silver mirror (grey column) stands in the center of a dark ballroom, dividing it into two symmetrical wings. Guests in colorful attire are scattered across both wings—some linger only on the left, some only on the right, and the mirror reflects them all.

Do: The mirror shatters and vanishes. The guests who were standing in the right wing see their reflections released—each reflection walks across to the matching position on the left side. Wherever a real guest or a freed reflection stands, they remain visible. The right wing crumbles into darkness, leaving only the left wing populated by everyone who gathered from both sides.

Grid: The ballroom is as tall as before but now only half as wide—the mirror and everything beyond it are gone. The dark floor (black) fills any spot where no guest stands. The silver mirror leaves no trace.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (29093 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Visuals:** A "tall silver mirror (grey column)" stands in the center. It divides the grid into two wings (left and right).
*   **Elements:** "Guests" (colored pixels) are scattered.
*   **Action:** The mirror shatters/vanishes.
*   **Reflection:** Guests on the right wing see their reflections released. Each reflection walks to the matching position on the left side.
*   **Result:** The right wing crumbles (disappears). The output grid is the left wing, but populated by the union of the original left wing guests and the reflected right wing guests.
*   **Grid Details:** The output grid is half the width of the input grid. The mirror column (grey 'X') is gone.

**2. Analyze the Training Examples:**
*   **Example 1 Input:**
    *   Grid size: 10 rows x 9 columns.
    *   Center column (index 4, 0-indexed) is all 'X' (grey).
    *   Left side (cols 0-3): Contains some colored pixels (R, M).
    *   Right side (cols 5-8): Contains some colored pixels (R, M).
*   **Example 1 Output:**
    *   Grid size: 10 rows x 4 columns.
    *   This confirms the width is halved (9 -> 4, ignoring the center column).
    *   Let's check the content.
    *   Input Row 0: `. . . . X . . . .` -> Output Row 0: `. . . .` (Left side matches).
    *   Input Row 1: `. . . R X . . . .` -> Output Row 1: `. . . R` (Left side matches).
    *   Input Row 2: `. . . R X R M . .` -> Left side: `. . . R`. Right side: `R M . .`.
        *   Wait, the right side is `R M . .`? Let's look closer at the input string.
        *   Input Row 2: `. . . R X R M . .`
        *   Indices: 0:., 1:., 2:., 3:R, 4:X, 5:R, 6:M, 7:., 8:.
        *   Left side (0-3): `. . . R`
        *   Right side (5-8): `R M . .`
        *   Output Row 2: `. . M R`
        *   Wait, the output is `. . M R`.
        *   Let's re-read the metaphor: "Guests who were standing in the right wing see their reflections released—each reflection walks across to the matching position on the left side."
        *   Reflection usually implies mirroring. If I am at position (row, col) on the right, my reflection is at (row, mirrored_col) on the left.
        *   Let's map indices.
        *   Input width = 9. Center = 4.
        *   Left indices: 0, 1, 2, 3.
        *   Right indices: 5, 6, 7, 8.
        *   Mirroring logic:
            *   Right index 5 is adjacent to center. Mirrors to Left index 3.
            *   Right index 6 mirrors to Left index 2.
            *   Right index 7 mirrors to Left index 1.
            *   Right index 8 mirrors to Left index 0.
        *   Let's check Row 2 again.
            *   Left: `.` `.` `.` `R` (indices 0,1,2,3)
            *   Right: `R` `M` `.` `.` (indices 5,6,7,8)
            *   Reflection of Right index 5 ('R') goes to Left index 3. Left index 3 is already 'R'. Result 'R'.
            *   Reflection

... [26849 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.37)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 910: "A dance troupe passes choreography down the line at each reh ... [59 chars truncated]" k=2 alts: 0/15 e78887d1

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Literal Description

See: The input grid is organized into two or more horizontal groups of 3×3 colored blocks, separated by rows of all-black cells. Within each group, there are N colored blocks (e.g., R, G, B, X) arranged left to right, each occupying a 3×3 region and separated by a single column of black cells. Every block uses exactly one non-black color but has its own unique pattern of filled and empty cells within its 3×3 space. The same set of colors appears in the same left-to-right order in every group. From one group to the next, the patterns (filled/empty arrangements) shift cyclically among the color positions: each color adopts the pattern that belonged to the color immediately to its right in the previous group, with the rightmost color's pattern wrapping around to the leftmost color.

Do: 1. Identify the horizontal groups separated by all-black rows. Each group is exactly 3 rows tall. 2. Within each group, identify the N colored 3×3 blocks arranged left to right, noting their color order (e.g., R, G, B, X). 3. Extract the 3×3 pattern (which cells are filled vs. black) for each color block in the last group. 4. Produce the output by applying one more cyclic left-shift of patterns: assign to each color position the pattern that belonged to the color one step to its right in the last group. The rightmost color receives the pattern from the leftmost color. 5. Render the output as a single 3-row group with the same color order and column spacing, filling each color's 3×3 region with its new pattern in that color.

Grid: The input grid has a width of (N × 3 + (N−1)) columns, where N is the number of colored blocks per group, and a height of (G × 3 + (G+1)) rows, where G is the number of groups (the extra rows are all-black separator rows including top and bottom borders). The output grid is always exactly 3 rows tall and the same width as the input, containing a single group with no surrounding black separator rows. The background color is black (.).

Figurative Descriptions (16 variants)

"A dance troupe passes choreography down the line at each rehearsal, and the final performance reveals the next routine."

qwen3.6-35b: k=2

See: Troupes of colored dancers—R, G, B, and sometimes X—stand in a line on a dark stage, each performing their own signature 3×3 choreography. The stage is divided into rehearsal rounds stacked vertically, separated by blackout curtains. In each new round, every dancer has learned the moves of the neighbor to their right, while the dancer on the far right loops back to mimic the one on the far left—a rolling relay of stolen choreography passing through the lineup.

Do: Watch the dancers rehearse through all their rounds, paying close attention to the final rehearsal. Now predict the opening night performance: each dancer steps forward wearing their own color but performing the choreography that belonged to the dancer one step to their right in that last rehearsal. The dancer at the end of the line inherits the first dancer's routine, completing the circle. The curtain rises on a single, final performance—no blackouts, no intermissions.

Grid: The dark stage spans enough room for each dancer's 3×3 spotlight with a single dark column between them. Blackout rows frame each rehearsal round top and bottom. Opening night strips away all the darkness—just one three-row performance under the lights, same stage width, no curtains.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (28982 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description**

*   **Input:** A grid representing a "dark stage" with "rehearsal rounds" stacked vertically.
    *   "Troupes of colored dancers—R, G, B, and sometimes X—stand in a line on a dark stage".
    *   "Each performing their own signature 3x3 choreography".
    *   "Stage is divided into rehearsal rounds stacked vertically, separated by blackout curtains".
    *   "Blackout rows frame each rehearsal round top and bottom".
    *   "Dark column between them" (between dancers).
*   **Process (Rehearsal):**
    *   "In each new round, every dancer has learned the moves of the neighbor to their right".
    *   "Dancer on the far right loops back to mimic the one on the far left—a rolling relay".
    *   This implies a cyclic shift of the "choreography" (the 3x3 blocks) to the right.
*   **Output (Opening Night):**
    *   "Predict the opening night performance: each dancer steps forward wearing their own color but performing the choreography that belonged to the dancer one step to their right in that last rehearsal."
    *   "The dancer at the end of the line inherits the first dancer's routine".
    *   "Strips away all the darkness—just one three-row performance under the lights, same stage width, no curtains."
    *   This means the output is a single 3xN grid (where N is the width of the stage) containing the final state of the dancers' choreographies.

**2. Analyze the Grid Details**

*   **Input Structure:**
    *   Rows of dots (`.`) act as separators (blackout curtains).
    *   The "dancers" are 3x3 blocks of non-dot characters.
    *   There is a single column of dots (`.`) separating the 3x3 blocks horizontally.
    *   The input grid contains multiple "rehearsal rounds" (groups of 3 rows of dancers) separated by rows of dots.
*   **Output Structure:**
    *   A single block of 3 rows.
    *   Width matches the input width.
    *   Contains the final state of the dancers.

**3. Analyze Training Examples**

**Example 1:**
Input:
```
. . . . . . . . . . . . . . .  (Row 0: Curtain)
R R R . G . . . B . . . X . X  (Row 1: Dancer 1, 2, 3, 4)
. . R . G . . . . B B . X . X  (Row 2: Dancer 1, 2, 3, 4)
. . R . G G G . B . . . X . X  (Row 3: Dancer 1, 2, 3, 4)
. . . . . . . . . . . . . . .  (Row 4: Curtain)
```
Wait, looking at the input, it seems there are only 3 rows of dancers?
Let's check the text description again. "Blackout rows frame each rehearsal round top and bottom."
In Example 1, there is a row of dots at the top and bottom.
The rows with data are 1, 2, 3.
Wait, the input has 5 rows total.
Row 0: `.`s
Row 1: `R R R . G . . . B . . . X . X`
Row 2: `. . R . G . . . . B B . X . X`
Row 3: `. . R . G G G . B . . . X . X`
Row 4: `.`s

Wait, the description says "rehearsal rounds stacked vertically".
In Example 1, there is only one block of 3 rows of dancers.
Let's look

... [26156 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.09)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 915: "A doctor diagnoses dark wounds on grey skin — their co ... [47 chars truncated]" k=3 alts: 0/0 e8593010

Training Examples

Example 1

Input

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Output

Example 2

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Output

Example 3

Input

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Output

Literal Description

See: The input is a 10x10 grid containing only two cell types: grey (X) cells and black (.) cells. The grey cells form a dense background, while the black cells appear scattered throughout, forming isolated singles, pairs, or small clusters. These black cells form connected components under 4-connected adjacency (up, down, left, right — not diagonal).

Do: 1. Identify all connected components of black (.) cells using 4-connected adjacency (cells sharing an edge, not diagonal). 2. Count the number of cells in each connected component. 3. Recolor each component based on its size: size 1 becomes green (G), size 2 becomes red (R), size 3 becomes blue (B). 4. All grey (X) cells remain unchanged.

Grid: The grid is 10x10. Grey (X) serves as the static background and is never modified. Black (.) cells are the only cells that change, and they always appear in connected components of size 1, 2, or 3. The output grid has the same dimensions, with every cell either grey (X), green (G), red (R), or blue (B).

Figurative Descriptions (1 variants)

"A doctor diagnoses dark wounds on grey skin — their color reveals how badly the infection has spread."

qwen3.6-35b: k=3

See: A grey skin stretches across the board, but it is pocked with dark wounds — some are tiny pinpricks, others have spread to neighbors, forming small infections of two or three cells that cling together edge-to-edge.

Do: The doctor examines each wound cluster and diagnoses its severity by how many cells the infection touches. A lone pinprick gets a mild green salve. A wound that has spread to one neighbor is marked with urgent red. The deepest infections — those that have claimed three connected cells — receive the blue dye of serious treatment. The healthy grey skin is left alone.

Grid: The skin is a 10×10 patch. Grey is healthy tissue that never changes. Every dark wound belongs to exactly one infection cluster, and no cluster grows larger than three cells. After diagnosis, the darkness is gone — replaced entirely by the color of its treatment.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

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Reasoning (23256 chars)

The user wants me to solve a grid transformation puzzle.

**1. Understand the Goal:**
I need to transform an input grid of characters into an output grid based on a specific set of rules described metaphorically.

**2. Analyze the Input/Output Format:**
- Input: A 10x10 grid of characters.
- Characters: `.` (black), `X` (grey), and potentially others (though the examples only show `.` and `X` in the input, the output introduces `R`, `G`, `B`).
- Output: A 10x10 grid of characters.
- Colors: `.` (black), `X` (grey), `R` (red), `G` (green), `B` (blue).

**3. Analyze the Metaphorical Description:**
- **Visuals:** "Grey skin" (`X`) is the background. "Dark wounds" (`.`) are the features to be processed.
- **Clusters:** The dark wounds (`.`) form clusters.
    - "Tiny pinpricks" = isolated cells (size 1).
    - "Small infections of two or three cells" = clusters of size 2 or 3.
    - "Cling together edge-to-edge" = 4-connectivity (up, down, left, right).
- **Transformation Rule (Diagnosis):**
    - **Lone pinprick (size 1):** "mild green salve" -> Change `.` to `G`.
    - **Spread to one neighbor (size 2):** "urgent red" -> Change `.` to `R`.
    - **Deepest infections (size 3):** "blue dye" -> Change `.` to `B`.
    - **Healthy grey skin (`X`):** "left alone" -> Remains `X`.
- **Constraint:** "Every dark wound belongs to exactly one infection cluster, and no cluster grows larger than three cells." This simplifies things; I don't need to handle clusters of size 4+.

**4. Analyze the Training Examples to Verify:**

*Example 1:*
Input has `.` and `X`.
Let's look at a specific cluster.
Row 0: `X X X X X . . X X X` -> Indices 5, 6 are `.`. They are adjacent. Size 2.
Output Row 0: `X X X X X R R X X X`. `.` became `R`. Correct (size 2 -> Red).

Row 1: `. . X . X X X X X .`
Indices 0, 1 are `.`. Adjacent. Size 2.
Index 3 is `.`. Isolated? Let's check neighbors.
(1,3) neighbors: (0,3)=X, (2,3)=X, (1,2)=X, (1,4)=X. Yes, isolated. Size 1.
Index 9 is `.`. Neighbors: (0,9)=X, (2,9)=X, (1,8)=X. Isolated. Size 1.
Output Row 1: `R R X G X X X X X G`.
(1,0), (1,1) became `R`. Correct (size 2).
(1,3) became `G`. Correct (size 1).
(1,9) became `G`. Correct (size 1).

Row 6: `. . X X . X . . X .`
Indices 0, 1 are `.`. Adjacent. Size 2.
Index 4 is `.`. Neighbors: (5,4)=., (6,3)=X, (6,5)=X, (7,4)=X. Wait, (5,4) is `.`.
Let's check Row 5: `X X X X . X X X X X`. Index 4 is `.`.
So (5,4) and (6,4) are connected.
Let's check neighbors of (6,4): (5,4)=., (7,4)=X, (6,3)=X, (6,5)=X.
So cluster is {(5,4), (6,4)}. Size 2.
Output Row 5: `X X X X R X X X X X`. (5,4) became `R`.
Output Row 6: `R R X X R X B B X G`. (6,4) became `R`.
Wait, look at Row 6 indices 6, 7. `.` `.`.
(6,6) neighbors: (5,6)=X, (7,6)=X, (6,5)=X, (6,7)=..
(6,7) neighbors: (5,7)=X, (7,7)=., (6,6)=., (6,8)=X.
(7,7) is `.`.
Let's check Row 7: `X X X X X X X . X X`. Index 7 is `.`.
So we have a cluster at (6,6), (6,7), (7,7).
(6,6) connects to (6,7).
(6,7) connects to (7,7).
Is (7,7) connected to 

... [20724 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.54)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 916: "A night sky remembers each river it has swallowed, plus the ... [31 chars truncated]" k=1 alts: 7/15 e872b94a

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Output

Literal Description

See: The input grid has a black (.) background with grey (X) cells that form one or more snake-like connected components. Each component is a path one cell wide, meaning X cells connect to each other orthogonally (up, down, left, right) to form continuous, non-branching shapes. The components are spatially separated from one another — no X cell in one component is orthogonally adjacent to an X cell in another.

Do: 1. Identify all grey (X) cells in the input grid. 2. Determine the number of distinct connected components formed by these X cells, where two X cells are connected if they are orthogonally adjacent (share an edge horizontally or vertically). 3. Count the total number of connected components and add 1 to that count. 4. Produce an output grid that has exactly that many rows (count + 1), each row containing a single black (.) cell.

Grid: The output grid is always a single column (width 1). Its height equals the number of connected components of grey cells in the input plus one. Every cell in the output is black (.).

Figurative Descriptions (16 variants)

"A night sky remembers each river it has swallowed, plus the darkness that was there before."

qwen3.6-35b: k=1

See: Against a vast dark sky, grey rivers wind across the landscape — each one a single, unbroken current that never forks or touches another. They twist and turn like serpents asleep on the void, each keeping a respectful distance from its neighbors.

Do: The sky is an ancient scribe who tallies every river it has absorbed. For each grey river swallowed into the darkness, the scribe places one drop of ink on a scroll. But the scribe always begins with one drop already on the page — a mark for the original emptiness that existed before any river flowed. Roll up the scroll when the counting is done.

Grid: The scroll is a single column of pure night. Its length is the scribe's tally — one drop for the void, one for each river the sky consumed.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (26405 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**

*   **Input:** "Against a vast dark sky, grey rivers wind across the landscape — each one a single, unbroken current that never forks or touches another. They twist and turn like serpents asleep on the void, each keeping a respectful distance from its neighbors."
    *   "Dark sky" likely refers to the background color, which is `.` (black).
    *   "Grey rivers" refers to the color `X` (grey).
    *   "Single, unbroken current that never forks or touches another" implies connected components of `X` that are paths (1-pixel wide) and don't intersect.
    *   "Twist and turn" implies they can be curved or zig-zag.
    *   "Respectful distance" might just be flavor text, or imply they don't touch.

*   **Transformation:**
    *   "The sky is an ancient scribe who tallies every river it has absorbed." -> Count the number of "rivers" (connected components of `X`).
    *   "For each grey river swallowed into the darkness, the scribe places one drop of ink on a scroll." -> Each river adds 1 to the count.
    *   "But the scribe always begins with one drop already on the page — a mark for the original emptiness that existed before any river flowed." -> Base count is 1.
    *   "Roll up the scroll when the counting is done." -> The output is a vertical column (scroll).
    *   "The scroll is a single column of pure night. Its length is the scribe's tally — one drop for the void, one for each river the sky consumed." -> The output grid is a single column of `.` (black) characters. The height of the grid is equal to (1 + number of rivers).

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input Grid:
        ```
        . X . . . . .
        . X X . . . .
        . . X . . X X
        . X X . . X .
        . X . . X X .
        . X . . X . .
        . X . . X . .
        ```
    *   Let's identify the "rivers" (connected components of `X`).
        *   Row 0: `X` at (0,1).
        *   Row 1: `X` at (1,1), (1,2). Connected to (0,1).
        *   Row 2: `X` at (2,2), (2,5), (2,6). (2,2) connects to (1,2). So far, one big component.
        *   Row 3: `X` at (3,1), (3,2), (3,5). (3,1) connects to (2,2)? No, (2,2) is at col 2. (3,1) is at col 1. (3,2) is at col 2. (3,2) connects to (2,2). (3,1) connects to (3,2).
        *   Let's trace carefully.
        *   Component 1:
            *   (0,1)
            *   (1,1), (1,2)
            *   (2,2)
            *   (3,1), (3,2)
            *   (4,1)
            *   (5,1)
            *   (6,1)
            *   Wait, let's look at the grid again.
            ```
            . X . . . . .  (0,1)
            . X X . . . .  (1,1), (1,2)
            . . X . . X X  (2,2), (2,5), (2,6)
            . X X . . X .  (3,1), (3,2), (3,5)
            . X . . X X .  (4,1), (4,4), (4,5)
            . X . . X . .  (5,1), (5,4)
 

... [23750 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.03)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 921: "Four royal houses compete for territory, and the crown goes ... [35 chars truncated]" k=6 alts: 2/15 e99362f0

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Example 5

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Example 6

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Literal Description

See: The input is a rectangular grid divided into four quadrants by a yellow cross — a horizontal row of all yellow cells and a vertical column of all yellow cells that intersect at one point. This cross splits the grid into four equally-sized rectangular regions. Each quadrant contains a pattern made from one signature color on a black background: the top-left quadrant uses orange (O), the top-right uses white (W), the bottom-left uses red (R), and the bottom-right uses azure (A). Each quadrant has the same dimensions.

Do: 1. Identify the yellow cross (one full yellow row and one full yellow column) and extract the four quadrants, ignoring the yellow dividers. All four quadrants share the same dimensions — this will be the output size. 2. For each cell position in the output grid, examine the corresponding cell in all four quadrants. Each quadrant cell is either its signature color or black. 3. Determine which quadrants have a non-black (colored) value at that position. If none do, the output cell is black. 4. If one or more quadrants are non-black at that position, select the winner using the fixed priority order: azure (A) > orange (O) > white (W) > red (R). The highest-priority non-black color wins and is placed in the output cell.

Grid: The input grid is 11 rows by 9 columns, with a yellow row (row 5) and a yellow column (column 4) forming a cross that divides the grid into four 5×4 quadrants. The output grid matches the quadrant dimensions: 5 rows by 4 columns. The background color is black (.). The four signature colors — orange, white, red, azure — each appear exclusively in their respective quadrant in the input but may all appear in the output.

Figurative Descriptions (16 variants)

"Four royal houses compete for territory, and the crown goes to whoever has the strongest claim."

qwen3.6-35b: k=6

See: A golden cross — like two roads meeting at a crossroads — carves the land into four kingdoms. Each kingdom flies a single banner over its domain: orange in the northwest, white in the northeast, red in the southwest, and azure in the southeast. Within each kingdom, some plots are settled (colored) and some lie fallow (black).

Do: The golden borders dissolve, and all four kingdoms collapse onto the same contested map. Where no kingdom has planted a flag, the land remains barren. Where multiple houses claim the same plot, the dispute is settled by ancient right of succession: the Azure throne outranks all, Orange bows only to Azure, White yields to both Orange and Azure, and Red — the least of the four — wins only when no other house stands on the ground.

Grid: The golden crossroads splits the realm into four provinces of equal size. When the borders fall, the contested map matches the size of a single province. Every plot on this final map bears the color of whichever surviving house holds the strongest claim there.

qwen3.6-35b — MARC valid, solved with 6 examples

Input

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Prediction

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Expected

Reasoning (26373 chars)

The user wants me to solve a grid transformation puzzle.

**1. Understand the Goal:**
The goal is to transform an input grid into an output grid based on a specific set of rules described metaphorically.

**2. Analyze the Metaphorical Description:**
*   **Input Structure:** A grid containing a "golden cross" (yellow 'Y's) that splits the land into four kingdoms (quadrants).
*   **Kingdoms:**
    *   Northwest (Top-Left): Orange (O)
    *   Northeast (Top-Right): White (W) - Wait, the key says W=maroon, but the text says "white". Let's check the key. Key: W=maroon. Text says "white". This is a discrepancy. Let's look at the training examples. In Example 1, the top right quadrant has 'W's. The text says "white". The key says "W=maroon". Usually, in these puzzles, the letter code is the ground truth. Let's assume W stands for the color represented by the letter, even if the text description calls it "white" (maybe a translation quirk or just a name). Actually, looking at the key: `W=maroon`. The text says "white". Let's look at the colors in the grid. 'W' is used. I will stick to the letter codes provided in the key.
    *   Southwest (Bottom-Left): Red (R)
    *   Southeast (Bottom-Right): Azure (A)
*   **The "Golden Cross":** The letter 'Y' (yellow) forms a cross shape. It seems to act as a separator.
*   **Transformation:**
    *   The borders (the 'Y's) dissolve.
    *   The four kingdoms collapse onto the same map.
    *   The final map size is equal to a single province (quadrant).
    *   **Overlap Resolution (Succession):**
        *   Azure (A) is highest.
        *   Orange (O) is second.
        *   White/Maroon (W) is third.
        *   Red (R) is lowest.
        *   Black (.) is empty/fallow.
    *   **Priority Order:** A > O > W > R > . (Black).
    *   Wait, let's re-read carefully: "Azure throne outranks all, Orange bows only to Azure, White yields to both Orange and Azure, and Red — the least of the four — wins only when no other house stands on the ground."
    *   Hierarchy: A (highest) > O > W > R (lowest).
    *   If a cell in the final grid is covered by multiple colors from the quadrants, the highest priority color wins.
    *   If a cell is covered by only one color, that color wins.
    *   If a cell is empty (black '.') in all quadrants, it remains black.

**3. Analyze the Grid Structure:**
*   The input grid has a central cross of 'Y's.
*   Let's check the dimensions.
    *   Example 1 Input: 11 rows, 9 columns.
    *   The 'Y' cross seems to be a full row and a full column.
    *   Row 6 (index 5) is all 'Y's.
    *   Column 5 (index 4) is all 'Y's.
    *   This divides the grid into 4 quadrants.
    *   Top-Left (NW): Rows 0-4, Cols 0-3. Size 5x4.
    *   Top-Right (NE): Rows 0-4, Cols 5-8. Size 5x4.
    *   Bottom-Left (SW): Rows 6-10, Cols 0-3. Size 5x4.
    *   Bottom-Right (SE): Rows 6-10, Cols 5-8. Size 5x4.
    *   Wait, the output size in Example 1 is 5x4.
    *   Let's verify the 

... [23829 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.40)

Prediction

Expected

Figurative + 6 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 939: "A secret society's signet ring stamps its color onto a wax s ... [4 chars truncated]" k=3 alts: 14/15 ed74f2f2

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Example 5

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Example 6

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Literal Description

See: The input is a 5×9 grid with a black background. Embedded within it are two 3×3 patterns made of grey (X) cells, separated by a column of black cells. The left pattern occupies rows 1-3, columns 1-3, and the right pattern occupies rows 1-3, columns 5-7. Each pattern is a distinct arrangement of grey cells against the black background.

Do: 1. Extract the left 3×3 subgrid (rows 1-3, columns 1-3) and the right 3×3 subgrid (rows 1-3, columns 5-7). 2. Identify the shape of the left subgrid to determine the output color: (a) If the left pattern is a T-shape (top row all filled, middle and bottom rows only center filled: XXX / .X. / .X.), the color is Blue (B). (b) If the left pattern is an S-shape (top row right two filled, middle row center filled, bottom row left two filled: .XX / .X. / XX.), the color is Green (G). (c) If the left pattern is a Z-shape (top row left two filled, middle row center filled, bottom row right two filled: XX. / .X. / .XX), the color is Red (R). 3. Create a 3×3 output grid by taking the right subgrid and replacing every grey (X) cell with the determined color. Black (.) cells remain black.

Grid: The input grid is always 5 rows by 9 columns with a black (.) background. Row 0 and row 4 are entirely black, forming borders. The two 3×3 patterns are always located at fixed positions: left pattern at rows 1-3, columns 1-3 and right pattern at rows 1-3, columns 5-7, separated by a black column (column 4). The output grid is always 3×3.

Figurative Descriptions (16 variants)

"A secret society's signet ring stamps its color onto a wax seal."

qwen3.6-35b: k=3

See: A dark hall holds two artifacts side by side on a velvet display, separated by a thin shadow. On the left sits a signet ring — a grey emblem whose silhouette belongs to one of three ancient orders. On the right lies a blank wax seal, also shaped in grey, waiting to receive the ring's impression.

Do: Read the heraldry of the left signet ring to learn which order it belongs to — each order claims a sacred color. Then press the ring into the wax seal on the right: wherever the seal bears grey, it absorbs the order's color, and wherever the seal is empty darkness, it stays untouched. The seal, now branded, is all that remains.

Grid: The display case is a narrow corridor of darkness. The two artifacts always sit in the same positions within it, like twin pedestals in a museum wing, divided by a single strip of shadow. Only the branded seal — small and square — is carried out of the hall.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

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Expected

Reasoning (29960 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Analyze the Metaphorical Description:**
*   **Scene:** A dark hall (grid of dots `.`).
*   **Artifacts:** Two artifacts side by side, separated by a shadow.
    *   Left: A signet ring (grey emblem `X`).
    *   Right: A blank wax seal (grey shape `X`).
*   **Action:**
    *   Read the heraldry of the left signet ring to find its "sacred color".
    *   Press the ring into the wax seal on the right.
    *   Where the seal has grey (`X`), it absorbs the color.
    *   Where the seal is empty (`.`), it stays empty.
*   **Output:** Only the branded seal remains. It is "small and square".

**2. Analyze the Grid Structure in Examples:**
Let's look at the input grids provided in the examples. They are 5x9 grids (5 rows, 9 columns).
The output grids are 3x3 grids.

Let's break down the input grid structure based on the description "narrow corridor... twin pedestals... divided by a single strip of shadow".
The input grid looks like this:
Row 0: `.` `.` `.` `.` `.` `.` `.` `.` `.` (Empty top border?)
Row 1: `.` `X` `X` `X` `.` `X` `.` `X` `.` (Left object, gap, Right object)
Row 2: `.` `.` `X` `.` `.` `X` `X` `X` `.`
Row 3: `.` `.` `X` `.` `.` `X` `X` `.` `.`
Row 4: `.` `.` `.` `.` `.` `.` `.` `.` `.` (Empty bottom border?)

Wait, looking at the columns:
Col 0: `.`
Col 1: `X` or `.`
Col 2: `X` or `.`
Col 3: `X` or `.`
Col 4: `.` (The "shadow" or separator)
Col 5: `X` or `.`
Col 6: `X` or `.`
Col 7: `X` or `.`
Col 8: `.`

Actually, looking at the examples, the grid is 5 rows high.
Row 0 is all dots.
Row 4 is all dots.
Rows 1, 2, 3 contain the patterns.
Columns 1, 2, 3 seem to form the left object (3x3 area).
Column 4 is the separator (all dots).
Columns 5, 6, 7 seem to form the right object (3x3 area).
Column 8 is empty.

Let's verify this hypothesis.
Input Example 1:
Row 1: `. X X X . X . X .` -> Left: `X X X`, Right: `X . X` (Wait, indices 5,6,7 are `X`, `.`, `X`? No, index 5 is `X`, 6 is `.`, 7 is `X`. Wait, let's count carefully.)
String: `. X X X . X . X .`
Indices:
0: .
1: X
2: X
3: X
4: .
5: X
6: .
7: X
8: .
So Left Object (cols 1-3):
Row 1: X X X
Row 2: . X . (from `. . X . . X X X .` -> indices 1,2,3 are `.`, `X`, `.`)
Row 3: . X . (from `. . X . . X X . .` -> indices 1,2,3 are `.`, `X`, `.`)
Wait, let's re-read the input string for Example 1 carefully.
Input:
`. . . . . . . . .`
`. X X X . X . X .`
`. . X . . X X X .`
`. . X . . X X . .`
`. . . . . . . . .`

Row 1: `.` `X` `X` `X` `.` `X` `.` `X` `.`
Cols 1-3: `X` `X` `X`
Cols 5-7: `X` `.` `X`

Row 2: `.` `.` `X` `.` `.` `X` `X` `X` `.`
Cols 1-3: `.` `X` `.`
Cols 5-7: `X` `X` `X`

Row 3: `.` `.` `X` `.` `.` `X` `X` `.` `.`
Cols 1-3: `.` `X` `.`
Cols 5-7: `X` `X` `.`

So the Left Object (Signet Ring) is a 3x3 grid:
`X X X`
`. X .`
`. X .`
This looks like a cross or a plus sign, but the top bar is full. Actually, it's a 'T' shape or a cross with a long top.
Wait, let's l

... [27281 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 960: "Scattered travelers heed gravity's call and fall into their ... [40 chars truncated]" k=1 alts: 0/0 f3cdc58f

Training Examples

Example 1

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Example 2

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Example 3

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Literal Description

See: The input is a 10×10 grid with a black (.) background. Scattered across the grid are cells of exactly four colors: Blue (B), Red (R), Green (G), and Yellow (Y). Each color appears some number of times at various positions throughout the grid.

Do: 1. Count the total number of occurrences of each of the four colors in the input grid: Blue (B), Red (R), Green (G), and Yellow (Y). 2. Construct the output as a 10×10 grid initialized entirely to black (.). 3. Assign each color to a fixed column: B → column 0, R → column 1, G → column 2, Y → column 3. 4. For each color, draw a vertical bar in its assigned column, bottom-aligned to row 9, with height equal to that color's count. That is, fill the cells from row (10 − count) through row 9 in that column with the color. 5. All other cells remain black.

Grid: Both input and output grids are 10×10. The background color is black (.). The output uses only columns 0–3 for the bar chart; columns 4–9 are entirely black. The bars are bottom-aligned (anchored to row 9) and grow upward.

Figurative Descriptions (1 variants)

"Scattered travelers heed gravity's call and fall into their designated silos, pooling at the bottom."

qwen3.6-35b: k=1

See: A dark night sky is dotted with wandering fireflies of four clans — Blue, Red, Green, and Yellow — each drifting aimlessly across the 10×10 darkness, their positions random and meaningless.

Do: Dawn breaks and gravity awakens. Each clan feels the pull of its ancestral well — a narrow shaft near the western edge of the world. The fireflies abandon their scattered positions and plummet downward through their clan's shaft, stacking upon one another at the bottom like coins dropped into tubes. The more numerous the clan, the taller their glowing column rises from the earth. No firefly is lost; every wanderer finds its well.

Grid: The world is a 10×10 night field. The four ancestral wells stand side by side at the western wall, one per clan, in order of tradition: Blue closest to the edge, then Red, Green, and Yellow. Each column of light grows upward from the ground, its height a census of its scattered kin. The rest of the sky goes dark — the fireflies have all come home.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (24667 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Background:** Black dots (`.`) representing the "dark night sky".
    *   **Fireflies (Objects):** Colored characters representing different clans:
        *   `B` = Blue
        *   `R` = Red
        *   `G` = Green
        *   `Y` = Yellow
    *   **Wells (Destinations):** Four vertical columns located at the western edge (left side) of the grid.
        *   Column 1 (index 0): Blue well.
        *   Column 2 (index 1): Red well.
        *   Column 3 (index 2): Green well.
        *   Column 4 (index 3): Yellow well.
    *   **Rest of the world:** Becomes empty (black `.`).

*   **AFFORDANCES (Actions/Properties):**
    *   Fireflies move.
    *   They move "downward" (gravity).
    *   They move into specific "wells" (columns).
    *   They stack up at the bottom.
    *   The height of the stack corresponds to the count of that color in the input grid.
    *   The order of wells is fixed: Blue (col 0), Red (col 1), Green (col 2), Yellow (col 3).

*   **TRANSFORMATION RULE:**
    1.  **Count:** Count the total number of fireflies for each color (B, R, G, Y) in the input grid.
    2.  **Locate Wells:** Identify the target columns. Based on the description "Blue closest to the edge, then Red, Green, and Yellow", and looking at the output of Example 1, the wells are in columns 0, 1, 2, and 3 respectively.
    3.  **Fill:** In the output grid, fill these columns from the bottom up with the respective colors.
        *   Column 0 (Blue): Fill bottom $N_B$ cells with 'B'.
        *   Column 1 (Red): Fill bottom $N_R$ cells with 'R'.
        *   Column 2 (Green): Fill bottom $N_G$ cells with 'G'.
        *   Column 3 (Yellow): Fill bottom $N_Y$ cells with 'Y'.
    4.  **Clear:** All other cells in the grid become `.` (black).

**2. Analyzing Example 1 to Verify**

*   **Input Grid (10x10):**
    Row 0: `. . . . . Y . G G .` -> 1 Y, 2 G
    Row 1: `. B G . . . G . . .` -> 1 B, 2 G
    Row 2: `. . . . B . . B . Y` -> 2 B, 1 Y
    Row 3: `G . . . R . . . R .` -> 1 G, 2 R
    Row 4: `. . . . . . . . . .` -> 0
    Row 5: `. . B . . . . . . .` -> 1 B
    Row 6: `. . R . . . . R . .` -> 2 R
    Row 7: `. G . . . Y G R . .` -> 1 Y, 2 G, 1 R
    Row 8: `. . . B . . . . G .` -> 1 B, 1 G
    Row 9: `. . Y . . Y . B . B` -> 2 Y, 2 B

    *Let's recount carefully.*
    **Blue (B):**
    Row 1: 1
    Row 2: 2
    Row 5: 1
    Row 8: 1
    Row 9: 2
    Total B = 1 + 2 + 1 + 1 + 2 = 7.

    **Red (R):**
    Row 3: 2
    Row 6: 2
    Row 7: 1
    Total R = 2 + 2 + 1 = 5.

    **Green (G):**
    Row 0: 2
    Row 1: 2
    Row 3: 1
    Row 7: 2
    Row 8: 1
    Total G = 2 + 2 + 1 + 2 + 1 = 8.

    **Yellow (Y):**
    Row 0: 1
    Row 2: 1
    Row 7: 1
    Row 9: 2
    Total Y = 1 + 1 + 1 + 2 = 5.

    *Wait, let me double check the counts from the input text provided

... [21883 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.54)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 971: "A popularity contest among rare wildflowers in a vast meadow" k=1 alts: 9/15 f8b3ba0a

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Literal Description

See: The input grid is composed of 2×2 colored blocks arranged in a regular grid pattern, separated by single-cell-wide black (.) borders. One color serves as the dominant background, appearing far more frequently than the others. The remaining minority colors each appear in one or more 2×2 block positions scattered among the background blocks.

Do: 1. Identify all distinct 2×2 colored blocks by scanning the grid at every position where blocks occur (they are spaced 3 cells apart both horizontally and vertically, starting at row 1, column 1). 2. Count the occurrences of each color across all block positions. 3. The color with the highest count is the background color — set it aside. 4. For each remaining minority color, record its count. 5. Sort the minority colors in descending order by count (most frequent first). 6. Output each minority color as a single row, one per line, from most frequent to least frequent.

Grid: The output grid is a single column with one row per minority color (typically 3 rows, 1 column). Each cell contains the color code of a minority color, ordered from most to least frequent. The input grid dimensions vary but always follow the pattern (2k+1) rows by (2m+1) columns, where k and m reflect the number of block rows and columns, with single-cell black borders separating all 2×2 blocks.

Figurative Descriptions (16 variants)

"A popularity contest among rare wildflowers in a vast meadow"

qwen3.6-35b: k=1

See: A meadow stretches before you, tiled with patches of flowers. One species dominates the landscape so thoroughly it has become the grass itself — the wallpaper of the world. But scattered among this sea of sameness, a few rare wildflowers have taken root, their colors defiant against the monotony. Each flower bed is a small square plot, and the black soil paths between them form a quiet grid.

Do: The meadow keeper conducts an annual census of the rare species. She walks every plot, ignoring the common ground-cover entirely — it is invisible to her practiced eye. For each rare bloom she encounters, she places a tally mark in her notebook. When the walk is done, she ranks the rare species from most abundant to least, crowning the one closest to overtaking the meadow as the first name on her list. The rarest flower, barely clinging to existence, goes last.

Grid: The keeper's final report is a single column in her ledger — one flower color per line, written top to bottom from the most commonly spotted rarity down to the loneliest bloom in the field.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (36238 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **Input Grid:** A 2D grid of characters representing colors.
    *   `.` represents black (background/soil).
    *   Other letters (R, G, B, A, Y, etc.) represent colored squares (flowers).
*   **Metaphorical Description:**
    *   "Meadow... tiled with patches of flowers."
    *   "One species dominates... wallpaper of the world." -> This implies a background color or a very frequent color. In the examples, `.` (black) seems to be the background, but the text says "One species dominates... it is invisible to her practiced eye." Wait, looking at the examples, the background is `.`. The text says "ignoring the common ground-cover entirely". This likely refers to the `.` characters.
    *   "Scattered among this sea of sameness, a few rare wildflowers have taken root." -> The non-`.` characters are the "rare wildflowers".
    *   "Each flower bed is a small square plot." -> Looking at the input grids, the colored characters appear in 2x2 blocks. For example, `G G` on one line, and `G G` on the next line below it. Let's verify this structure.
    *   "Black soil paths between them form a quiet grid." -> The `.` characters separate the blocks.
    *   "The keeper's final report is a single column in her ledger — one flower color per line, written top to bottom from the most commonly spotted rarity down to the loneliest bloom in the field." -> This is the output format. It's a list of colors sorted by frequency (descending).

*   **Training Example 1 Analysis:**
    *   **Input:**
        ```
        . . . . . . . . . .
        . G G . G G . G G .
        . . . . . . . . . .
        . B B . G G . G G .
        . . . . . . . . . .
        . G G . A A . G G .
        . . . . . . . . . .
        . G G . A A . G G .
        . . . . . . . . . .
        . G G . R R . R R .
        . . . . . . . . . .
        . R R . G G . G G .
        . . . . . . . . . .
        ```
    *   **Structure:**
        *   Rows 0, 2, 4, 6, 8, 10, 12 are all `.`.
        *   Rows 1, 3, 5, 7, 9, 11 contain colored blocks.
        *   Let's look at the blocks.
        *   Row 1: `G G` at cols 1-2, `G G` at cols 4-5, `G G` at cols 7-8.
        *   Row 3: `B B` at cols 1-2, `G G` at cols 4-5, `G G` at cols 7-8.
        *   Row 5: `G G` at cols 1-2, `A A` at cols 4-5, `G G` at cols 7-8.
        *   Row 7: `G G` at cols 1-2, `A A` at cols 4-5, `G G` at cols 7-8.
        *   Row 9: `G G` at cols 1-2, `R R` at cols 4-5, `R R` at cols 7-8.
        *   Row 11: `R R` at cols 1-2, `G G` at cols 4-5, `G G` at cols 7-8.
    *   **Interpretation of "Flower Bed":**
        *   The text says "Each flower bed is a small square plot".
        *   Looking at the grid, the colored characters form 2x2 squares.
        *   Example: Row 1 has `G G` and Row 3 has `B B`? No, Row 2 is empty.
        *   Let's check the coordinates.
       

... [33478 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 975: "Lost siblings calling out across the wilderness, finding pat ... [57 chars truncated]" k=1 alts: 0/0 f8f52ecc

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The grid has a blue (B) background. Scattered across the grid are individual colored dots (non-blue, non-A cells) of various colors. Some colors appear exactly once; others appear two or more times. Additionally, there may be horizontal or vertical bars of azure (A) cells that act as structural obstacles. Each colored dot sits isolated on the blue background.

Do: 1. Identify every non-background, non-A color in the grid. Group cells by color. 2. For any color that appears exactly once, leave it unchanged. 3. For any color that appears two or more times, connect all instances of that color into a single connected component by drawing orthogonal (horizontal and vertical) line segments between them using the shortest rectilinear paths. Specifically, form a minimum spanning tree over the instances of that color, where edges are L-shaped or straight orthogonal paths. Fill all intermediate cells along these connecting paths with that color. 4. Connecting paths must route around A cells — never overwrite an A cell. If a straight path is blocked by A cells, route around them using an L-shaped or multi-segment orthogonal detour. 5. A cells, single-instance colored cells, and the background elsewhere remain unchanged.

Grid: Grids are rectangular, varying in size (roughly 8-12 rows and 10-12 columns). The background color is blue (B). Azure (A) cells may form horizontal or vertical bars that act as impassable obstacles. The coordinate system is row-major with (0,0) at the top-left. Grid dimensions and content vary per instance but the transformation rules apply uniformly.

Figurative Descriptions (1 variants)

"Lost siblings calling out across the wilderness, finding paths home to each other while respecting the ancient walls."

qwen3.6-35b: k=1

See: A vast blue meadow stretches out under an open sky. Scattered across it are lonely travelers dressed in different colors — some red, some maroon, some yellow — each one calling out for others who share their color. Here and there, ancient azure stone walls cut across the landscape, immovable and sacred. Some travelers are truly alone — the only one of their kind — and they sit quietly, content in solitude.

Do: Each traveler who hears a kindred voice — another soul wearing the same color — feels an irresistible pull to reunite. They reach out toward one another, leaving colored footprints in the grass as they walk along straight roads running north-south or east-west. Where two siblings of the same color are separated, a trail of their shared hue blooms between them until every family is linked in one unbroken chain. But the ancient azure walls are holy ground — no footprint may touch them. Travelers must detour around these barriers, bending their paths at right angles to skirt the stone. A traveler with no kin simply stays put, leaving no trail at all. The meadow itself remembers nothing — only the reunion paths remain.

Grid: The meadow is a rectangular expanse of blue grass. Azure stone walls may run in straight horizontal or vertical lines across the terrain, acting as impassable ruins. Colored travelers appear as single dots scattered about. The sky watches from the top-left corner, and the meadow stretches downward and to the right.

qwen3.6-35b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (32946 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Background (B - Blue):** The "meadow" or empty space.
    *   **Obstacles (A - Azure):** "Ancient azure stone walls". Impassable.
    *   **Travelers (R, Y, M, O, G, etc. - various colors):** "Lonely travelers". They are single dots of specific colors.
    *   **Output (Trail):** "Colored footprints" connecting travelers of the same color.

*   **AFFORDANCES (Capabilities):**
    *   **Travelers:** Can move North, South, East, West. Can connect to other travelers of the same color.
    *   **Obstacles (A):** Cannot be crossed or touched by the trail.
    *   **Background (B):** Can be overwritten by the trail color.

*   **TRANSFORMATION RULE:**
    *   Identify all pairs (or groups) of identical colored non-background, non-obstacle pixels.
    *   For each color group, connect them with a path.
    *   The path must be a straight line (Manhattan distance logic, but specifically "straight roads running north-south or east-west").
    *   Wait, the description says: "leaving colored footprints in the grass as they walk along straight roads running north-south or east-west." and "Where two siblings of the same color are separated, a trail of their shared hue blooms between them".
    *   It also says: "Travelers must detour around these barriers, bending their paths at right angles to skirt the stone."
    *   This implies finding a path between same-colored pixels.
    *   However, looking at Example 1:
        *   Input has Red (R) at (1,4) and (2,4) [0-indexed? No, let's look at the grid].
        *   Let's parse Example 1 Input carefully.
        *   Row 0: B B B B B B B B B B
        *   Row 1: B B B B R B B B B B  -> R at (1, 4)
        *   Row 2: B B B B R B B B B B  -> R at (2, 4)
        *   Row 3: B B A A A A A A B B  -> A's at (3, 2) to (3, 7)
        *   Row 4: B B B B B B B B B B
        *   Row 5: B R B R B B B B B B  -> R at (5, 1) and (5, 3)
        *   Row 6-9: All B.

        *   Output:
        *   Row 1: B B B B R B B B B B (R at 1,4 stays)
        *   Row 2: B R R R R B B B B B (R at 2,1, 2,2, 2,3, 2,4). Wait, input had R at (2,4). Output has R at (2,1) to (2,4).
        *   Row 3: B R A A A A A A B B (R at 3,1). A's are preserved.
        *   Row 4: B R B B B B B B B B (R at 4,1).
        *   Row 5: B R R R B B B B B B (R at 5,1, 5,2, 5,3). Input had R at (5,1) and (5,3).

    *   Let's re-examine the connections.
    *   Input Reds: (1,4), (2,4), (5,1), (5,3).
    *   Output Reds:
        *   (1,4) is connected to (2,4) directly? Yes, vertical line.
        *   (2,4) is connected to (2,1)? Horizontal line?
        *   (2,1) is connected to (3,1)? Vertical line?
        *   (3,1) is connected to (4,1)? Vertical line?
        *   (4,1) is connected to (5,1)? Vertical line?
        *   (5,1) is connected to (5,3)? Horizontal line?
    *   It s

... [30276 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

No grid

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 977: "A tapestry weaver mends a moth-eaten hole by reading the rhy ... [29 chars truncated]" k=2 alts: 5/15 f9012d9b

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input grid contains a pattern of colored cells that tiles periodically in both rows and columns, forming a repeating 2D mosaic. A rectangular region of the grid has been replaced with black (.) cells, creating a 'hole' in the otherwise regular tiling pattern. The non-black portion of the grid is fully consistent with a single repeating tile.

Do: 1. Identify the repeating tile by finding the row period and column period of the non-black cells. Compare rows and columns in the intact (non-black) region to determine the smallest periods P_r (row period) and P_c (column period) such that the pattern repeats every P_r rows and every P_c columns. 2. Extract one copy of the repeating tile: a P_r × P_c subgrid from any fully intact region of the grid. 3. Locate the rectangular region of black (.) cells. 4. For each black cell at position (r, c), compute the tile value as tile[r mod P_r][c mod P_c]. 5. Output only the rectangular block of restored values that replaces the black cells, matching the dimensions of the hole.

Grid: The grid dimensions vary across instances. The grid is composed entirely of colored cells arranged in a periodic tiling pattern, with one contiguous rectangular region of black (.) cells representing the missing portion. The output grid has the same dimensions as the missing rectangular region and contains the tile values that fill the hole.

Figurative Descriptions (16 variants)

"A tapestry weaver mends a moth-eaten hole by reading the rhythm of the surviving threads."

qwen3.6-35b: k=2

See: A grand tapestry hangs on the wall, its colored threads woven in a endlessly repeating motif — a small melodic phrase played over and over across rows and columns. But moths have eaten through one corner, leaving a rectangle of bare black canvas where the pattern should continue. The surviving fabric hums with perfect regularity, every stitch loyal to the same small refrain.

Do: Listen to the tapestry's song — find the shortest melodic phrase that, when looped, reproduces every intact thread. Once you know the refrain by heart, hold it up to the moth-eaten hole and let the melody fill in what the moths stole. Sing only the missing notes — the patch that makes the tapestry whole again.

Grid: The tapestry varies in size but is always woven from a small repeating motif of colored threads tiling seamlessly in both directions. The moth-eaten hole is a contiguous rectangle of bare black canvas. Your repair patch matches the hole's dimensions exactly, carrying only the colors the refrain demands at each position.

qwen3.6-35b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (28138 chars)

The user wants me to solve a grid transformation puzzle.

**1. Analyze the Input and Task:**
*   **Input:** A grid of characters representing colors. Some characters are '.', representing black (the "moth-eaten" hole).
*   **Task:** Fill in the '.' characters based on a repeating pattern found in the rest of the grid.
*   **Metaphor:** A tapestry with a repeating motif. A hole is cut out. I need to figure out the motif and fill the hole.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input:
        ```
        A M . M
        M A M A
        A M A M
        M A M A
        ```
    *   Output:
        ```
        A
        ```
    *   Observation: The hole is at (0, 2) (0-indexed). The grid is 4x4.
    *   Let's look at the pattern.
        Row 0: A M [?] M
        Row 1: M A M A
        Row 2: A M A M
        Row 3: M A M A
    *   Looking at columns:
        Col 0: A, M, A, M -> Pattern A, M repeating?
        Col 1: M, A, M, A -> Pattern M, A repeating?
        Col 2: ?, M, A, M -> If pattern is M, A, A, M? Or maybe the whole grid is a tiling.
    *   Let's check the periodicity.
        Row 1: M A M A. Period 2 (M A).
        Row 2: A M A M. Period 2 (A M).
        Row 3: M A M A. Period 2 (M A).
        Row 0: A M . M. If period is 2, A M A M. So the missing char is A.
    *   Let's check vertical periodicity.
        Col 0: A M A M. Period 2.
        Col 1: M A M A. Period 2.
        Col 2: . M A M. If period 2, it should be A M A M. So top is A.
        Col 3: M A M A. Period 2.
    *   The missing character is 'A'. The output is just the patch, which is 'A'.

*   **Example 2:**
    *   Input:
        ```
        R B R B R
        B B B B B
        R B R B R
        . . B B B
        . . R B R
        ```
    *   Output:
        ```
        B B
        R B
        ```
    *   Hole location: Bottom-left 2x2 area.
        (3,0), (3,1)
        (4,0), (4,1)
    *   Let's analyze the pattern in the visible parts.
        Row 0: R B R B R. Looks like period 2 (R B).
        Row 1: B B B B B. Looks like period 1 (B) or period 2 (B B).
        Row 2: R B R B R. Period 2 (R B).
        Row 3: . . B B B. The visible part is B B B.
        Row 4: . . R B R. The visible part is R B R.
    *   Let's look at columns.
        Col 0: R, B, R, ., .
        Col 1: B, B, B, ., .
        Col 2: R, B, R, B, R. Period 2 (R B).
        Col 3: B, B, B, B, B. Period 1 (B).
        Col 4: R, B, R, B, R. Period 2 (R B).
    *   Let's hypothesize a 2D repeating pattern.
        Row 0: R B R B R
        Row 1: B B B B B
        Row 2: R B R B R
        Row 3: ? ? B B B
        Row 4: ? ? R B R
    *   If the pattern repeats every 2 rows:
        Row 0 == Row 2 == Row 4?
        Row 0: R B R B R
        Row 2: R B R B R
        Row 4: . . R B R. Matches R B R B R if the missing parts are R B.
        So Row 4 should be R B R B R. The missing chars at (4,0) and (4,1) are R and B.
    *   If the pattern repeats every 2 rows, Row 1 == Row 3?
  

... [25288 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.06)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 983: "A pair of scissors snips along the dotted line, and the scra ... [19 chars truncated]" k=3 alts: 13/15 fbf15a0b

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

Input

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Output

Literal Description

See: The input grid has an azure (A) background containing one or more rectangular regions of colored pattern (repeating motifs of a non-azure color on every other cell). Exactly two grey (X) marker cells appear on one edge of the grid, positioned two cells apart from each other along that edge. The X markers always sit on the outermost row or column.

Do: 1. Locate the two X marker cells. They will be on the same edge (top row, bottom row, left column, or right column), spaced 2 cells apart. 2. Determine the axis the X markers define: if they are on the top or bottom row, the axis is vertical (columns); if on the left or right column, the axis is horizontal (rows). 3. Halve the grid along that axis, splitting it into two equal parts. If the axis is vertical, split into a left half and right half; if horizontal, split into a top half and bottom half. 4. Keep the half that contains the X markers; discard the other half. 5. In the kept half, replace every X cell with azure (A). The result is the output grid.

Grid: The input grid has even dimensions along the axis being halved (so it splits cleanly in two). The output grid is exactly half the size of the input along the halved axis and the same size along the other axis. The background color is azure (A). The colored pattern regions and their internal spacing are preserved unchanged in the output, except that X markers become A.

Figurative Descriptions (16 variants)

"A pair of scissors snips along the dotted line, and the scrap paper falls away."

qwen3.6-35b: k=3

See: An azure canvas stretches out, decorated with repeating tapestry patterns woven in various colors. Somewhere along one edge, two grey pins have been pressed into the frame — a perforation mark, like the tear-here dots on a coupon.

Do: The two pins mark where the scissors should cut. They whisper which direction to slice — across or down — like a dotted line on wrapping paper. Cut the canvas in half along that line. The half with the pins is the keeper; the other half flutters to the floor like a trimmed margin. Once you've kept your piece, pull out the pins and patch the tiny holes with azure, leaving no trace they were ever there.

Grid: The canvas is always sized so the scissors cut cleanly in two — no ragged edges. The kept piece is exactly half the original in one direction, unchanged in the other. The woven tapestry patterns survive the cut perfectly intact; only the pin-holes vanish.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (33101 chars)

The user wants me to solve a grid transformation puzzle based on a metaphorical description and training examples.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Canvas:** The main grid background, usually filled with a specific color (Azure 'A' in the description, but in examples, it's 'A' or 'A' mixed with patterns). In the test input, 'A' seems to be the background color.
    *   **Tapestry Patterns:** The repeating colored elements (like 'W' for maroon in the test input, or 'B' for blue in Ex 1, 'O' for orange in Ex 2, 'G' for green in Ex 3).
    *   **Pins:** The 'X' (grey) characters. They appear in pairs.
    *   **Scissors/Cut:** The action performed based on the position of the pins.

*   **AFFORDANCES (Capabilities/Actions):**
    *   **Pins ('X'):** They mark a location. They indicate a cut line.
    *   **Cut:** The grid is split into two halves.
    *   **Keeper:** One half is kept, the other is discarded.
    *   **Repair:** The spots where pins were are filled with the background color ('A').

*   **TRANSFORMATION RULE:**
    *   **Locate Pins:** Find the two 'X' characters in the input grid.
    *   **Determine Cut Direction:**
        *   If the pins are in the same row (same Y coordinate), the cut is vertical (across columns).
        *   If the pins are in the same column (same X coordinate), the cut is horizontal (across rows).
        *   Wait, let's look at the examples to confirm.
    *   **Determine Cut Position:** The cut happens *between* the pins or *at* the pins? The description says "The two pins mark where the scissors should cut." and "Cut the canvas in half along that line."
    *   **Select Half:** "The half with the pins is the keeper". This implies the pins are on the edge or define the boundary. Let's look at the examples.

**2. Analyzing Training Examples**

*   **Example 1:**
    *   Input size: 21 rows x 20 columns.
    *   Pins ('X') are at:
        *   Row 0, Col 0 (0-indexed) -> (0, 0)
        *   Row 2, Col 0 -> (2, 0)
    *   Wait, looking at the input text:
        Row 0: `X A A ...`
        Row 1: `A A A ...`
        Row 2: `X B A ...`
    *   Pins are at (0,0) and (2,0). They are in the same column (Column 0).
    *   Wait, the description says "Somewhere along one edge".
    *   Let's check the output.
    *   Output size: 10 rows x 20 columns.
    *   The input had 21 rows. The output has 10 rows.
    *   Wait, 21 rows -> 10 rows? That's not exactly half. 21/2 = 10.5.
    *   Let's re-read the input carefully.
    *   Input rows:
        0: X A A ...
        1: A A A ...
        2: X B A ...
        3: A A A ...
        4: A B A ...
        5: A A A ...
        6: A B A ...
        7: A B A ...
        8: A A A ...
        9: A B A ...
        10: A B A ...
        11: A A A ...
        12: A B A ...
        13: A A A ...
        14: A B A ...
        15: A A A ...
        16: A A A ...
        17: A A A ...
        18: A A A ...
        19: A A A ...
        20: A A A ...
 

... [30278 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.44)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 988: "Each building casts a green shadow whose length reveals how ... [29 chars truncated]" k=3 alts: 0/0 fcc82909

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

See: The input grid contains several 2x2 blocks of non-black colored cells, each placed at different positions on a black background. Each block occupies exactly a 2-column by 2-row region. The cells within each block may contain repeated or distinct colors.

Do: For each 2x2 colored block in the input: (1) Count the number of unique colors present in that block's four cells. (2) Directly below the block, fill a region that is 2 columns wide (matching the block's columns) and extends downward for a number of rows equal to the unique color count. Fill this region with green (G). (3) Leave the original 2x2 block unchanged.

Grid: The grid is 10x10 with a black (.) background. All non-background content consists of 2x2 blocks of colored cells that do not overlap or touch each other. The output grid has the same dimensions, with the original blocks preserved and green extensions added below each block.

Figurative Descriptions (1 variants)

"Each building casts a green shadow whose length reveals how many departments work inside."

qwen3.6-35b: k=3

See: Scattered across a dark cityscape, small 2×2 buildings stand like colorful office blocks, each floor painted in the livery of the departments housed within.

Do: When the sun rises, every building casts a green shadow straight downward onto the pavement. The more distinct departments (unique colors) sharing a building, the longer its shadow stretches — one story of green for each department. The buildings themselves remain standing, unchanged.

Grid: The city is a 10×10 block of dark pavement. Buildings never crowd each other, and each shadow falls neatly below its building, exactly as wide as the building itself.

qwen3.6-35b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (33983 chars)

The user wants me to solve a grid transformation puzzle.

**1. Conceptual Digestion**

*   **CAST (Roles):**
    *   **Background:** The grid is mostly filled with `.` (black/dark pavement).
    *   **Buildings:** 2x2 blocks of colored cells. These represent "office blocks".
    *   **Shadows:** 2x2 blocks of `G` (green) that appear below the buildings.
    *   **Sun:** The source of the shadows, implied to be coming from above (since shadows fall downward).

*   **AFFORDANCES (Capabilities/Properties):**
    *   **Buildings:** They are static. They don't move. They are composed of 4 cells in a 2x2 square.
    *   **Colors within buildings:** The colors inside the 2x2 building determine the length of the shadow.
    *   **Shadows:** They are cast "straight downward". They are exactly as wide as the building (2 columns). They are green (`G`).
    *   **Shadow Length:** "one story of green for each department". A "story" usually implies a row. So, the number of rows of green `G` below the building equals the number of *unique* colors in that 2x2 building.

*   **TRANSFORMATION RULE:**
    1.  Identify all 2x2 blocks of non-black (`.`) cells in the input grid. These are the "buildings".
    2.  For each building:
        *   Determine the set of unique colors present in its 4 cells.
        *   Count the number of unique colors ($N$).
        *   Generate a shadow of color `G` (green) directly below the building.
        *   The shadow will be 2 columns wide (same as the building).
        *   The shadow will be $N$ rows high.
        *   The shadow starts immediately below the bottom row of the building.
    3.  The original building cells remain unchanged.
    4.  If shadows overlap or go off the grid, handle accordingly (though the prompt implies neat placement). If a shadow overlaps another building, usually in these puzzles, the shadow might overwrite or be overwritten, but looking at the examples, shadows seem to just fill empty space. Let's check for overlaps in examples.
    5.  The background remains `.` where no building or shadow exists.

**2. Analyzing Training Examples**

*   **Example 1:**
    *   Building 1: Top-left-ish.
        *   Cells: (1,2)=Y, (1,3)=A, (2,2)=W, (2,3)=Y.
        *   Colors: {Y, A, W}. Note: Y appears twice.
        *   Unique colors: Y, A, W. Count = 3.
        *   Shadow: 2x3 block of G below it.
        *   Building is at rows 1-2, cols 2-3.
        *   Shadow should be at rows 3-5, cols 2-3.
        *   Let's check output.
        *   Row 3: `G G` at cols 2-3.
        *   Row 4: `G G` at cols 2-3.
        *   Row 5: `G G` at cols 2-3.
        *   Wait, the output shows:
            Row 3: `. . G G . . . . . .`
            Row 4: `. . G G . . R B . .`
            Row 5: `. . G G . . B R . .`
            Row 6: `. . . . . . G G . .`
            Row 7: `. . . . . . G G . .`
        *   Wait, let's look closer at Example 1 Input.
            Row 1: `.`
            Row 2: `. . Y A . . . . . .` (Indices 2,3 are Y, A

... [31070 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.58)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

MARC2 Puzzle Inspector March 26, 2026

▶ Task 1: "A narcissistic painting reproduces itself wherever it sees i ... [18 chars truncated]" k=1 alts: 0/0 007bbfb7

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 25: "A stone skipping across a dark lake leaves ripples where it ... [88 chars truncated]" k=2 alts: 0/0 0b17323b

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 27: "A costume party where everyone swaps disguises according to ... [25 chars truncated]" k=2 alts: 0/0 0becf7df

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 35: "Seeds dropped in soil grow into sedimentary rock layers, eac ... [44 chars truncated]" k=1 alts: 10/15 0f63c0b9

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 45: "Small tribes without enough members to survive are absorbed ... [20 chars truncated]" k=2 alts: 3/15 12eac192

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 52: "Three stars form a constellation; the night sky traces their ... [25 chars truncated]" k=1 alts: 0/0 1478ab18

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 69: "Two teams combine their footprints to map everywhere anyone ... [10 chars truncated]" k=1 alts: 0/0 195ba7dc

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 82: "Two monarchs divide a kingdom, each stamping their seal upon ... [22 chars truncated]" k=1 alts: 0/0 1bfc4729

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 96: "A king in his castle banishes all imposters wearing his colo ... [20 chars truncated]" k=2 alts: 0/0 1e81d6f9

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 119: "A drumline marches in formation, and every third beat strike ... [36 chars truncated]" k=1 alts: 0/0 22a4bbc2

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 128: "Lighthouses signaling across the darkness" k=1 alts: 0/0 253bf280

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 132: "A volcano erupts a beam of light through its crater in the d ... [18 chars truncated]" k=3 alts: 0/0 25d487eb

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 146: "Four royal courts compete for territory, and the strongest c ... [28 chars truncated]" k=1 alts: 0/0 281123b4

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 161: "A ghost haunts a lonely grave, conjuring an echo of the cath ... [24 chars truncated]" k=3 alts: 0/0 2c737e39