MARC2 Puzzle Inspector

▶ Task 14: "Each star casts a shadow of everything it is not." k=1 alts: 0/0 0692e18c

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 3×3 grid containing some cells filled with a single foreground color and the remaining cells black (empty).

Do: First, create the inverse of the input grid: swap every foreground-colored cell to black and every black cell to the foreground color. This produces a 3×3 'stamp' pattern. Next, construct a 9×9 output grid initialized to all black. For each cell in the original input that contains the foreground color, place a copy of the stamp pattern into the corresponding 3×3 block of the output grid. The output is a 3×3 arrangement of 3×3 blocks; the block at row r, column c corresponds to input cell (r, c). Blocks corresponding to black input cells remain all black.

Grid: The input grid is always 3×3. The output grid is always 9×9, composed of a 3×3 tiling of 3×3 blocks. The background color is black (.). Only one foreground color appears in any given puzzle.

Figurative Descriptions (1 variants)

"Each star casts a shadow of everything it is not."

gemma-4-31b: k=1

See: A small constellation of bright stars floats in a 3×3 night sky. Some cells glow with a single color; the rest are dark void.

Do: Every star is narcissistic — it refuses to look at itself. Instead, it gazes into a mirror and sees only what it is not: where it was bright, the reflection is dark, and where the sky was empty, the reflection glows. Now imagine the night sky expanding into a grand 3×3 mosaic of smaller skies. Each star gets to project its inside-out reflection into the patch of sky that matches its home position. The empty patches of the original sky — the voids where no star lived — remain pure darkness, with nothing to cast a shadow there.

Grid: The constellation is always a 3×3 patch. The grand mosaic is a 9×9 canvas — think of it as nine little 3×3 rooms arranged in the same shape as the original sky. Only rooms belonging to stars receive the inverted reflection; rooms belonging to the void stay unlit.

gemma-4-31b — MARC valid, solved with 1 example

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Reasoning (2980 chars)

### Conceptual Digestion

**1. Identify the CAST:**
*   **The Constellation (Input Grid):** A 3x3 grid where colored cells represent "stars" and black cells (`.`) represent the "void".
*   **The Grand Mosaic (Output Grid):** A 9x9 grid composed of nine 3x3 "rooms" (sub-grids).
*   **The Reflection:** An inverted version of the original 3x3 grid.

**2. Identify the AFFORDANCES:**
*   **Stars (Colored Cells):** Act as triggers. If a cell at position $(r, c)$ in the 3x3 input is colored, the corresponding 3x3 room at $(r, c)$ in the 9x9 output is filled with the "inverted reflection".
*   **Void (Black Cells):** Act as inhibitors. If a cell at position $(r, c)$ in the 3x3 input is black, the corresponding 3x3 room at $(r, c)$ in the 9x9 output remains entirely black.
*   **Inversion:** In the reflection, a cell that was colored in the original 3x3 grid becomes black, and a cell that was black becomes the color of the star that triggered the room.

**3. Identify the TRANSFORMATION RULE:**
1.  Analyze the 3x3 input grid.
2.  For each cell $(r, c)$ in the 3x3 grid:
    *   If `input[r][c]` is black (`.`): The 3x3 block in the output starting at `(r*3, c*3)` is all black.
    *   If `input[r][c]` is a color (e.g., `G`): The 3x3 block in the output starting at `(r*3, c*3)` is filled based on the original 3x3 grid:
        *   If `input[i][j]` was black, `output[r*3 + i][c*3 + j]` becomes the color `G`.
        *   If `input[i][j]` was colored, `output[r*3 + i][c*3 + j]` becomes black (`.`).

---

### Applying the Rule to Test Input

**Input:**
`. . G`
`G G .`
`. G .`

**Step 1: Identify Star Positions**
*   (0, 2): Green (G)
*   (1, 0): Green (G)
*   (1, 1): Green (G)
*   (2, 1): Green (G)

**Step 2: Determine the Inverted Reflection (for Green)**
Original:
`. . G`
`G G .`
`. G .`
Inverted (Black $\leftrightarrow$ Green):
`G G .`
`. . G`
`G . G`

**Step 3: Map to 9x9 Grid**
*   Room (0, 0): Void $\rightarrow$ All `.`
*   Room (0, 1): Void $\rightarrow$ All `.`
*   Room (0, 2): Star (G) $\rightarrow$ Inverted Reflection
*   Room (1, 0): Star (G) $\rightarrow$ Inverted Reflection
*   Room (1, 1): Star (G) $\rightarrow$ Inverted Reflection
*   Room (1, 2): Void $\rightarrow$ All `.`
*   Room (2, 0): Void $\rightarrow$ All `.`
*   Room (2, 1): Star (G) $\rightarrow$ Inverted Reflection
*   Room (2, 2): Void $\rightarrow$ All `.`

**Constructing the rows:**
Row 0: `.` `.` `.` | `.` `.` `.` | `G` `G` `.`
Row 1: `.` `.` `.` | `.` `.` `.` | `.` `.` `G`
Row 2: `.` `.` `.` | `.` `.` `.` | `G` `.` `G`
Row 3: `G` `G` `.` | `G` `G` `.` | `.` `.` `.`
Row 4: `.` `.` `G` | `.` `.` `G` | `.` `.` `.`
Row 5: `G` `.` `G` | `G` `.` `G` | `.` `.` `.`
Row 6: `.` `.` `.` | `G` `G` `.` | `.` `.` `.`
Row 7: `.` `.` `.` | `.` `.` `G` | `.` `.` `.`
Row 8: `.` `.` `.` | `G` `.` `G` | `.` `.` `.`

ANSWER:
. . . . . . G G .
. . . . . . . . G
. . . . . . G . G
G G . G G . . . .
. . G . . G . . .
G . G G . G . . .
. . . G G . . . .
. . . . . G . . .
. . . G . G . . .

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.25)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 35: "Seeds dropped in soil grow into sedimentary rock layers, eac ... [44 chars truncated]" k=3 alts: 11/15 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."

gemma-4-31b: k=3

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.

gemma-4-31b — MARC valid, solved with 3 examples

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Reasoning (3211 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Mineral Seeds**: Single colored pixels in the input grid.
    *   **Strata**: Horizontal sections of the grid assigned to a specific seed.
    *   **Solid Veins**: Full horizontal lines of color.
    *   **Hollow Corridors**: Rows with color only on the left and right edges.

2.  **AFFORDANCES**:
    *   The **y-coordinate (row)** of a seed determines which color controls which section of the grid.
    *   The **x-coordinate (column)** of a seed is ignored.
    *   The **top row (0)** and **bottom row (14)** are always solid veins of the color controlling that section.

3.  **TRANSFORMATION RULE**:
    *   Identify the row indices of all seeds in order: $S_1, S_2, \dots, S_n$.
    *   The grid is divided into $n$ regions.
    *   The boundary between region $i$ and region $i+1$ is the midpoint between seed $S_i$ and seed $S_{i+1}$: $\text{Boundary}_i = \lfloor (S_i + S_{i+1}) / 2 \rfloor$.
    *   **Region 1** (Seed $S_1$): Rows $0$ to $\text{Boundary}_1$.
    *   **Region $i$** (Seed $S_i$): Rows $\text{Boundary}_{i-1} + 1$ to $\text{Boundary}_i$.
    *   **Region $n$** (Seed $S_n$): Rows $\text{Boundary}_{n-1} + 1$ to $14$.
    *   **Within each region**:
        *   The row containing the seed $S_i$ is a **solid line** of color $C_i$.
        *   The very first row (0) and very last row (14) of the entire grid are **solid lines** of the color of the region they belong to.
        *   All other rows in the region are **hollow** (color $C_i$ at index 0 and 14, black `.` in between).

### Applying the Rule to Test Input

**Seeds**:
1.  Azure (A) at row 2
2.  Red (R) at row 4
3.  Blue (B) at row 9
4.  Green (G) at row 12

**Boundaries**:
*   B1 (A to R): $\lfloor (2+4)/2 \rfloor = 3$
*   B2 (R to B): $\lfloor (4+9)/2 \rfloor = 6$
*   B3 (B to G): $\lfloor (9+12)/2 \rfloor = 10$

**Regions**:
*   **Region A (Rows 0-3)**: Seed at row 2. Solid: 0, 2. Hollow: 1, 3.
*   **Region R (Rows 4-6)**: Seed at row 4. Solid: 4. Hollow: 5, 6.
*   **Region B (Rows 7-10)**: Seed at row 9. Solid: 9. Hollow: 7, 8, 10.
*   **Region G (Rows 11-14)**: Seed at row 12. Solid: 12, 14. Hollow: 11, 13.

**Row-by-Row Construction**:
0: A A A A A A A A A A A A A A A (Top edge)
1: A . . . . . . . . . . . . . A
2: A A A A A A A A A A A A A A A (Seed A)
3: A . . . . . . . . . . . . . A
4: R R R R R R R R R R R R R R R (Seed R)
5: R . . . . . . . . . . . . . R
6: R . . . . . . . . . . . . . R
7: B . . . . . . . . . . . . . B
8: B . . . . . . . . . . . . . B
9: B B B B B B B B B B B B B B B (Seed B)
10: B . . . . . . . . . . . . . B
11: G . . . . . . . . . . . . . G
12: G G G G G G G G G G G G G G G (Seed G)
13: G . . . . . . . . . . . . . G
14: G G G G G G G G G G G G G G G (Bottom edge)

ANSWER:
A A A A A A A A A A A A A A A
A . . . . . . . . . . . . . A
A A A A A A A A A A A A A A A
A . . . . . . . . . . . . . A
R R R R R R R R R R R R R R R
R . . . . . . . . . . . . . R
R . . . . . . . . . . . . . R
B . . . . . . . . . . . . . 

... [211 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.97)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 90: "A compass rose unfurls its cardinal and diagonal beams from ... [64 chars truncated]" k=1 alts: 0/0 1d398264

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 a single 3x3 block of non-black colored cells. The block consists of nine distinct cells arranged in three rows: a top row, a middle row, and a bottom row, each containing three colored cells.

Do: 1. Locate the 3x3 block of non-black cells. Label its cells as: top-left (TL), top-center (TC), top-right (TR), mid-left (ML), center (C), mid-right (MR), bottom-left (BL), bottom-center (BC), bottom-right (BR). 2. The middle row becomes a horizontal axis spanning the full width of the grid. Fill every cell to the left of ML in that row with ML's color. Fill every cell to the right of MR in that row with MR's color. The center cell C remains unchanged. 3. From TC, draw a vertical ray upward (same column) using TC's color, extending to the top edge of the grid. 4. From TL, draw a diagonal ray going up-and-left (one step up, one step left per cell) using TL's color, until hitting a grid edge. 5. From TR, draw a diagonal ray going up-and-right (one step up, one step right per cell) using TR's color, until hitting a grid edge. 6. From BC, draw a vertical ray downward (same column) using BC's color, extending to the bottom edge of the grid. 7. From BL, draw a diagonal ray going down-and-left (one step down, one step left per cell) using BL's color, until hitting a grid edge. 8. From BR, draw a diagonal ray going down-and-right (one step down, one step right per cell) using BR's color, until hitting a grid edge. 9. The original 3x3 block cells remain in place. All other cells stay black.

Grid: The output grid has the same dimensions as the input grid. The background is black (.). The 3x3 block remains at its original position, with six rays emanating from the top and bottom rows and the middle row extended horizontally across the full grid width.

Figurative Descriptions (1 variants)

"A compass rose unfurls its cardinal and diagonal beams from a jeweled core, while the equator belt cinches the world in two."

gemma-4-31b: k=1

See: A tiny jeweled brooch—three gems across, three deep—sits pinned to a vast dark tapestry. Its middle row is the equator, its center stone the heart.

Do: The equator awakens: the left and right stones spill their color outward like mercury, flooding the entire horizontal band from edge to edge. Meanwhile, the top three gems each launch a flare into the darkness above—the center gem fires straight up like a lighthouse beam, while its two neighbors shoot outward along their respective diagonals, streaking toward the corners of the sky. The bottom three gems mirror this below: the center drops a plumb line straight down, and its neighbors scatter along falling diagonals like sparks tumbling away from a firework. Each flare carries the color of the gem that launched it.

Grid: The tapestry keeps its original size and darkness. The brooch remains pinned in place, untouched. Six colored rays radiate from the top and bottom gems—two diagonals and one vertical above, two diagonals and one vertical below—while the equator band stretches unbroken from edge to edge through the middle row.

gemma-4-31b — MARC valid, solved with 1 example

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Prediction

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Reasoning (4766 chars)

### Conceptual Digestion

1.  **The CAST**:
    *   **The Tapestry**: The background grid (black `.`).
    *   **The Brooch**: A $3 \times 3$ block of colored gems located at a specific position in the grid.
    *   **The Equator**: The middle row of the $3 \times 3$ brooch.
    *   **The Heart**: The center gem of the brooch.
    *   **The Flares/Rays**: Lines of color extending from the top and bottom rows of the brooch.

2.  **The AFFORDANCES**:
    *   The **Equator** (middle row) can expand horizontally to fill the entire width of the grid.
    *   The **Top Row** gems can project lines upwards:
        *   Left gem $\rightarrow$ Diagonal (up-left).
        *   Center gem $\rightarrow$ Vertical (straight up).
        *   Right gem $\rightarrow$ Diagonal (up-right).
    *   The **Bottom Row** gems can project lines downwards:
        *   Left gem $\rightarrow$ Diagonal (down-left).
        *   Center gem $\rightarrow$ Vertical (straight down).
        *   Right gem $\rightarrow$ Diagonal (down-right).

3.  **The TRANSFORMATION RULE**:
    *   **Step 1 (Equator)**: Identify the middle row of the $3 \times 3$ brooch. Fill the entire row of the grid with the colors of the left and right gems of that row, while keeping the center gem (the heart) as is. Specifically, the left gem's color fills from the left edge to the center, and the right gem's color fills from the center to the right edge.
    *   **Step 2 (Top Flares)**:
        *   From the top-left gem $(r, c)$, draw a line of its color diagonally up-left until the grid boundary.
        *   From the top-center gem $(r, c+1)$, draw a line of its color vertically up until the grid boundary.
        *   From the top-right gem $(r, c+2)$, draw a line of its color diagonally up-right until the grid boundary.
    *   **Step 3 (Bottom Flares)**:
        *   From the bottom-left gem $(r+2, c)$, draw a line of its color diagonally down-left until the grid boundary.
        *   From the bottom-center gem $(r+2, c+1)$, draw a line of its color vertically down until the grid boundary.
        *   From the bottom-right gem $(r+2, c+2)$, draw a line of its color diagonally down-right until the grid boundary.
    *   **Step 4**: The original $3 \times 3$ brooch remains in place.

### Applying to Test Input
*   **Brooch Position**: Top-left corner at $(2, 3)$ (0-indexed).
    *   Row 2: `Y R X`
    *   Row 3: `R W X`
    *   Row 4: `Y B B`
*   **Equator (Row 3)**: Left gem `R`, Center `W`, Right `X`.
    *   Fill Row 3: `R R R W X X X X X X X X X X X` (Wait, the rule says "left and right stones spill their color outward").
    *   Left side (cols 0-2) becomes `R`. Right side (cols 5-15) becomes `X`.
    *   Row 3: `R R R R W X X X X X X X X X X X`
*   **Top Flares (Row 2)**:
    *   Left `Y` at $(2, 3)$: Diagonal up-left $\rightarrow (1, 2), (0, 1)$.
    *   Center `R` at $(2, 4)$: Vertical up $\rightarrow (1, 4), (0, 4)$.
    *   Right `X` at $(2, 5)$: Diagonal up-right $\rightarrow (1, 6), (0, 7)$.
*   *

... [1766 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 1.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 100: "Finding the one bird that stayed with its flock while all ot ... [26 chars truncated]" k=1 alts: 3/15 1f85a75f

Training Examples

Example 1

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Example 2

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Output

Literal Description

See: The input is a large grid (typically 30x30) with a black background. Several colors are scattered sparsely and seemingly randomly across the grid as noise pixels. Among all the colors present, exactly one color appears only in a small, compact, contiguous cluster rather than being scattered widely. This rare color forms a distinct shape, typically spanning only a few rows and columns, while every other non-black color appears many times distributed broadly across the entire grid.

Do: 1. For each non-black color in the grid, count how many disconnected pixels or small groups it forms and assess its spatial distribution. 2. Identify the one color whose pixels are all concentrated in a single small, compact region rather than scattered across the grid. This is the signal color; all other colors are noise. 3. Find the bounding box of all pixels of the signal color — the smallest rectangle that contains every pixel of that color. 4. Extract that bounding box from the grid, preserving the signal-color pixels in their positions and replacing all other cells (black or noise-colored) within the bounding box with black. 5. Output the extracted bounding box as the result.

Grid: The input grid is large (e.g., 30x30) with a black (.) background. The output grid is small, matching the dimensions of the bounding box of the signal-color cluster — typically between 3x3 and 5x5. The output contains only black (.) and the signal color.

Figurative Descriptions (16 variants)

"Finding the one bird that stayed with its flock while all others scattered in a storm."

gemma-4-31b: k=1

See: A vast dark night sky is filled with fireflies of various colors, each species flung far and wide by the wind — their lights blinking in lonely isolation across the expanse. But one species refused to scatter. Somewhere in the darkness, a small family of identically-colored lights huddles together, their glow forming a tiny constellation. They are the only ones who kept their formation while every other color drifted apart into solitary wandering.

Do: Search the sky for the loyal flock — the one color whose members never abandoned each other. Every other color is a diaspora, its individuals lost across the void. But this one color held hands. Once you find the huddled family, draw a frame around their gathering and lift it out of the darkness. Let the scattered loners fade away; only the constellation and the night around it remain.

Grid: The night sky is a large dark canvas sprinkled with colored sparks. The rescued constellation is a small portrait — a tight frame holding just the huddled family against the dark, no bigger than a few steps across.

gemma-4-31b — MARC valid, solved with 1 example

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Prediction

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Reasoning (2232 chars)

**Conceptual Digestion**

1.  **CAST**:
    *   **Night Sky**: The black background (`.`).
    *   **Scattered Loners (Diaspora)**: Colors that appear in multiple isolated locations across the grid.
    *   **Loyal Flock (Constellation)**: A single color that appears only in one contiguous cluster (connected orthogonally or diagonally).
    *   **Frame**: The smallest rectangular bounding box that contains the entire "Loyal Flock."

2.  **AFFORDANCES**:
    *   The grid can be scanned to count the number of separate clusters for each color.
    *   The "Loyal Flock" is the unique color that forms exactly one connected component.
    *   The output is a crop of the original grid, specifically the bounding box of that single cluster.

3.  **TRANSFORMATION RULE**:
    *   Identify all colors present in the grid.
    *   For each color, determine if all pixels of that color form a single connected component.
    *   The color that forms exactly one connected component is the target.
    *   Find the minimum and maximum row and column indices that contain this color.
    *   Extract the subgrid defined by these boundaries.

**Applying the Rule to Test Input**

*   **Blue (B)**: Scattered throughout (e.g., (0,2), (1,27), (2,0), (3,12), etc.). Multiple clusters.
*   **Green (G)**: Scattered throughout (e.g., (0,4), (0,19), (1,3), (3,19), etc.). Multiple clusters.
*   **Azure (A)**: Scattered throughout (e.g., (0,6), (0,20), (1,17), (1,19), etc.). Multiple clusters.
*   **Red (R)**: Located at:
    (12, 20), (12, 21), (12, 22)
    (13, 19), (13, 20), (13, 22)
    (14, 19), (14, 20), (14, 22)
    (15, 20), (15, 21), (15, 22)
    Checking connectivity: All Red pixels are connected to each other (forming a 4x3 block with some holes). There are no other Red pixels elsewhere in the grid.
*   **Red is the Loyal Flock.**

**Bounding Box for Red (R):**
*   Rows: Min = 12, Max = 15
*   Cols: Min = 19, Max = 22

**Extracting the subgrid:**
Row 12: (12,19)=`.`, (12,20)=`R`, (12,21)=`R`, (12,22)=`R`
Row 13: (13,19)=`R`, (13,20)=`R`, (13,21)=`.`, (13,22)=`R`
Row 14: (14,19)=`R`, (14,20)=`R`, (14,21)=`.`, (14,22)=`R`
Row 15: (15,19)=`.`, (15,20)=`R`, (15,21)=`R`, (15,22)=`R`

ANSWER:
. R R R
R R . R
R R . R
. R R R

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.88)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 108: "A painter's palette holds swatches above a workbench, and sc ... [62 chars truncated]" k=1 alts: 0/0 20fb2937

Training Examples

Example 1

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Output

Example 2

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Output

Literal Description

See: The input grid has three sections. (1) A color palette in the top three rows: three 3x3 colored blocks positioned at column groups 0-2, 4-6, and 8-10, separated by orange (O) columns. (2) A key row (row 4) containing exactly three single-cell symbols, each positioned at the center column of one of the three color block zones (columns 1, 5, and 9). These symbols establish a mapping from symbol to color block. (3) A magenta (M) divider spanning the full width at row 6. Below the divider (rows 7 onward) is a canvas of orange (O) cells with scattered single-cell symbols — the same symbols that appear in the key row.

Do: Step 1: Read the key row (row 4) to build a symbol-to-color mapping. The symbol at column 1 maps to the 3x3 color block at columns 0-2 (left block). The symbol at column 5 maps to the block at columns 4-6 (center block). The symbol at column 9 maps to the block at columns 8-10 (right block). Step 2: Extract the canvas region below the magenta divider — rows 7 through the last row. This becomes the basis for the output. Subtract 7 from each row index to get output row coordinates. Step 3: For each symbol found on the canvas, look up its mapped 3x3 color block. Place that 3x3 block centered on the symbol's position — meaning the symbol's (row, col) becomes the center cell, and the block fills a 3x3 area from (row-1, col-1) to (row+1, col+1) in output coordinates. Step 4: All non-symbol cells remain orange (O). Where 3x3 blocks overlap (if ever), later placements overwrite earlier ones.

Grid: The input grid is always 20 rows tall and 11 columns wide. The output grid is 13 rows tall (the canvas portion: input rows 7-19) and 11 columns wide. The background color is orange (O). The top section (rows 0-5) and divider (row 6) are consumed by the transformation and do not appear in the output. Column 3 and column 7 act as orange separators between the three color block zones in the palette.

Figurative Descriptions (1 variants)

"A painter's palette holds swatches above a workbench, and scattered paint drops on the bench bloom into full brushstrokes."

gemma-4-31b: k=1

See: Above a magenta curtain, three paint swatches sit on a shelf like proud samples in a hardware store. Just below the shelf, a registry card shows which secret stamp belongs to which swatch — each stamp placed directly beneath its color. Below the curtain stretches an orange workbench, where someone has flicked tiny drops of paint — each drop bearing the invisible signature of one of the swatches above.

Do: Read the registry card to learn each stamp's true color identity. Then pull away the curtain and everything above it — the workbench is your canvas now. Wherever a paint drop landed, it blooms outward like a flower opening: the tiny seed at its center expands into a full 3×3 blossom of its swatch color, spreading one cell in every direction. The rest of the bench stays bare orange, the neutral wood showing through. If two blossoms happen to overlap, the one that opened last covers the petals beneath.

Grid: The shelf and registry occupy the upper floors of the studio (the first six rows), with the curtain drawn across the seventh. Everything below the curtain — thirteen rows of workbench — becomes the finished painting. The bench is eleven columns wide, same as the shelf, and its orange surface is the bare canvas waiting to be colored by blooming drops.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (3140 chars)

**Conceptual Digestion**

1.  **CAST**:
    *   **Paint Swatches**: The three 3x3 blocks in the first three rows. In the test input: Red (R), Blue (B), and Grey (X).
    *   **Registry Card**: Row 5. It maps the "stamps" (colors found in the workbench) to the swatches.
        *   Stamp 'A' (Azure) is at index 1 $\rightarrow$ maps to Swatch 1 (Red).
        *   Stamp 'M' (Magenta) is at index 5 $\rightarrow$ maps to Swatch 2 (Blue).
        *   Stamp 'W' (Maroon) is at index 9 $\rightarrow$ maps to Swatch 3 (Grey).
    *   **Curtain**: Row 7 (Magenta line).
    *   **Workbench**: Rows 8 through 20. This is the canvas.
    *   **Paint Drops**: The non-orange cells in the workbench area.

2.  **AFFORDANCES**:
    *   The registry card defines the color mapping: $A \rightarrow R$, $M \rightarrow B$, $W \rightarrow X$.
    *   Each paint drop acts as a center for a 3x3 bloom of its mapped color.
    *   The background is Orange (O).
    *   Overlaps are handled by the order of appearance (though in this specific test, drops are processed sequentially).

3.  **TRANSFORMATION RULE**:
    *   Discard rows 1-7.
    *   Start with a 13x11 grid of Orange (O).
    *   Identify all "drops" in the input workbench (rows 8-20).
    *   For each drop at $(r, c)$:
        *   Determine its mapped color: $A \rightarrow R$, $M \rightarrow B$, $W \rightarrow X$.
        *   Fill a 3x3 area centered at $(r, c)$ with that color.
    *   The output is the final 13x11 grid.

**Applying the Rule to Test Input**

*   **Mapping**: $A=R, M=B, W=X$.
*   **Drops in Workbench (Rows 8-20, relative to row 8 as 0)**:
    1.  Row 1 (Input Row 9), Col 5: 'M' $\rightarrow$ Blue (B). Bloom: (0,4) to (2,6).
    2.  Row 1 (Input Row 9), Col 9: 'W' $\rightarrow$ Grey (X). Bloom: (0,8) to (2,10).
    3.  Row 2 (Input Row 10), Col 2: 'W' $\rightarrow$ Grey (X). Bloom: (1,1) to (3,3).
    4.  Row 5 (Input Row 13), Col 2: 'A' $\rightarrow$ Red (R). Bloom: (4,1) to (6,3).
    5.  Row 5 (Input Row 13), Col 7: 'A' $\rightarrow$ Red (R). Bloom: (4,6) to (6,8).
    6.  Row 9 (Input Row 17), Col 2: 'W' $\rightarrow$ Grey (X). Bloom: (8,1) to (10,3).
    7.  Row 9 (Input Row 17), Col 5: 'A' $\rightarrow$ Red (R). Bloom: (8,4) to (10,6).
    8.  Row 10 (Input Row 18), Col 9: 'W' $\rightarrow$ Grey (X). Bloom: (9,8) to (11,10).

**Constructing the Grid (13x11)**:
- (0,4)-(2,6) = B
- (0,8)-(2,10) = X
- (1,1)-(3,3) = X
- (4,1)-(6,3) = R
- (4,6)-(6,8) = R
- (8,1)-(10,3) = X
- (8,4)-(10,6) = R
- (9,8)-(11,10) = X

**Row by Row**:
0: O O O O B B B O X X X
1: O X X X B B B O X X X
2: O X X X B B B O X X X
3: O X X X O O O O O O O
4: O R R R O O R R R O O
5: O R R R O O R R R O O
6: O R R R O O R R R O O
7: O O O O O O O O O O O
8: O X X X R R R O O O O
9: O X X X R R R O X X X
10: O X X X R R R O X X X
11: O O O O O O O O X X X
12: O O O O O O O O O O O

ANSWER:
O O O O B B B O X X X
O X X X B B B O X X X
O X X X B B B O X X X
O X X X O O O O O O O
O R R R O O R R R O O
O R R R O O R R R O O
O R R R O O R

... [140 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.48)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 114: "Green footsteps leave echoes that scatter like reflections i ... [20 chars truncated]" k=3 alts: 0/0 22233c11

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 two identical green rectangular blocks (which may be single cells or larger NxN squares) arranged diagonally — one block offset from the other by a consistent row and column step, forming a two-step staircase. The rest of the grid is black background. There may be one such staircase pair or two independent staircase pairs in the grid.

Do: For each green staircase pair (two identical green blocks offset diagonally by some step vector (dr, dc)): 1. Compute the position of a hypothetical extension block one step before the first green block (subtract the step vector from the first block's position) and one step after the second green block (add the step vector to the second block's position). These extensions have the same dimensions as the green blocks. 2. Swap the column ranges of the two extension blocks while keeping their row ranges unchanged. That is, the before-extension keeps its rows but takes the columns of the after-extension, and vice versa. 3. Place azure cells at the resulting positions. If any part of an extension falls outside the grid boundary, clip it — only draw the portion that fits within the grid. 4. Leave all original green cells unchanged.

Grid: The grid is square (typically 10x10) with a black (.) background. Green (G) cells form one or two diagonal staircase pairs. Azure (A) cells are added by the transformation but never overlap green cells. The grid boundary acts as a hard clip — extensions that would fall outside are truncated to whatever portion remains inside the grid.

Figurative Descriptions (1 variants)

"Green footsteps leave echoes that scatter like reflections in a funhouse mirror."

gemma-4-31b: k=3

See: Someone has walked diagonally across a dark room in green boots, leaving one or two trails of paired footprints on a staircase. Each footprint is a perfect square stamp, and the walker always takes exactly two steps before stopping.

Do: Each pair of green footprints hints at where the walker came from and where they were headed next — one ghost step before the first footprint, one ghost step after the last. But these phantom steps are shy: each one steals the other's lane. The ghost that would have appeared above swaps sideways to stand in the column of the ghost below, and vice versa, as if they crossed paths mid-flight. Mark these confused phantoms in azure. If a phantom tries to step outside the room, only the part still on the floor is visible — the rest vanishes into the wall. The original green bootprints remain untouched.

Grid: The room is a dark square floor of black tiles. Green boot-stamps mark the walker's path in diagonal pairs. Azure phantoms appear where echoes of the walk would continue, but with their horizontal positions swapped — as if reflected across the staircase's spine. Phantoms never land on boots, and the walls clip anything that drifts out of bounds.

gemma-4-31b — MARC valid, solved with 3 examples

Input

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Prediction

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Expected

Reasoning (4275 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Green (G)**: The "bootprints." They appear in pairs (or blocks) moving diagonally.
    *   **Azure (A)**: The "phantoms." These are the ghost steps that appear before the first bootprint and after the last bootprint of a sequence.
    *   **Black (.)**: The empty room.

2.  **AFFORDANCES**:
    *   The green blocks define a path.
    *   The path has a direction (diagonal).
    *   The "ghost steps" are calculated by extending the diagonal path one step backward and one step forward.
    *   The "swap" rule: The ghost steps are reflected across the "spine" of the staircase. In practical grid terms, if the path moves from $(r, c)$ to $(r+1, c+1)$, the ghost steps are at $(r-1, c-1)$ and $(r+n, c+n)$. However, the description says they "steal the other's lane" and "swap sideways." Looking at the examples:
        *   Example 1: Green blocks at (3,3)-(4,4) and (5,1)-(6,2). Path: (3,3) $\to$ (4,4) $\to$ (5,1) $\to$ (6,2) is not quite right. Rather, it's two pairs.
        *   Wait, let's re-examine Example 1: Green blocks are $2\times2$ squares. Block 1: rows 3-4, cols 3-4. Block 2: rows 5-6, cols 1-2.
        *   The path is from Block 1 to Block 2 (down-left).
        *   Ghost 1 (before Block 1): Should be at row 2, col 5 (up-right). But it swaps lanes? The output shows A at (1,0) and (2,0).
        *   Let's re-read: "The ghost that would have appeared above swaps sideways to stand in the column of the ghost below, and vice versa."
        *   Example 1 again: Path is (3,3) $\to$ (5,1). The "ghost before" would be at (2,4). The "ghost after" would be at (7, -1).
        *   Actually, look at the blocks: Block 1 is at $C=3,4$. Block 2 is at $C=1,2$.
        *   The "ghost before" (above Block 1) would be at $C=5,6$ (following the diagonal trend). The "ghost after" (below Block 2) would be at $C=-1,0$.
        *   The rule says they swap lanes. Ghost before (C=5,6) moves to the lane of Ghost after (C=-1,0). Ghost after (C=-1,0) moves to the lane of Ghost before (C=5,6).
        *   Result: Ghost before is now at $C=0$ (clipped). Ghost after is now at $C=5,6$.
        *   Check Example 1 Output: Azure at (1,0), (2,0) and (7,5), (7,6), (8,5), (8,6). This matches!

3.  **TRANSFORMATION RULE**:
    1.  Identify the two green blocks.
    2.  Determine the diagonal direction (e.g., Block 1 $\to$ Block 2).
    3.  Determine the "natural" ghost positions:
        *   Ghost Before: One step backward from Block 1.
        *   Ghost After: One step forward from Block 2.
    4.  Swap the column indices of the Ghost Before and Ghost After.
    5.  Place Azure (A) at these swapped positions, keeping the original row indices.
    6.  Clip any positions outside the grid.

### Applying to Test Input

1.  **Identify Green Blocks**:
    *   Block 1: Rows 2-4, Cols 6-8.
    *   Block 2: Rows 5-7, Cols 3-5.
2.  **Determine Direction**:
    *   From (2-4, 6-8) to (5-7, 3-5). This is a move of $\Delta r = +3, \Delta c = -

... [1275 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.74)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 142: "A stained-glass window template is filled with light filtere ... [31 chars truncated]" k=1 alts: 0/0 278e5215

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 two distinct objects: (1) A color palette block consisting of three rows — two identical rows that define a repeating color pattern and one row filled entirely with a single uniform color (the background color). The palette rows are always the same width. (2) An irregular shape made entirely of grey (X) cells, forming a connected region elsewhere in the grid. The rest of the grid is black (empty).

Do: 1. Locate the color palette block: find the three adjacent rows that form a rectangular region of non-black, non-grey colors. Two of these rows are identical (the pattern row) and one row is a single repeated color (the background color). Extract the pattern row (the repeating color sequence) and the background color (the uniform row's color). 2. Locate the grey (X) shape and compute its bounding box (the smallest rectangle enclosing all X cells). 3. Create an output grid with the dimensions of that bounding box. 4. For each cell in the bounding box: if the corresponding cell in the input is X, assign it the color from the pattern row at the matching column offset (i.e., map the bounding box's column index to the pattern row's column index, aligning the bounding box's left edge with the pattern row's first element). If the cell is not X (empty/black), assign it the background color.

Grid: The output grid dimensions match the bounding box of the grey shape. The width of the grey shape's bounding box always equals the length of the pattern row in the palette. There is no fixed size — both depend on the specific input. The output contains no black or grey cells; every cell is either a pattern color or the background color.

Figurative Descriptions (1 variants)

"A stained-glass window template is filled with light filtered through a colored lens strip."

gemma-4-31b: k=1

See: Somewhere in the cathedral lies a narrow strip of stained glass — a ribbon of colors repeated twice for emphasis, bordered by a single band of lead (the uniform color). Elsewhere on the floor, a grey paper template has been cut into an irregular shape, waiting to be held up to the light.

Do: The artisan lifts the grey template to the stained-glass ribbon. Wherever the template has substance — wherever grey paper blocks the view — the colored light shines through, painting each column with the hue from the ribbon directly behind it. But wherever the template has been cut away, only the dull gleam of the lead border color fills the gap, as if no glass exists there at all. The template drinks in the ribbon's colors column by column, perfectly aligned edge to edge.

Grid: The finished window is exactly the size of the template — no larger, no smaller. Every opening has been sealed: grey becomes jeweled color, and empty becomes lead. No darkness or grey remains in the final piece.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (5757 chars)

### Conceptual Digestion

**1. Identify the CAST:**
*   **The Stained-Glass Ribbon:** A small rectangular block of colors. It consists of a sequence of colors repeated twice (the "ribbon") and a final row of a single uniform color (the "lead border").
*   **The Grey Template:** A shape made of grey pixels (`X`) located elsewhere in the grid.
*   **The Background:** Black pixels (`.`) which are ignored.

**2. Identify the AFFORDANCES:**
*   The **Ribbon** provides a color mapping for each column. If the ribbon is $W$ columns wide, column $j$ of the template corresponds to column $j$ of the ribbon.
*   The **Template** defines the dimensions of the output grid (its bounding box) and which pixels in that box will take a color from the ribbon versus the lead border color.

**3. Identify the TRANSFORMATION RULE:**
1.  **Extract the Ribbon:** Find the colored block. Identify the "lead border color" (the uniform color of the bottom row of the ribbon). Identify the "ribbon colors" (the colors in the top two rows).
2.  **Extract the Template:** Find the bounding box of the grey `X` pixels.
3.  **Map Colors:** For every cell $(r, c)$ within the template's bounding box:
    *   If the cell is grey (`X`), it takes the color from the ribbon's column $c$ (relative to the template's left edge). Since the ribbon is repeated twice, the color at column $c$ is the same for row 0 and row 1 of the ribbon.
    *   If the cell is empty (`.`), it takes the "lead border color".
4.  **Output:** The resulting grid is the size of the template's bounding box.

---

### Applying the Rule to Test Input

**1. Extract the Ribbon:**
The ribbon is at the top right:
Row 0: `R Y Y Y A A G G M M`
Row 1: `R Y Y Y A A G G M M`
Row 2: `W W W W W W W W W W`
*   **Ribbon Colors (per column):** `R, Y, Y, Y, A, A, G, G, M, M`
*   **Lead Border Color:** `W` (maroon)

**2. Extract the Template:**
The grey `X` pixels are located from:
*   Row 5 to Row 11 (Height = 7)
*   Column 2 to Column 10 (Width = 9)
*Wait, let's re-count the columns for the template:*
Row 5: `. . X X . . X . X X X` (Cols 2, 3, 6, 8, 9, 10)
Row 6: `. X X X X X X X X X X` (Cols 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
Row 7: `. . . X . X X . . X X` (Cols 3, 5, 6, 9, 10)
Row 8: `. X X X X X . . . X .` (Cols 1, 2, 3, 4, 5, 9)
Row 9: `. . X . . X . . X X .` (Cols 2, 5, 8, 9)
Row 10: `. . X X X X X X X X X` (Cols 2, 3, 4, 5, 6, 7, 8, 9, 10)
Row 11: `. . . X X . . . . X X` (Cols 3, 4, 9, 10)

Bounding box:
Rows: 5 to 11
Cols: 1 to 10
Width = 10, Height = 7.

**3. Map Colors:**
Ribbon columns (0-9): `R Y Y Y A A G G M M`
Lead color: `W`

*   **Row 5 (Template Row 0):** `. . X X . . X . X X X` (Relative to Col 1: `. X X . . X . X X X`)
    *   Col 1: `.` $\rightarrow$ W
    *   Col 2: `X` $\rightarrow$ Y
    *   Col 3: `X` $\rightarrow$ Y
    *   Col 4: `.` $\rightarrow$ W
    *   Col 5: `.` $\rightarrow$ W
    *   Col 6: `X` $\rightarrow$ A
    *   Col 7: `.` $\rightarrow$ W
    *   Col 8: `X` $\rightarrow$ G
    *   Col 9: `X` $\rightarro

... [2757 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 151: "Lightning rods on a rooftop attract bolts from storms on the ... [9 chars truncated]" k=2 alts: 9/15 29700607

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 has a black background with two key features: (1) A horizontal 'header segment' of exactly 3 consecutive colored pixels in row 0, and (2) scattered 'anchor' pixels elsewhere in the grid, each matching one of the header colors. Each anchor pixel appears at most once per header color. Some header colors may have no corresponding anchor pixel.

Do: For each of the 3 header colors, from left to right occupying columns L, M, R in row 0: (1) Find whether an anchor pixel of that color exists elsewhere in the grid. (2) If an anchor exists at position (row_a, col_a): fill that color's header column from row 0 down through row_a, then fill row_a horizontally from col_a to the header column (inclusive), connecting the anchor to the column. (3) If no anchor exists for that color: extend that color's header column from row 0 all the way down to the last row of the grid. All other cells remain black.

Grid: The grid dimensions match the input exactly (no resizing). The background is black (.). Row 0 contains a contiguous 3-pixel colored segment; the rest of the grid is black except for isolated anchor pixels. The coordinate system is row-major with (0,0) at the top-left.

Figurative Descriptions (16 variants)

"Lightning rods on a rooftop attract bolts from storms on the horizon."

gemma-4-31b: k=2

See: A rooftop runs along the top of the grid — three lightning rods stand side by side, each a different color. Scattered across the dark sky below, lone storm clouds drift, each glowing with the same color as one of the rods that calls to it.

Do: Each lightning rod reaches downward through the darkness, searching for its matching storm cloud. When a rod finds its cloud, a bolt of lightning strikes — the rod's color streams straight down from the rooftop and then arcs horizontally to meet the cloud, forging an L-shaped path of light. If a rod has no cloud to attract, its energy simply pours all the way down to the ground, an unbroken pillar of color with nowhere else to go.

Grid: The rooftop sits along the top edge — three adjacent colored rods against a pitch-black sky. The storm clouds are single colored sparks floating in the darkness. Lightning bolts are vertical then horizontal, always connecting rod to cloud by the shortest L-shaped route through the rod's own column.

gemma-4-31b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (2581 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Rooftop/Lightning Rods**: Three adjacent colored cells at the top of the grid (row 0).
    *   **Storm Clouds**: Single colored cells scattered in the grid.
    *   **Lightning Bolts**: Paths of the same color connecting a rod to its matching cloud.
    *   **Ground**: The bottom edge of the grid.

2.  **AFFORDANCES**:
    *   Each rod (color $C$) searches for a cloud of the same color $C$.
    *   If a cloud of color $C$ exists at $(row, col)$, the rod at $(0, rod\_col)$ creates a path:
        *   Vertical segment from $(0, rod\_col)$ down to $(row, rod\_col)$.
        *   Horizontal segment from $(row, rod\_col)$ to $(row, col)$.
    *   If no cloud of color $C$ exists, the rod creates a vertical pillar from $(0, rod\_col)$ all the way to the bottom of the grid.

3.  **TRANSFORMATION RULE**:
    *   Identify the three rods at the top (adjacent colors).
    *   For each rod color $C$ at column $j$:
        *   Find the cell $(i, k)$ where the color is $C$ (excluding the rod itself).
        *   If found: Fill all cells $(r, j)$ for $0 \le r \le i$ with color $C$, and all cells $(i, c)$ between $j$ and $k$ (inclusive) with color $C$.
        *   If not found: Fill all cells $(r, j)$ for $0 \le r < \text{height}$ with color $C$.

### Applying the Rule to Test Input

**Input Analysis**:
*   Grid size: 11 rows x 11 columns.
*   Rods at row 0: Column 3 (Y), Column 4 (A), Column 5 (X).
*   Clouds:
    *   Yellow (Y) at (7, 0).
    *   Azure (A) - None found.
    *   Grey (X) at (9, 10).

**Path Construction**:
1.  **Yellow (Y)**: Rod at (0, 3), Cloud at (7, 0).
    *   Vertical: (0, 3) to (7, 3).
    *   Horizontal: (7, 3) to (7, 0).
2.  **Azure (A)**: Rod at (0, 4), No cloud.
    *   Vertical: (0, 4) to (10, 4).
3.  **Grey (X)**: Rod at (0, 5), Cloud at (9, 10).
    *   Vertical: (0, 5) to (9, 5).
    *   Horizontal: (9, 5) to (9, 10).

**Final Grid Construction**:
*   Row 0: `. . . Y A X . . . . .`
*   Row 1: `. . . Y A X . . . . .`
*   Row 2: `. . . Y A X . . . . .`
*   Row 3: `. . . Y A X . . . . .`
*   Row 4: `. . . Y A X . . . . .`
*   Row 5: `. . . Y A X . . . . .`
*   Row 6: `. . . Y A X . . . . .`
*   Row 7: `Y Y Y Y A X . . . . .`
*   Row 8: `. . . . A X . . . . .`
*   Row 9: `. . . . A X X X X X X`
*   Row 10: `. . . . A . . . . . .`

ANSWER:
. . . Y A X . . . . .
. . . Y A X . . . . .
. . . Y A X . . . . .
. . . Y A X . . . . .
. . . Y A X . . . . .
. . . Y A X . . . . .
. . . Y A X . . . . .
Y Y Y Y A X . . . . .
. . . . A X . . . . .
. . . . A X X X X X X
. . . . A . . . . . .

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.92)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 181: "A stained-glass window reveals the hidden garden beneath the ... [7 chars truncated]" k=2 alts: 0/0 32597951

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 repeating background pattern made of blue (B) and black (.) cells arranged in a regular tile. Overlaid on this background is a cluster of azure (A) cells forming a rectangular region. Within the bounding box of the azure cells, some cells are azure (A), some are blue (B), and some are black (.). The blue cells inside this bounding box are part of the original background pattern that continues underneath the azure overlay.

Do: 1. Find all azure (A) cells in the grid. 2. Compute the bounding box of these azure cells (the smallest rectangle containing all of them). 3. For every cell inside this bounding box: if it is blue (B), replace it with green (G). If it is azure (A) or black (.), leave it unchanged. 4. All cells outside the bounding box remain unchanged.

Grid: The grid is 17 rows by 17 columns. The background is a repeating pattern of blue (B) and black (.) cells. Azure (A) cells mark a rectangular overlay region somewhere in the grid. The grid uses colors 0-9 mapped to: .=black, B=blue, A=azure, G=green. The transformation only affects blue cells within the bounding box of the azure region.

Figurative Descriptions (1 variants)

"A stained-glass window reveals the hidden garden beneath the frost."

gemma-4-31b: k=2

See: A blue and black tapestry repeats endlessly like wallpaper in an old house. Somewhere on this wall, a patch of azure glass has been mounted — a window frame. Behind the glass, the old wallpaper continues, but you can see through to it.

Do: Wherever the window frame casts its shadow, the blue threads of the wallpaper bloom into green — as if sunlight through the azure glass awakens dormant seeds in the fabric. The black threads are too deep to reach and stay asleep. The azure frame itself remains unchanged, proud of its work. Beyond the window's reach, the wallpaper knows nothing of spring.

Grid: A 17×17 woven tapestry of blue and black in a tiling pattern. Azure cells form a windowpane mounted on the surface. Green appears only where blue once lived within the window's shadow. The rest of the house remains untouched by the light.

gemma-4-31b — MARC valid, solved with 2 examples

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Prediction

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Reasoning (5310 chars)

### Conceptual Digestion

1.  **The CAST**:
    *   **Blue (B)**: The "threads of the wallpaper." These are the target cells for transformation.
    *   **Black (.)**: The "deep threads." These are inert and do not change.
    *   **Azure (A)**: The "window frame." These cells define the boundary/area of effect and remain unchanged.
    *   **Green (G)**: The "bloomed" result. This is the output color for Blue cells located inside the Azure frame.

2.  **The AFFORDANCES**:
    *   The Azure (A) cells act as a mask.
    *   Any cell *inside* the perimeter formed by the Azure cells (or specifically, any cell that is part of the Azure shape's interior/boundary) is subject to the rule.
    *   Looking at the training examples, the "window" is the region enclosed by or consisting of the Azure cells. Specifically, any cell that is **not** Azure but is **surrounded by or within the bounding box/area** of the Azure frame is checked.
    *   Wait, looking closer at Example 1 and 2:
        *   Example 1: Azure cells form a rough rectangle. Blue cells *inside* that rectangle (where the Azure cells are the border) turn Green.
        *   Example 2: Azure cells form a hollow rectangle. Blue cells *inside* the hollow area turn Green.
        *   Crucially: Azure cells themselves **do not** change. Black cells **do not** change. Only Blue cells located within the Azure region change to Green.

3.  **The TRANSFORMATION RULE**:
    *   Identify the region defined by the Azure (A) cells.
    *   For every cell $(r, c)$ in the grid:
        *   If $\text{grid}[r][c] == 'A'$, it remains 'A'.
        *   If $\text{grid}[r][c] == 'B'$ AND it is located within the area enclosed/defined by the Azure frame, it becomes 'G'.
        *   Otherwise, it remains unchanged.

### Applying the Rule to Test Input

**Test Input Analysis**:
The Azure (A) cells are located at:
Row 11: Col 7, 9, 10, 12
Row 12: Col 7, 8, 10, 11, 12
Row 13: Col 8, 9, 10, 11, 12
Row 14: Col 7, 9, 10, 12

Let's map the Azure region:
Row 11: `. . . . . . . A . B A A B A . B . .` (Wait, let me re-count)
Test Input Row 11: `. . B . . B . A B A A B A . B . .`
Indices (0-indexed):
R11: Col 7(A), 9(A), 10(A), 12(A)
R12: Col 7(A), 8(A), 10(A), 11(A), 12(A)
R13: Col 8(A), 9(A), 10(A), 11(A), 12(A)
R14: Col 7(A), 9(A), 10(A), 12(A)

The bounding box of Azure is Row 11-14 and Col 7-12.
Let's check the Blue (B) cells within this box:
R11: Col 8 is B $\rightarrow$ becomes G. Col 11 is B $\rightarrow$ becomes G.
R12: Col 9 is B $\rightarrow$ becomes G.
R13: Col 7 is B $\rightarrow$ becomes G. Col 13 is B (outside box).
R14: Col 8 is B $\rightarrow$ becomes G. Col 11 is B $\rightarrow$ becomes G.

Wait, let's re-examine the Azure shape:
R11: `_ _ _ _ _ _ _ A B A A B A _ _ _ _`
R12: `_ _ _ _ _ _ _ A A B A A B _ _ _ _`
R13: `_ _ _ _ _ _ _ _ A A B A A _ _ _ _` (Wait, let me re-read the test input carefully)

Test Input:
R11: `. . B . . B . A B A A B A . B . .` (Col 7=A, 8=B, 9=A, 10=A, 11=B, 12=A)
R12: `B . . B . . B A A

... [2310 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 1.00)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 184: "A river runs through a canyon, and the colored rock strata f ... [56 chars truncated]" k=1 alts: 0/0 332202d5

Training Examples

Example 1

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Example 2

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Example 3

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Output

Literal Description

See: The input is a 16-row grid with a single vertical column of azure (A) cells acting as a vertical divider. Scattered among the rows are horizontal 'divider rows' — rows filled with a non-orange color where the vertical divider column contains blue (B) instead of azure (A). All other rows are filled with orange (O) and have azure (A) at the vertical divider column. The divider rows partition the grid into segments of consecutive orange rows.

Do: 1. Identify the vertical divider column (the column that is all A/B). 2. Identify all horizontal divider rows — rows where every cell is a single non-orange color, with B at the divider column. Record each divider's color and row position. 3. Transform each divider row: replace every cell with B, except at the vertical divider column, which becomes A. 4. For each segment of orange rows between two adjacent dividers (or between a grid edge and the nearest divider), fill the rows as follows: (a) If the segment borders only one divider (i.e., it is at the top or bottom edge of the grid), fill all rows in the segment with that divider's color, placing B at the vertical divider column. (b) If the segment is between two dividers of the same color, fill all rows with that color, placing B at the vertical divider column. (c) If the segment is between two dividers of different colors, split the segment in half: the rows closer to the top divider get the top divider's color, the rows closer to the bottom divider get the bottom divider's color, each with B at the vertical divider column. If the segment has an odd number of rows, insert an all-B row in the middle (with B at every position including the vertical divider column).

Grid: The grid is always 16 rows by 16 columns. The background color is orange (O). One column serves as a vertical structural divider (azure/blue). The output grid has the same dimensions as the input. No cells remain orange in the output — every orange row is replaced by a divider color or a blue separator row.

Figurative Descriptions (1 variants)

"A river runs through a canyon, and the colored rock strata flood outward to reclaim the empty sediment between them."

gemma-4-31b: k=1

See: A river of azure flows vertically through a canyon of orange sediment. At certain depths, horizontal veins of colored mineral — maroon, magenta, green, yellow, grey, black — cut across the canyon wall from edge to edge, turning the river blue where they cross it. Between these mineral veins, the canyon is filled with plain orange sediment waiting to be claimed.

Do: Each mineral vein erupts and floods the empty sediment above and below it with its own color. The sediment absorbs the color of whichever vein is nearest. When two different veins compete for the same stretch of sediment, they each saturate their half — the rows closer to each vein take on that vein's hue. If they meet at an exact midpoint, a seam of pure blue river-stone forms where their territories collide. Meanwhile, the original mineral veins themselves are consumed by the flooding — they dissolve into blue river-stone, except where the river runs through them, which crystallizes into azure. The river itself turns blue everywhere except at these dissolved vein lines.

Grid: The canyon is 16 layers deep and 16 columns wide. Orange sediment is the unclaimed fill. One vertical column is the azure river, which becomes blue everywhere in the output except at dissolved vein crossings. After the flood, no orange sediment remains — every grain has been stained by its nearest mineral vein.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Reasoning (3883 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Azure (A)**: The "river" (vertical column).
    *   **Orange (O)**: The "sediment" (empty space to be filled).
    *   **Colored Mineral Veins (W, M, G, Y, X, .)**: Horizontal lines that act as sources of color.
    *   **Blue (B)**: The "river-stone". It appears in the river column normally, and as a "seam" or "dissolved vein" marker.

2.  **AFFORDANCES**:
    *   The mineral veins expand vertically to fill the orange sediment.
    *   The river column (A) is transformed based on whether it intersects a vein.

3.  **TRANSFORMATION RULE**:
    *   **Sediment Filling**: Every row of orange sediment takes the color of the nearest mineral vein (above or below).
    *   **Midpoint Seams**: If a row is exactly equidistant between two different mineral veins, it becomes Blue (B).
    *   **Vein Dissolution**: The original rows that contained mineral veins become Blue (B), except for the cell in the river column, which remains Azure (A).
    *   **River Transformation**: The river column (A) becomes Blue (B) everywhere, except on the rows where the original mineral veins were located (where it stays A).

### Step-by-Step Application to Test Input

**Input Analysis**:
*   River Column: Index 4 (0-indexed).
*   Vein 1: Row 2 (W - Maroon)
*   Vein 2: Row 5 (M - Magenta)
*   Vein 3: Row 9 (M - Magenta)
*   Vein 4: Row 13 (X - Grey)

**Row-by-Row Calculation**:
*   Row 0: Nearest vein is Row 2 (W). Color: **W**
*   Row 1: Nearest vein is Row 2 (W). Color: **W**
*   Row 2: Original Vein (W). Dissolves to **B**, River stays **A**.
*   Row 3: Between Row 2 (W) and Row 5 (M). Distance to W is 1, to M is 2. Color: **W**
*   Row 4: Between Row 2 (W) and Row 5 (M). Distance to W is 2, to M is 1. Color: **M**
*   Row 5: Original Vein (M). Dissolves to **B**, River stays **A**.
*   Row 6: Between Row 5 (M) and Row 9 (M). Nearest is M. Color: **M**
*   Row 7: Between Row 5 (M) and Row 9 (M). Midpoint is Row 7. Since both are M, it stays **M**.
*   Row 8: Between Row 5 (M) and Row 9 (M). Nearest is M. Color: **M**
*   Row 9: Original Vein (M). Dissolves to **B**, River stays **A**.
*   Row 10: Between Row 9 (M) and Row 13 (X). Distance to M is 1, to X is 3. Color: **M**
*   Row 11: Between Row 9 (M) and Row 13 (X). Midpoint is Row 11. Different colors (M vs X). Color: **B**
*   Row 12: Between Row 9 (M) and Row 13 (X). Distance to M is 3, to X is 1. Color: **X**
*   Row 13: Original Vein (X). Dissolves to **B**, River stays **A**.
*   Row 14: Nearest vein is Row 13 (X). Color: **X**
*   Row 15: Nearest vein is Row 13 (X). Color: **X**

**River Column (Index 4) Final Check**:
*   Rows 2, 5, 9, 13: **A**
*   All other rows: **B**

### Final Grid Construction

Row 0: W W W W B W W W W W W W W W W W
Row 1: W W W W B W W W W W W W W W W W
Row 2: B B B B A B B B B B B B B B B B
Row 3: W W W W B W W W W W W W W W W W
Row 4: M M M M B M M M M M M M M M M M
Row 5: B B B B A B B B B B B B B B B B
Row 6: M M M M B M M M M M M M M 

... [883 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.94)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 202: "A scale weighs azure ice against red fire, and the balance t ... [16 chars truncated]" k=1 alts: 0/0 37ce87bb

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 has an orange (O) background. Vertical bars of azure (A) and red (R) cells grow upward from the bottom row. These bars are always located at odd-numbered columns (0-indexed: columns 1, 3, 5, 7, …). Each bar is a contiguous vertical strip of a single color anchored to the bottom edge of the grid. Some odd columns are empty (all orange). The bars vary in height (number of filled cells counting from the bottom row upward).

Do: 1. Identify every odd-numbered column (1, 3, 5, 7, …) that contains a vertical bar of azure (A) or red (R) cells rising from the bottom row. Record each bar's color and height (number of contiguous colored cells from the bottom). 2. Compute the sum of all azure bar heights and the sum of all red bar heights. 3. Calculate the result height: (sum of azure heights) minus (sum of red heights). 4. Find the first odd-numbered column (scanning left to right) that is entirely empty (all orange). 5. Place a grey (X) bar in that column, anchored to the bottom row, with height equal to the result calculated in step 3. All other cells remain unchanged.

Grid: The grid dimensions vary (rows and columns differ across instances). The background color is orange (O). Columns are 0-indexed. Bars only appear at odd-indexed columns. The grid is tall enough to accommodate all bars and the resulting grey bar. The output grid has the same dimensions as the input grid, with the only change being the addition of the grey (X) bar.

Figurative Descriptions (1 variants)

"A scale weighs azure ice against red fire, and the balance tips into shadow."

gemma-4-31b: k=1

See: Against a sunset-orange sky, pillars rise from the earth like stalagmites in a cave. Some are carved from frozen azure crystal, others forged from red flame. They stand in every other lane of a colonnade, growing to different heights—some towering, some mere stumps. A few lanes in the colonnade stand vacant, waiting.

Do: The azure pillars and red pillars are locked in a tug-of-war. The ice accumulates weight on one side of the scale, the fire on the other. Whatever force the ice musters beyond the fire's resistance crystallizes as a grey shadow—a new pillar that fills the first empty lane it can find, rising from the ground to a height that reflects how much the ice overpowered the flame.

Grid: The colonnade stretches across an orange plain. Pillars only grow in the odd-numbered lanes, and the grey shadow obeys the same rule, claiming the first unclaimed odd lane from the left. The world's dimensions shift from scene to scene, but the colonnade's bones remain the same.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Reasoning (5656 chars)

### Conceptual Digestion

**1. Identify the CAST:**
*   **Background (O):** The "sunset-orange sky" or "orange plain."
*   **Azure Pillars (A):** "Frozen azure crystal."
*   **Red Pillars (R):** "Forged from red flame."
*   **Grey Shadow (X):** The result of the "tug-of-war."
*   **Lanes:** The vertical columns of the grid. The description specifies that pillars only grow in "odd-numbered lanes" (using 1-based indexing: 1, 3, 5, 7, 9, 11, 13, 15).

**2. Identify the AFFORDANCES:**
*   The height of a pillar is the number of colored cells in that specific odd-numbered column.
*   The "tug-of-war" is a calculation: Total height of Azure (A) minus Total height of Red (R).
*   The result of this subtraction determines the height of a new Grey (X) pillar.
*   The Grey pillar is placed in the first available (empty) odd-numbered lane from the left.

**3. Identify the TRANSFORMATION RULE:**
1.  Calculate the total number of Azure (A) cells in the grid.
2.  Calculate the total number of Red (R) cells in the grid.
3.  Calculate the difference: `Difference = Total A - Total R`.
4.  If `Difference > 0`, a Grey (X) pillar of height `Difference` is created.
5.  Find the first odd-numbered column (1, 3, 5...) that contains no A or R cells.
6.  Fill that column from the bottom up with `Difference` number of X cells.

---

### Applying the Rule to Test Input

**Step 1: Count Azure (A) cells**
*   Col 2 (Even): Ignore
*   Col 1 (Odd): Rows 3, 4, 5, 6, 7, 8, 9 $\rightarrow$ 7 cells
*   Col 3 (Odd): Empty
*   Col 5 (Odd): Rows 7, 8 $\rightarrow$ 2 cells
*   Col 7 (Odd): Rows 5, 6, 7, 8, 9 $\rightarrow$ 5 cells
*   Col 9 (Odd): Empty
*   Col 11 (Odd): Empty
*   Col 13 (Odd): Empty
*   Col 15 (Odd): Empty
*   **Total A = 7 + 2 + 5 = 14**

**Step 2: Count Red (R) cells**
*   Col 4 (Even): Ignore
*   Col 5 (Odd): Rows 7, 8, 9 $\rightarrow$ 3 cells (Wait, let me re-check the input grid carefully)

*Re-evaluating Test Input Grid:*
Row 1: O O O O O O O O O O O O O O O
Row 2: O O O O O O O O O O O R O O O (Col 12 - Even)
Row 3: O A O O O O O O O O O R O O O (Col 2 - Even, Col 12 - Even)
Row 4: O A O O O O O O O O O R O O O (Col 2 - Even, Col 12 - Even)
Row 5: O A O O O O O A O O O R O O O (Col 2 - Even, Col 8 - Even, Col 12 - Even)
Row 6: O A O O O O O A O O O R O O O (Col 2 - Even, Col 8 - Even, Col 12 - Even)
Row 7: O A O R O O O A O O O R O O O (Col 2 - Even, Col 4 - Even, Col 8 - Even, Col 12 - Even)
Row 8: O A O R O A O A O O O R O O O (Col 2 - Even, Col 4 - Even, Col 6 - Even, Col 8 - Even, Col 12 - Even)
Row 9: O A O R O A O A O R O R O O O (Col 2 - Even, Col 4 - Even, Col 6 - Even, Col 8 - Even, Col 10 - Even, Col 12 - Even)

*Wait, let me re-read the grid coordinates carefully. The columns are separated by spaces.*
Col 1: O O O O O O O O O
Col 2: O A A A A A A A (Azure)
Col 3: O O O O O O O O O
Col 4: O O O O O R R R (Red)
Col 5: O O O O O O O O O
Col 6: O O O O O O A A (Azure)
Col 7: O O O O O O O O O
Col 8: O O O O A A A A A (Azure)
Col 9: O O O O O O O O O
C

... [2659 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.93)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 206: "A gemstone is cut open, and its internal layers spill out li ... [25 chars truncated]" k=2 alts: 0/0 3979b1a8

Training Examples

Example 1

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Example 2

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Literal Description

See: A 5×5 grid containing exactly three colors arranged in a concentric diamond pattern. The four corner cells (top-left, top-right, bottom-left, bottom-right) share one color — call this the 'corner color' (level 0). The central plus-sign shape (center cell plus its 4 orthogonal neighbors) uses a second color — the 'center color' (level 2). All remaining cells use a third color — the 'body color' (level 1). The pattern has 4-fold symmetry.

Do: 1. Identify the three colors and assign levels: corner color (the color at position (0,0)) = level 0, body color (the color at position (0,1)) = level 1, center color (the color at position (2,2)) = level 2. 2. Create a 10×10 output grid, divided into four 5×5 quadrants. 3. TOP-LEFT quadrant (rows 0–4, cols 0–4): Copy the original 5×5 input unchanged. 4. Define a 'band sequence' of 5 colors: band[k] is the color whose level equals (−k) mod 3. Concretely: band[0]=corner, band[1]=center, band[2]=body, band[3]=corner, band[4]=center. 5. TOP-RIGHT quadrant (rows 0–4, cols 5–9): Fill each column uniformly with the corresponding band color. Column 5 gets band[0], column 6 gets band[1], column 7 gets band[2], column 8 gets band[3], column 9 gets band[4]. 6. BOTTOM-LEFT quadrant (rows 5–9, cols 0–4): Fill each row uniformly with the corresponding band color. Row 5 gets band[0], row 6 gets band[1], row 7 gets band[2], row 8 gets band[3], row 9 gets band[4]. 7. BOTTOM-RIGHT quadrant (rows 5–9, cols 5–9): Use local coordinates i′=row−5, j′=col−5 (each 0–4). For off-diagonal cells (i′≠j′), set the color to band[max(i′,j′)]. For diagonal cells (i′=j′=k), set the color to the color whose level is (−k−1) mod 3. This produces a staircase of nested L-shapes using the band colors, with the diagonal shifted one level down.

Grid: Input is always a 5×5 grid with exactly three colors in the concentric diamond arrangement described above. Output is always a 10×10 grid (double the input dimensions in both directions). The four 5×5 quadrants tile the output: top-left is the original, top-right and bottom-left are uniform bands, and bottom-right is a staircase pattern. Colors 0–9 from the ARC palette may appear in any three-color combination maintaining the concentric diamond structure.

Figurative Descriptions (1 variants)

"A gemstone is cut open, and its internal layers spill out like light through a prism."

gemma-4-31b: k=2

See: A small gemstone sits at the center of a 5×5 setting. It has three mineral layers arranged in concentric diamond rings: a rare ore at the four compass points of the corners, a commonite filling the bulk of the stone, and a core vein running through the center in a plus shape. The gem has perfect four-fold symmetry, like a jeweler's ideal cut.

Do: The jeweler cleaves the gemstone and places the original stone in the top-left of a display case twice its size. The cut releases the mineral layers — they unspool to the right and downward like ribbons pulled from a spool, cycling through the three minerals in order of depth: corner ore, then core vein, then common ite, repeating. To the right of the stone, each ribbon hangs as a vertical stripe. Below the stone, each ribbon stretches as a horizontal stripe. In the bottom-right corner of the case, the freed ribbons settle into a staircase — each deeper layer nests inside the previous one like an L-shaped frame, with the diagonal seam between steps always showing the next mineral in the cycle, one step ahead of its surroundings.

Grid: The gemstone is always 5×5 with exactly three mineral colors in the concentric diamond arrangement. The display case is always 10×10 — the stone plus three regions where its layers have been 'refracted' outward. The cycling order of minerals always follows the same depth sequence, wrapping around after three. Any three colors from the palette can serve as the three minerals.

gemma-4-31b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (7251 chars)

### Conceptual Digestion

1.  **The CAST**:
    *   **The Gemstone**: A 5x5 input grid with three colors arranged in concentric diamond rings.
    *   **Mineral Layers (Depth Sequence)**:
        *   Layer 1 (Corner Ore): The four corners (0,0), (0,4), (4,0), (4,4).
        *   Layer 2 (Core Vein): The central plus shape (row 2 and col 2).
        *   Layer 3 (Commonite): The remaining bulk filling the diamond.
    *   **The Display Case**: A 10x10 output grid.

2.  **The AFFORDANCES**:
    *   The 5x5 input is placed in the top-left (0-4, 0-4).
    *   The layers "unspool" into the remaining regions:
        *   **Right Region (0-4, 5-9)**: Vertical stripes.
        *   **Bottom Region (5-9, 0-4)**: Horizontal stripes.
        *   **Bottom-Right Region (5-9, 5-9)**: A nested L-shaped staircase.

3.  **The TRANSFORMATION RULE**:
    *   **Identify Colors**:
        *   $C_1$ (Corner Ore): Color at (0,0).
        *   $C_2$ (Core Vein): Color at (2,2).
        *   $C_3$ (Commonite): Color at (0,1).
    *   **Cycle**: $C_1 \rightarrow C_2 \rightarrow C_3 \rightarrow C_1 \dots$
    *   **Right Region (Columns 5-9)**: Each column $j$ (from 5 to 9) is a solid vertical stripe of color $Cycle[(j-5) \pmod 3]$.
        *   Col 5: $C_1$, Col 6: $C_2$, Col 7: $C_3$, Col 8: $C_1$, Col 9: $C_2$.
    *   **Bottom Region (Rows 5-9)**: Each row $i$ (from 5 to 9) is a solid horizontal stripe of color $Cycle[(i-5) \pmod 3]$.
        *   Row 5: $C_1$, Row 6: $C_2$, Row 7: $C_3$, Row 8: $C_1$, Row 9: $C_2$.
    *   **Bottom-Right Region (5-9, 5-9)**: A staircase pattern.
        *   The cell $(i, j)$ where $i, j \in [5, 9]$ follows the rule:
        *   If $i > j$, the color is determined by the row index $i$.
        *   If $j > i$, the color is determined by the column index $j$.
        *   If $i = j$, the color is the *next* one in the cycle relative to the surrounding layer.
        *   Looking at the training examples, the bottom-right 5x5 is filled as:
            Row 5: $C_1, C_1, C_2, C_3, C_1$ (Wait, let's re-examine Example 1).
            Example 1: $C_1=R, C_2=X, C_3=G$.
            Row 5: $X X X X X$ (Wait, the training output shows Row 5 Col 5-9 as $X X G R X$).
            Let's re-evaluate the Bottom-Right:
            Example 1 Bottom-Right (5-9, 5-9):
            Row 5: $X X G R X$
            Row 6: $X G G R X$
            Row 7: $G G G R R$
            Row 8: $R R R R X$
            Row 9: $X X X X X$ (Wait, the training output is slightly different).

    *   **Correcting the Bottom-Right Logic**:
        The bottom-right is a 5x5 grid.
        Col 5: $C_1, C_2, C_3, C_1, C_2$ (vertical)
        Row 5: $C_1, C_2, C_3, C_1, C_2$ (horizontal)
        Actually, looking at Example 1 again:
        Col 9 is $X, X, X, X, G$. (Wait, $C_2=X, C_3=G, C_1=R$).
        Col 9 is $C_2, C_2, C_2, C_2, C_3$.
        Let's look at the diagonal: (5,5)=X, (6,6)=G, (7,7)=R, (8,8)=X, (9,9)=G.
        This is $C_2, C_3, C_1, C_2, C_3$.
        The cells $(i, j)

... [4257 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 227: "Russian nesting dolls carved from colored sticks" k=1 alts: 3/15 3ee1011a

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 input grid has a black background containing several colored line segments (horizontal or vertical). Each segment is a contiguous run of a single non-black color, either all in one row or all in one column. The segments vary in length — some are just a single cell, others span multiple cells. No two segments share the same color.

Do: 1. Identify all distinct colored line segments in the input grid. For each segment, record its color and its length (number of cells). 2. Sort the segments by length in descending order (longest first). 3. The longest segment has length L. Create an L×L output grid. 4. Fill the output grid in layers from outside to inside: the longest segment's color fills the entire grid as the outermost border ring. The second-longest segment's color fills the next inner rectangle (inset by 1 on all sides). Continue for each subsequent segment, each forming the next inner ring, inset by 1 additional cell on each side from the previous. 5. The shortest segment (which may be a single cell) fills the center of the grid. If a segment has length 1, it fills only the single center cell (for odd-sized grids) or a 2×2 center block is not needed — each layer's thickness is exactly 1 cell on each side.

Grid: The output grid is a square with side length equal to the length of the longest segment found in the input. It contains concentric rectangular rings of color, one ring per segment, with no black background remaining. The outermost ring is 1 cell thick on each side, as is each subsequent inner ring.

Figurative Descriptions (16 variants)

"Russian nesting dolls carved from colored sticks"

gemma-4-31b: k=1

See: Scattered across a vast dark field lie colored sticks of different lengths — each a single pure color, each lying perfectly straight, no two alike. They look abandoned, but each one remembers its size.

Do: The longest stick claims authority and bends itself into a square frame — the outermost shell of a nesting doll. The next longest stick, humbled, curls inside that frame to form a smaller shell within. Each remaining stick, from longest to shortest, takes its turn nestling inside the one before it, like matryoshka dolls stacking inward. The tiniest stick — perhaps just a splinter — finds itself cradled at the very heart.

Grid: The result is a perfect square portrait of nested shells, each exactly one layer thick, with the mightiest stick's color as the outer skin and the smallest stick's color glowing at the core. No darkness remains — every inch is claimed by a shell.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (2569 chars)

### Conceptual Digestion

1.  **Identify the CAST:**
    *   **Sticks:** Contiguous lines of a single color (vertical or horizontal) on a black background.
    *   **Length:** The number of cells occupied by a stick.
    *   **Shells:** Concentric square rings of color in the output grid.

2.  **Identify the AFFORDANCES:**
    *   Sticks can be measured for length.
    *   Sticks can be sorted by length (descending).
    *   The sorted colors determine the order of the nested shells from the outermost layer to the innermost core.

3.  **Identify the TRANSFORMATION RULE:**
    *   **Step 1: Find all sticks.** Identify every contiguous line of color and record its color and length.
    *   **Step 2: Sort sticks.** Order the colors from the longest stick to the shortest stick.
    *   **Step 3: Determine output size.** The output is a square grid. The size is determined by the number of unique colors (shells). If there are $N$ colors, the grid size is $(2N - 1) \times (2N - 1)$ if $N$ is the number of layers to reach a center point, or more simply, the smallest square that can accommodate the nesting. Looking at Example 1: 3 colors (B=6, G=5, M=2) $\rightarrow$ $6 \times 6$ output. Wait, let's re-examine Example 1.
    *   **Example 1 Analysis:**
        *   B: length 6
        *   G: length 5
        *   M: length 2
        *   Output: $6 \times 6$. Outer ring B, next ring G, center $2 \times 2$ M.
    *   **Test Input Analysis:**
        *   A (Azure): length 7 (rows 12-18, col 10)
        *   M (Magenta): length 5 (row 11, cols 2-6)
        *   O (Orange): length 3 (rows 6-8, col 10)
        *   G (Green): length 1 (row 4, col 6)
    *   **Sorting by length:** A (7), M (5), O (3), G (1).
    *   **Output Construction:**
        *   The longest stick (A) has length 7. The output grid will be $7 \times 7$.
        *   Layer 1 (Outer): A
        *   Layer 2: M
        *   Layer 3: O
        *   Layer 4 (Center): G

### Applying the Rule to Test Input

1.  **Colors sorted by length:** A (7), M (5), O (3), G (1).
2.  **Grid Size:** $7 \times 7$.
3.  **Layering:**
    *   Outer ring (Row 0, Row 6, Col 0, Col 6): **A**
    *   Second ring (Row 1, Row 5, Col 1, Col 5): **M**
    *   Third ring (Row 2, Row 4, Col 2, Col 4): **O**
    *   Center (Row 3, Col 3): **G**

**Grid Layout:**
Row 0: A A A A A A A
Row 1: A M M M M M A
Row 2: A M O O O M A
Row 3: A M O G O M A
Row 4: A M O O O M A
Row 5: A M M M M M A
Row 6: A A A A A A A

ANSWER:
A A A A A A A
A M M M M M A
A M O O O M A
A M O G O M A
A M O O O M A
A M M M M M A
A A A A A A A

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.44)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 245: "A book falls open and its pages splay apart from the spine." k=2 alts: 8/15 4364c1c4

Training Examples

Example 1

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Example 2

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Example 3

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Output

Literal Description

See: The input grid has a uniform background color. Against this background are one or more composite shapes, each consisting of two differently-colored rectangular regions stacked vertically (one color on top, another color on bottom). The two color regions share a horizontal boundary where they meet. Each region may have an irregular outline (not necessarily a perfect rectangle), but the top region and bottom region together form a single connected composite shape. The top region's leftmost column aligns with the bottom region's leftmost column in the input.

Do: For each composite shape in the grid, identify its two color regions: the upper color region and the lower color region. Shift the entire upper color region one column to the left, replacing vacated cells with the background color. Shift the entire lower color region one column to the right, replacing vacated cells with the background color. The two halves spread apart horizontally like opening a hinge — the top half moves left by one cell and the bottom half moves right by one cell. All other cells remain unchanged.

Grid: The grid dimensions remain the same from input to output. The background is a single uniform color filling all cells not occupied by the composite shapes. The grid is large enough that shifting regions by one column does not push any colored cells beyond the grid boundary.

Figurative Descriptions (16 variants)

"A book falls open and its pages splay apart from the spine."

gemma-4-31b: k=2

See: Against a calm, monochrome sky, you see one or more closed books standing upright. Each book has a colored cover on top and a differently colored cover on the bottom, pressed together along a shared spine where the two halves meet horizontally.

Do: A breeze catches each book and it falls open: the top cover fans to the left while the bottom cover fans to the right, each drifting exactly one step away from the spine. The sky fills in the thin gap each half leaves behind. The books breathe open, their two halves parting like wings unfolding from a single crease.

Grid: The sky is a single background color that fills every space not claimed by a book. The world is wide enough that no cover slides off the edge when the books fall open. Everything stays the same size — only the halves shift apart.

gemma-4-31b — MARC valid, solved with 2 examples

Input

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Prediction

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Reasoning (2932 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Sky (Background)**: The dominant color filling the grid (Azure 'A' in the test input).
    *   **Books**: Clusters of non-background colors. Each book consists of two halves: a **Top Cover** (upper block of color) and a **Bottom Cover** (lower block of color).
    *   **Spine**: The horizontal boundary where the Top Cover and Bottom Cover meet.

2.  **AFFORDANCES**:
    *   The **Top Cover** can shift one unit to the left.
    *   The **Bottom Cover** can shift one unit to the right.
    *   The **Sky** fills the void left by the shifting covers.

3.  **TRANSFORMATION RULE**:
    *   Identify each "book" (a contiguous vertical stack of two different colors).
    *   For each book:
        *   Identify the rows belonging to the Top Cover and the rows belonging to the Bottom Cover.
        *   Shift all cells of the Top Cover one column to the left.
        *   Shift all cells of the Bottom Cover one column to the right.
        *   Fill the vacated cells with the background color ('A').

### Applying the Rule to Test Input

**Background**: A (Azure)

**Book 1**:
*   Top Cover (Blue 'B'): Rows 1-3.
*   Bottom Cover (Red 'R'): Row 4.
*   Transformation:
    *   Rows 1-3: Shift 'B's left by 1.
    *   Row 4: Shift 'R's right by 1.

**Book 2**:
*   Top Cover (Red 'R'): Rows 9-10.
*   Bottom Cover (Yellow 'Y'): Rows 11-12.
*   Transformation:
    *   Rows 9-10: Shift 'R's left by 1.
    *   Rows 11-12: Shift 'Y's right by 1.

**Step-by-step Grid Construction**:
*   Row 0: `A A A A A A A A A A A A A` (No change)
*   Row 1: `A B A A B A A A A A A A A` $\rightarrow$ `A B A A B A A A A A A A A` (Wait, shift left: `A B A A B A...` becomes `A B A A B A...` No, the 'B' at col 2 moves to col 1, 'B' at col 5 moves to col 4). $\rightarrow$ `A B A A B A A A A A A A A` (Wait, let's re-examine: Input Row 1 is `A A B A A B A A A A A A A`. Shift left: `A B A A B A A A A A A A A`)
*   Row 2: `A A B B B B A A A A A A A` $\rightarrow$ `A B B B B A A A A A A A A`
*   Row 3: `A A B B B B A A A A A A A` $\rightarrow$ `A B B B B A A A A A A A A`
*   Row 4: `A A R R R R A A A A A A A` $\rightarrow$ `A A A R R R R A A A A A A`
*   Rows 5-8: No change.
*   Row 9: `A A A A A A R R R A A A A` $\rightarrow$ `A A A A A R R R A A A A A`
*   Row 10: `A A A A A A R R R A A A A` $\rightarrow$ `A A A A A R R R A A A A A`
*   Row 11: `A A A A A A Y Y Y A A A A` $\rightarrow$ `A A A A A A A Y Y Y A A A`
*   Row 12: `A A A A A A Y A Y A A A A` $\rightarrow$ `A A A A A A A Y A Y A A A`
*   Row 13: No change.

ANSWER:
A A A A A A A A A A A A A
A B A A B A A A A A A A A
A B B B B A A A A A A A A
A B B B B A A A A A A A A
A A A R R R R A A A A A A
A A A A A A A A A A A A A
A A A A A A A A A A A A A
A A A A A A A A A A A A A
A A A A A A A A A A A A A
A A A A A R R R A A A A A
A A A A A R R R A A A A A
A A A A A A A Y Y Y A A A
A A A A A A A Y A Y A A A
A A A A A A A A A A A A A

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 278: "A compass needle summons its companion — the red weath ... [70 chars truncated]" k=3 alts: 0/0 4c177718

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 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."

gemma-4-31b: k=3

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.

gemma-4-31b — MARC valid, solved with 3 examples

Input

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Prediction

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Expected

Reasoning (3122 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Blue Traveler**: A small blue (B) shape appearing twice: once on the "rooftop" (above the grey line) and once in the "field" (below the grey line).
    *   **Red Weathervane**: A small red (R) shape on the rooftop. Its orientation (where the bulk of the pixels are) determines the vertical placement of the companion.
    *   **Colorful Companion**: A small colored shape (O, Y, M, G) on the rooftop.
    *   **Horizon**: A grey (X) line dividing the grid.

2.  **AFFORDANCES**:
    *   The **Weathervane** acts as a switch:
        *   If the "heavy end" (the bulk of the red pixels) is at the bottom (row 3 of the rooftop area), the companion lands **below** the traveler.
        *   If the "heavy end" is at the top (row 1 of the rooftop area), the companion lands **above** the traveler.
    *   The **Blue Traveler** in the field acts as the anchor point for the final position.

3.  **TRANSFORMATION RULE**:
    *   Identify the Blue Traveler's position in the field (rows 6-14).
    *   Identify the Colorful Companion's shape from the rooftop.
    *   Check the Red Weathervane:
        *   In Example 1: Red is mostly in row 1 and 2 (top). Wait, looking closer: Example 1 Red is `R R R` (row 1), `. R .` (row 2), `. R .` (row 3). The "heavy end" is the top bar. Result: Companion (O) is **below** the traveler.
        *   In Example 2: Red is `R . .` (row 1), `R . .` (row 2), `R R R` (row 3). The "heavy end" is the bottom bar. Result: Companion (Y) is **above** the traveler.
        *   In Example 3: Red is `R R R` (row 1), `. R .` (row 2), `. R .` (row 3). The "heavy end" is the top bar. Result: Companion (M) is **below** the traveler.
    *   **Refined Rule**: If the Red shape is a "T" pointing down (bar at top), the companion goes **below**. If the Red shape is a "T" pointing up (bar at bottom), the companion goes **above**.
    *   The output grid is a 9x15 crop of the field area. The traveler and companion are stacked vertically with no gap.

### Applying to Test Input:
*   **Blue Traveler (Field)**:
    Row 9: `. B .`
    Row 10: `. B B .`
    Row 11: `. B B B .`
    (Columns 1, 2, 3)
*   **Colorful Companion (Rooftop)**:
    Row 1: `G G G`
    Row 2: `G . G`
    Row 3: `G G G`
*   **Red Weathervane**:
    Row 1: `R R R`
    Row 2: `. R .`
    Row 3: `. R .`
    (Bar is at the top $\rightarrow$ Companion goes **below**).
*   **Final Assembly**:
    Traveler (Rows 9-11)
    Companion (Rows 12-14)
    Columns: 1, 2, 3.

The output grid is the 9x15 field area (rows 6-14 of the input).
Row 6: `.`
Row 7: `.`
Row 8: `.`
Row 9: `. B . . . . . . . . . . . . .`
Row 10: `. B B . . . . . . . . . . . .`
Row 11: `. B B B . . . . . . . . . . .`
Row 12: `. G G G . . . . . . . . . . .`
Row 13: `. G . G . . . . . . . . . . .`
Row 14: `. G G G . . . . . . . . . . .`

ANSWER:
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. B . . . . . . . . . . . . .
. B B . . . . . . . . . . .

... [122 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.56)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 284: "A bathtub overflows through its broken edge, flooding both t ... [30 chars truncated]" k=2 alts: 0/0 4e469f39

Training Examples

Example 1

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Example 2

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Example 3

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Output

Literal Description

See: The input grid contains one or more grey (X) rectangular containers on a black background. Each container is a closed rectangle of X cells except for exactly one missing cell (a gap) in its top wall. The gap is always adjacent to either the left wall or the right wall of the container, leaving the rest of the top wall intact. The interior of each container is initially black.

Do: For each grey container: (1) Fill all interior cells (those enclosed by the X walls, not including the X walls themselves but including the gap cell in the top wall) with red (R). (2) Determine which end of the top wall the gap is on: if the gap is adjacent to the container's left wall, the spill direction is rightward; if adjacent to the right wall, the spill direction is leftward. (3) In the row directly above the container's top wall, place red cells starting from the gap's column and extending in the spill direction all the way to the edge of the grid.

Grid: The grid is 10x10 with a black (.) background. Grey (X) cells form the container walls and are never on the grid boundary rows/columns in practice. Red (R) cells are output-only and may extend to the grid edges along spill rows. Multiple containers can coexist on the same grid without overlapping.

Figurative Descriptions (1 variants)

"A bathtub overflows through its broken edge, flooding both the tub and the hallway beyond."

gemma-4-31b: k=2

See: Grey porcelain bathtubs sit in a dark bathroom. Each tub is walled on all sides except for a crack near one corner of its rim — a chip where the edge has broken away. The tubs are empty inside.

Do: Turn on the faucet: red water fills each tub to the brim, including the cracked spot. But the crack can't hold — water spills over the broken edge and rushes across the bathroom floor in the direction away from the intact rim, streaming all the way until it hits the far wall.

Grid: The bathroom is a 10×10 tile floor, dark by default. Grey tiles form the porcelain walls of each tub. The red floodwater fills the hollow inside and pours out along the row just above the rim, racing from the crack to the edge of the room. Multiple tubs can sit in the same bathroom without touching.

gemma-4-31b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (6145 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Grey tiles (X)**: Represent the walls of the "porcelain bathtubs".
    *   **Black tiles (.)**: Represent the "dark bathroom floor" or the "empty inside" of the tubs.
    *   **Red tiles (R)**: Represent the "floodwater".

2.  **AFFORDANCES**:
    *   A "tub" is a rectangular ring of grey tiles.
    *   A "crack" is a missing grey tile in the perimeter of the tub.
    *   The "inside" of the tub is the area enclosed by the grey walls.
    *   The "spill" occurs at the crack and travels in a straight line (row or column) away from the center of the tub until it hits the edge of the grid.

3.  **TRANSFORMATION RULE**:
    *   **Step 1: Fill the Tub.** Identify all black tiles completely enclosed by grey tiles (the interior) and change them to red (R).
    *   **Step 2: Identify the Crack.** Find the gap in the grey perimeter.
    *   **Step 3: Spill the Water.** From the gap, extend a line of red tiles (R) from the gap to the edge of the grid. The direction is determined by the position of the gap relative to the tub's interior (it flows "outward").
    *   *Refining the spill direction based on examples*:
        *   Example 1: Tub is (3,3) to (7,7). Gap is at (3,4) - top edge. Water fills interior and spills from (3,4) across the top row (row 2) to the right edge. Wait, looking closer: Gap is at (3,4). Interior is (4,4) to (6,6). The gap is at the top wall. The water fills the interior and spills *up* into the row above the gap and then *across*? No, looking at Example 1 output: Row 2 (index 2) from col 4 to 9 is red. The gap is at (3,4). The water fills the interior and spills *up* to (2,4) and then *right* to the edge.
        *   Example 2: Tub is (3,2) to (6,5). Gap is at (3,4). Interior is (4,3) to (5,4). Gap is at the top wall. Water fills interior and spills *up* to (2,4) and then *left* to the edge.
        *   *Correction*: The "crack" is the missing piece of the wall. The water fills the interior and spills out of the crack. The spill direction is perpendicular to the wall containing the crack, moving away from the tub. If the crack is on the top wall, it spills up. If it's on the bottom, it spills down. If it's on the left, it spills left. If it's on the right, it spills right.
        *   *Re-evaluating Example 1*: Tub walls are at row 3, 7 and col 3, 7. Gap is at (3,4). Interior is (4,4) to (6,6). Gap is at top wall. Water fills interior and spills *up* to row 2, then continues *right*? No, the output shows row 2, col 4-9 is red. This means it spilled up to (2,4) and then flowed right.
        *   *Re-evaluating Example 2*: Tub walls are at row 3, 6 and col 2, 5. Gap is at (3,4). Interior is (4,3) to (5,4). Gap is at top wall. Water fills interior and spills *up* to row 2, then flows *left* to the edge.
        *   *Wait*, look at the "crack" again. In Example 1, the gap is at (3,4). The wall is `X . X X`. The gap is at index 4. In Example 2, the gap is at (3,4). The wall is `X X . X`

... [3145 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.91)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 292: "A ball bounces off a wall like light reflecting off a mirror ... [1 chars truncated]" k=3 alts: 2/15 508bd3b6

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 contains three elements: (1) a black (.) background, (2) a solid rectangular red (R) wall along one edge of the grid (it can be along the bottom, right, left, or top — occupying full rows or full columns), and (3) exactly two or three azure (A) cells arranged in a diagonal line. The A cells define a trajectory direction — moving from the first A to the last A gives a diagonal direction vector (e.g., down-right, down-left, up-right, or up-left). The A diagonal is positioned in the open black region, with the red wall nearby on one side.

Do: 1. Identify the diagonal direction of the A cells by looking at consecutive A positions. Compute the direction vector (row_delta, col_delta), each being +1 or -1. 2. Identify the red wall: it is a solid rectangular block of R cells occupying entire rows or columns along one edge of the grid. Determine which edge it lies on (top, bottom, left, or right). 3. Starting from the last A cell in the direction of travel, extend the trajectory one step at a time in the same diagonal direction, placing a green (G) cell at each new position. Continue until the next step would enter the red wall region or exit the grid. 4. When the trajectory reaches the red wall, reflect the ball: reverse the component of the direction vector that is perpendicular to the wall. If the wall is horizontal (top or bottom edge), negate the row_delta; if the wall is vertical (left or right edge), negate the col_delta. 5. Continue placing G cells in the new reflected direction, one step at a time, until the trajectory exits the grid boundary. 6. Leave all original A cells and R cells unchanged. Only add G cells on previously black cells.

Grid: The grid is rectangular (not necessarily square), typically around 12x12. The background is black (.). The red wall is a contiguous rectangular block spanning the full width or full height of the grid along one edge, and can be multiple rows or columns thick. The A cells and G cells occupy the open (non-red) portion of the grid. The output grid has the same dimensions as the input.

Figurative Descriptions (16 variants)

"A ball bounces off a wall like light reflecting off a mirror."

gemma-4-31b: k=3

See: A black night sky stretches across the grid. Along one edge, a solid red cliff face stands immovable — a wall of crimson stone. Out in the open darkness, a few azure sparks trace a diagonal path, like a ball mid-flight, hurtling toward the cliff.

Do: The azure sparks show where the ball has already been — its past trajectory frozen in place. Follow the ball's momentum forward, leaving a green phosphorescent trail as it streaks through the darkness. When the ball reaches the red cliff, it bounces — ricocheting like a billiard ball off a cushion, its angle of incidence equal to its angle of reflection. The green trail continues in the new direction until the ball flies off into the void beyond the grid's edge. The cliff and the original sparks remain untouched.

Grid: The arena is a rectangular court draped in black. The red cliff is a thick, immovable barrier running along one entire side. The azure marks and the green trail live only in the open darkness beyond the cliff. The court's dimensions stay fixed.

gemma-4-31b — MARC valid, solved with 3 examples

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Prediction

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Reasoning (3906 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Black (.)**: The empty space (void).
    *   **Red (R)**: The "cliff" (a reflective wall).
    *   **Azure (A)**: The "sparks" representing the ball's initial trajectory.
    *   **Green (G)**: The "phosphorescent trail" representing the ball's future path.

2.  **AFFORDANCES**:
    *   The **Azure sparks** define a vector (direction and speed).
    *   The **Red cliff** acts as a mirror; when the ball hits it, the perpendicular component of its velocity is reversed.
    *   The **Green trail** marks every cell the ball enters after the last Azure spark.

3.  **TRANSFORMATION RULE**:
    *   **Step 1: Determine Velocity**. Look at the sequence of Azure (A) cells. In the test input, A is at (0, 3) and (1, 4). The movement is $\Delta r = (+1, +1)$ per step.
    *   **Step 2: Project Forward**. Continue the path from the last A (1, 4) using the vector $(+1, +1)$.
    *   **Step 3: Handle Collision**. The path is: (2, 5), (3, 6), (4, 7), (5, 8).
    *   **Step 4: Reflection**. At (5, 8), the next step would be (6, 9). However, the Red cliff (R) starts at column 8. The ball hits the wall at the boundary between column 7 and 8.
    *   Wait, let's re-examine the grid:
        Columns 0-7 are black (.), Columns 8-11 are red (R).
        Last A is at (1, 4).
        Path:
        (2, 5) -> G
        (3, 6) -> G
        (4, 7) -> G
        At (5, 8), it hits the Red wall.
        The reflection rule: Angle of incidence = Angle of reflection.
        Incoming vector: $(+1, +1)$.
        Wall is vertical (x-axis constant).
        Reflected vector: $(+1, -1)$.
    *   **Step 5: Continue Path**. From the point of impact (approx 5, 7.5), the ball moves in direction $(+1, -1)$.
        (5, 7) is where it bounces? No, let's look at the training examples.
        Example 2: A at (10, 3), (11, 2). Vector $(-1, -1)$. Hits wall at col 10. Bounces to $(+1, -1)$? No, it bounces back to the left.
        Let's re-evaluate Example 2:
        A: (10, 3), (11, 2). Vector is $\Delta r = (-1, -1)$ per step (moving up and left).
        Wait, the A's are at (10, 3) and (11, 2). The ball is moving from (11, 2) to (10, 3).
        Vector: $\Delta r = (-1, +1)$.
        Path: (9, 4), (8, 5), (7, 6), (6, 7), (5, 8), (4, 9).
        At (4, 9), it hits the wall at col 10.
        Reflected vector: $(-1, -1)$.
        Path: (5, 8), (6, 7), (7, 6), (8, 5), (9, 4).
        Wait, the output for Example 2 shows G at (4, 9), then (5, 8), (6, 7)...
        Let's trace Example 2 again:
        A: (11, 2), (10, 3). Vector: $(-1, 1)$.
        G: (9, 4), (8, 5), (7, 6), (6, 7), (5, 8), (4, 9) [Hits wall], (3, 8), (2, 7), (1, 6), (0, 5).
        This matches the output!

    *   **Applying to Test Input**:
        A: (0, 3), (1, 4). Vector: $(+1, +1)$.
        Path:
        (2, 5) -> G
        (3, 6) -> G
        (4, 7) -> G
        (5, 8) -> Hits wall (R is at col 8).
        Wait, the wall is at col 8. The ball is at (4

... [927 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.88)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 310: "Every treasure chest needs a display case, and open chests r ... [18 chars truncated]" k=1 alts: 0/0 543a7ed5

Training Examples

Example 1

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Example 2

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Output

Literal Description

See: The input grid has an azure (A) background containing several distinct magenta (M) rectangles. Each rectangle is an axis-aligned closed border of magenta cells. Some rectangles are solid (filled entirely with magenta), while others are hollow — their outer perimeter is magenta but they contain azure cells in their interior.

Do: For each distinct magenta rectangle in the input: (1) Identify its bounding box — the smallest axis-aligned rectangle that contains all its magenta cells. (2) Add a 1-cell-wide green (G) border around the entire bounding box. This border occupies the ring of cells immediately surrounding the bounding box on all four sides, including corners. Any azure cells in those positions become green. (3) Find any azure cells that are enclosed inside the magenta rectangle's border (i.e., cells within the bounding box that are azure, not magenta). Replace those interior azure cells with yellow (Y). Solid rectangles (no interior azure cells) get only the green border and no yellow fill. All other azure background cells remain unchanged.

Grid: The grid is 15×15 with azure (A) as the background color. Magenta rectangles do not overlap and do not touch each other, leaving at least one cell of azure between any two rectangles and between any rectangle and the grid edge — ensuring there is always room for the 1-cell green border without conflict.

Figurative Descriptions (1 variants)

"Every treasure chest needs a display case, and open chests reveal gold inside."

gemma-4-31b: k=1

See: An azure sea stretches out, and scattered across it are magenta treasure chests of various sizes. Some chests are sealed shut — solid magenta through and through. Others have their lids cracked open, revealing the azure sea peeking through their hollow interiors.

Do: A museum curator arrives to put each chest on display. She builds a green glass case snugly around every chest, one pane thick on every side. Then she peers inside each one — if the chest is hollow, she fills its empty interior with golden yellow, as if the open space was always meant to hold treasure. Sealed chests get their display case but hold no gold; they are the treasure themselves.

Grid: The sea is a 15×15 azure expanse. The chests float apart from one another with breathing room between them, so every glass case fits without bumping into a neighbor or sliding off the edge of the world.

gemma-4-31b — MARC valid, solved with 1 example

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Reasoning (2739 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Azure (A)**: The background "sea".
    *   **Magenta (M)**: The "treasure chests".
    *   **Green (G)**: The "glass case" (border).
    *   **Yellow (Y)**: The "gold" (fill for hollow interiors).

2.  **AFFORDANCES**:
    *   **Magenta blocks** can be grouped into rectangular or irregular shapes (chests).
    *   **Hollow interiors** are areas of Azure (A) completely enclosed by Magenta (M).
    *   **Borders** are the perimeter of the Magenta shapes, extended by one pixel in all directions.

3.  **TRANSFORMATION RULE**:
    *   **Step 1 (The Case)**: For every connected component of Magenta (M), identify its bounding box or the set of all cells adjacent to it (including diagonals). Place a Green (G) border exactly one cell wide around the entire perimeter of the Magenta shape.
    *   **Step 2 (The Gold)**: Identify any Azure (A) cells that are completely enclosed by Magenta (M) cells. Change these internal Azure cells to Yellow (Y).
    *   **Step 3 (Preservation)**: All other Azure cells remain Azure. All Magenta cells remain Magenta.

### Applying the Rule to Test Input

**Chest 1 (Top Left):**
Input: (3,2) to (6,5)
M M M M
M A A M
M A A M
M M M M
*   **Border (G)**: Rows 2-7, Cols 1-6.
*   **Fill (Y)**: (4,3), (4,4), (5,3), (5,4) become Yellow.

**Chest 2 (Top Right):**
Input: (2,9) to (7,11)
M M M
M M M
M A M
M A M
M A M
M M M
*   **Border (G)**: Rows 1-8, Cols 8-12.
*   **Fill (Y)**: (4,10), (5,10), (6,10) become Yellow.

**Chest 3 (Bottom Center):**
Input: (11,4) to (13,10)
M M M M M M M
M M A A M M M
M M M M M M M
*   **Border (G)**: Rows 10-14, Cols 3-11.
*   **Fill (Y)**: (12,6), (12,7) become Yellow.

### Final Grid Construction

Row 0: A A A A A A A A A A A A A A A
Row 1: A A A A A A A A G G G G G A A
Row 2: A G G G G G G A G M M M G A A
Row 3: A G M M M M G A G M M M G A A
Row 4: A G M Y Y M G A G M Y M G A A
Row 5: A G M Y Y M G A G M Y M G A A
Row 6: A G M M M M G A G M Y M G A A
Row 7: A G G G G G G A G M M M G A A
Row 8: A A A A A A A A G G G G G A A
Row 9: A A A A A A A A A A A A A A A
Row 10: A A A G G G G G G G G G A A A
Row 11: A A A G M M M M M M M G A A A
Row 12: A A A G M M Y Y M M M G A A A
Row 13: A A A G M M M M M M M G A A A
Row 14: A A A G G G G G G G G G A A A

ANSWER:
A A A A A A A A A A A A A A A
A A A A A A A A G G G G G A A
A G G G G G G A G M M M G A A
A G M M M M G A G M M M G A A
A G M Y Y M G A G M Y M G A A
A G M Y Y M G A G M Y M G A A
A G M M M M G A G M Y M G A A
A G G G G G G A G M M M G A A
A A A A A A A A G G G G G A A
A A A A A A A A A A A A A A A
A A A G G G G G G G G G A A A
A A A G M M M M M M M G A A A
A A A G M M Y Y M M M G A A A
A A A G M M M M M M M G A A A
A A A G G G G G G G G G A A A

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 319: "Russian nesting dolls are packed away, each one's importance ... [24 chars truncated]" k=1 alts: 9/15 5587a8d0

Training Examples

Example 1

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Example 2

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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."

gemma-4-31b: k=1

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.

gemma-4-31b — MARC valid, solved with 1 example

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Reasoning (3196 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Input Grid**: A "workshop table" (background color `O` = orange) containing scattered "doll pieces" (blocks of other colors).
    *   **Doll Pieces**: Contiguous blocks of the same color.
    *   **Weight/Size**: The "heaviness" of a doll is determined by the total number of pixels (count) of that color in the input grid.
    *   **Output Grid**: A square grid representing concentric shells of colors.

2.  **AFFORDANCES**:
    *   The colors can be counted to determine their relative size.
    *   The colors can be ordered from largest (heaviest) to smallest (lightest).
    *   The output size is determined by the number of unique colors present (excluding the background `O`). If there are $N$ unique colors, the output is a square of size $(2N-1) \times (2N-1)$.

3.  **TRANSFORMATION RULE**:
    *   **Step 1**: Identify all unique colors in the input grid, excluding the background color `O`.
    *   **Step 2**: Count the number of pixels for each of these colors.
    *   **Step 3**: Sort the colors by count in descending order (Heaviest $\rightarrow$ Lightest).
    *   **Step 4**: Construct a square grid where the heaviest color forms the outermost perimeter, the second heaviest forms the next inner perimeter, and so on, until the lightest color occupies the center pixel.

---

### Applying the Rule to Test Input

**1. Identify and Count Colors (excluding `O`):**
*   `W` (maroon): 2 pixels
*   `R` (red): 4 pixels
*   `X` (grey): 4 pixels
*   `A` (azure): 1 pixel
*   `.` (black): 4 pixels
*   `B` (blue): 8 pixels

**2. Sort by Count (Descending):**
1.  `B` (blue): 8
2.  `R` (red): 4 (Tie - order usually follows appearance or specific logic, but let's check others)
3.  `X` (grey): 4
4.  `.` (black): 4
5.  `W` (maroon): 2
6.  `A` (azure): 1

*Wait, let's re-count carefully:*
*   `W`: (0,2), (1,2) $\rightarrow$ 2
*   `R`: (0,5), (0,6), (0,7), (1,5), (1,7) $\rightarrow$ 5
*   `X`: (2,0), (3,0), (3,1), (4,0) $\rightarrow$ 4
*   `A`: (3,3) $\rightarrow$ 1
*   `.`: (4,5), (5,5), (5,6), (6,6), (7,6), (7,7) $\rightarrow$ 6 (Wait, let me re-read the grid)

*Re-counting Test Input Grid:*
Row 0: O O W O O R R R (W:1, R:3)
Row 1: O O W O O R O R (W:1, R:2)
Row 2: X O O O O O O O (X:1)
Row 3: X X O A O O O O (X:2, A:1)
Row 4: X O O O O . O O (X:1, .:1)
Row 5: O O B O O . . O (B:1, .:2)
Row 6: O B B B O O . . (B:3, .:2)
Row 7: B B B B B O O . (B:5, .:1)

**Totals:**
*   `B` (blue): 1 + 3 + 5 = 9
*   `.` (black): 1 + 2 + 2 + 1 = 6
*   `R` (red): 3 + 2 = 5
*   `X` (grey): 1 + 2 + 1 = 4
*   `W` (maroon): 1 + 1 = 2
*   `A` (azure): 1 = 1

**3. Sorted Order (Heaviest to Lightest):**
1. `B` (9)
2. `.` (6)
3. `R` (5)
4. `X` (4)
5. `W` (2)
6. `A` (1)

**4. Construct Output Grid:**
Number of colors = 6. Output size = $(2 \times 6) - 1 = 11 \times 11$.
*   Layer 1 (Outer): `B`
*   Layer 2: `.`
*   Layer 3: `R`
*   Layer 4: `X`
*   Layer 5: `W`
*   Layer 6 (Center): `A`

ANSWER:
B B B B B B B B B B B
B . . . . . . . . . B
B

... [196 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 380: "A lighthouse beam reaches toward ships, and its twin on the ... [39 chars truncated]" k=1 alts: 0/0 673ef223

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 and contains two vertical red (R) bar segments, each spanning several consecutive rows. One bar is along the left edge (column 0) and the other along the right edge (rightmost column), but they occupy different row ranges — they do not overlap vertically. Scattered near one of the bars (but not touching it) are one or more azure (A) marker cells. These markers always appear on rows that fall within that bar's row range. The other bar has no markers near it.

Do: 1. Identify the two vertical red bars and which one has azure (A) markers in its vicinity. 2. For the bar WITH markers (the 'marked bar'): on each row containing an A marker, draw a horizontal line of A cells from the cell adjacent to the red bar outward toward the A marker's position. Replace the original A marker cell with yellow (Y). The fill runs from the bar to the marker position, with A's in between and Y at the marker's original location. The bar cells themselves remain R. 3. Determine the relative position of each marked row within the marked bar (e.g., if the bar spans rows 1–6 and a marker is on row 3, its relative index is 2). 4. For the bar WITHOUT markers (the 'mirror bar'): on the rows corresponding to the same relative indices within this bar, fill the entire row from the cell adjacent to this bar all the way to the opposite edge of the grid with A cells. The bar cells themselves remain R. 5. All other cells remain unchanged.

Grid: Rectangular grid of variable dimensions (roughly 8–12 columns, 19–20 rows). Background is black (.). The two red bars are always vertical segments along opposite left/right edges, occupying non-overlapping row ranges. Grid values use colors 0–9 mapped to single characters. The coordinate system is row-major with (0,0) at top-left.

Figurative Descriptions (1 variants)

"A lighthouse beam reaches toward ships, and its twin on the far shore shines across the entire sea."

gemma-4-31b: k=1

See: Two crimson lighthouses stand on opposite shores of a dark sea, each illuminating only its own stretch of coastline. One lighthouse has azure ships anchored at various distances in its waters. The other shore is empty — no ships, just darkness.

Do: Each lighthouse with ships casts a beam of azure light from its base toward each ship. Where the beam meets a ship, the ship catches fire and glows yellow — it has been found. The twin lighthouse on the opposite shore, though it has no ships of its own, senses a sympathetic pulse: for each beam its sibling cast, it fires a matching beam at the same relative position along its own coastline — but with no ship to stop it, the light floods all the way across the sea to the far shore. The lighthouses themselves always remain steadfast crimson.

Grid: A rectangular dark ocean with two crimson lighthouse towers built as vertical columns of red along opposite edges, never occupying the same latitudes. Azure ships float in the waters near one lighthouse. The coordinate system is nautical: origin at the top-left, rows are latitudes, columns are longitudes.

gemma-4-31b — MARC valid, solved with 1 example

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Reasoning (3609 chars)

### Conceptual Digestion

1.  **The CAST**:
    *   **Crimson Lighthouses (R)**: Vertical columns of red pixels on opposite edges of the grid.
    *   **Azure Ships (A)**: Blue pixels located in the "waters" (black area) near one of the lighthouses.
    *   **Dark Sea (.)**: The black background.
    *   **Beams (A)**: Azure lines created by the lighthouses.
    *   **Found Ships (Y)**: Azure ships that are hit by a beam from their own lighthouse.

2.  **The AFFORDANCES**:
    *   A lighthouse can "fire" a beam horizontally across its row if there is a ship (A) in that row.
    *   If a ship (A) is in the path of a beam from its own lighthouse, it turns yellow (Y).
    *   The "sympathetic" lighthouse on the opposite shore fires a beam in the same row relative to its own position. Since there are no ships on its side, this beam travels the full width of the grid.

3.  **The TRANSFORMATION RULE**:
    *   **Step 1**: Identify the two red columns (Lighthouse 1 and Lighthouse 2).
    *   **Step 2**: Identify which lighthouse has ships (A) in its vicinity.
    *   **Step 3**: For every row $r$ where Lighthouse 1 is present and there is a ship (A) at $(r, c)$:
        *   Fill the segment from the lighthouse column to the ship's column with Azure (A).
        *   Change the ship at $(r, c)$ to Yellow (Y).
    *   **Step 4**: For every row $r'$ where Lighthouse 2 is present that corresponds to the relative position of the ships found in Step 3:
        *   The relative position is determined by the index within the red column. If the red column starts at row $S$ and the ship is at row $S+k$, the sympathetic beam fires from the second lighthouse at its starting row $S' + k$.
        *   Fill the entire row from the opposite edge to the lighthouse column with Azure (A).
    *   **Step 5**: Red pixels (R) always remain Red.

### Applying the Rule to Test Input

*   **Lighthouse 1 (L1)**: Column 0, Rows 1-6.
*   **Lighthouse 2 (L2)**: Column 12, Rows 14-19.
*   **Ships (A)**:
    *   Row 2, Col 8
    *   Row 3, Col 7
    *   Row 5, Col 4
*   **L1 Beams**:
    *   Row 2: Col 1 to 7 become A, Col 8 becomes Y.
    *   Row 3: Col 1 to 6 become A, Col 7 becomes Y.
    *   Row 5: Col 1 to 3 become A, Col 4 becomes Y.
*   **L2 Sympathetic Beams**:
    *   L1 starts at row 1. Ships are at relative offsets +1 (Row 2), +2 (Row 3), and +4 (Row 5).
    *   L2 starts at row 14. Sympathetic beams fire at relative offsets +1, +2, and +4.
    *   Row 15 (14+1): Col 0 to 11 become A.
    *   Row 16 (14+2): Col 0 to 11 become A.
    *   Row 18 (14+4): Col 0 to 11 become A.

### Final Grid Construction

Row 0: . . . . . . . . . . . .
Row 1: R . . . . . . . . . . .
Row 2: R A A A A A A A Y . . .
Row 3: R A A A A A A Y . . . .
Row 4: R . . . . . . . . . . .
Row 5: R A A A Y . . . . . . .
Row 6: R . . . . . . . . . . .
Row 7-13: . . . . . . . . . . . .
Row 14: . . . . . . . . . . . R
Row 15: A A A A A A A A A A A R
Row 16: A A A A A A A A A A A R
Row 17: . . . . . . . . . . . R

... [609 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 1.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 406: "Heavy boulders sink to the riverbed while pebbles float in p ... [5 chars truncated]" k=1 alts: 0/0 6ca952ad

Training Examples

Example 1

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Example 2

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Example 3

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Output

Literal Description

See: The input grid has an orange (O) background with several distinct connected shapes made of a single non-orange color. Each shape is a connected component of colored cells (using 4-connectivity: up, down, left, right). Shapes vary in size from 1 cell to many cells.

Do: 1. Identify all connected components of non-background (non-orange) cells using 4-connectivity (horizontal and vertical adjacency only, not diagonal). 2. Count the number of cells in each connected component. 3. For each component with 3 or fewer cells: leave it exactly where it is. 4. For each component with 4 or more cells: apply gravity — slide the entire shape downward, preserving its internal structure and column positions, until its lowest cell(s) rest on the bottom row of the grid (or on top of another already-settled large shape). 5. Clear the original positions of all moved shapes to background (orange). Small shapes that stay may now overlap with where large shapes used to be — they remain unchanged regardless.

Grid: The output grid has the same dimensions as the input grid. The background color is orange (O). The grid uses a standard coordinate system with row 0 at the top and the last row at the bottom. Gravity acts downward toward the last row.

Figurative Descriptions (1 variants)

"Heavy boulders sink to the riverbed while pebbles float in place."

gemma-4-31b: k=1

See: An orange river carries stones of various sizes — some are mere pebbles, others are heavy boulders. Each stone is a cluster of same-colored cells clinging together through shared edges.

Do: The river obeys a simple law of nature: small pebbles (three cells or fewer) are light enough to hover where the current placed them. But boulders — any stone of four or more cells — are too heavy to resist gravity. They sink straight down through the orange water, keeping their shape intact, until they settle on the riverbed at the bottom of the grid or come to rest atop another sunken boulder. The water rushes in to fill the space they left behind.

Grid: The riverbed is the bottom row. The river flows orange from edge to edge, same dimensions as before. Pebbles remain suspended exactly where they were, even if a boulder once sat beside them. Boulders stack faithfully on the bottom, preserving their silhouettes.

gemma-4-31b — MARC valid, solved with 1 example

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Prediction

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Reasoning (3180 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Orange (O)**: The "river" (background).
    *   **Colored Clusters (Y, M, etc.)**: The "stones".
    *   **Pebbles**: Clusters of 3 cells or fewer.
    *   **Boulders**: Clusters of 4 cells or more.

2.  **AFFORDANCES**:
    *   **Pebbles**: Stationary. They stay in their original coordinates.
    *   **Boulders**: Dynamic. They "sink" (move vertically down) until they hit the bottom edge of the grid or another boulder.
    *   **River (O)**: Fills the void left by sinking boulders.

3.  **TRANSFORMATION RULE**:
    *   Identify all connected components (clusters) of non-orange cells.
    *   Calculate the size of each cluster.
    *   If size $\le 3$, the cluster remains in place.
    *   If size $\ge 4$, the cluster moves down as a unit. The lowest cell of the cluster will eventually touch the bottom row (row 13) or the top of another already-sunken boulder.
    *   Since the test input has only one color of stones (Yellow) and they are separated by orange, we treat each contiguous yellow block as a separate stone.

### Applying the Rule to Test Input

**Input Analysis (Yellow clusters):**
*   **Cluster 1**: (1,1), (1,2), (2,1), (2,2). Size = 4. **BOULDER**.
*   **Cluster 2**: (1,4), (2,4), (3,4). Size = 3. **PEBBLE**.
*   **Cluster 3**: (1,6). Size = 1. **PEBBLE**.
*   **Cluster 4**: (1,8), (1,9), (2,8), (2,9), (3,7), (3,8), (3,9), (4,7), (4,8), (4,9). Size = 10. **BOULDER**.
*   **Cluster 5**: (1,11), (1,12), (2,11), (2,12), (3,11), (3,12), (4,11), (4,12). Size = 8. **BOULDER**.

**Sinking Process:**
*   **Pebbles (Stay)**:
    *   (1,4), (2,4), (3,4)
    *   (1,6)
*   **Boulders (Sink)**:
    *   **Cluster 1** (2x2 square): Sinks to the bottom. Bottom row is 13. It occupies rows 12 and 13, columns 1 and 2.
    *   **Cluster 5** (2x4 rectangle): Sinks to the bottom. Bottom row is 13. It occupies rows 10, 11, 12, 13, columns 11 and 12.
    *   **Cluster 4** (Complex shape): Sinks to the bottom. The lowest point of the original shape is row 4. The shape spans 4 rows (1 to 4). It will occupy rows 10, 11, 12, 13.
        *   Original relative coords: (0,0), (0,1), (1,0), (1,1), (2,-1), (2,0), (2,1), (3,-1), (3,0), (3,1) relative to (1,1). Wait, let's use absolute:
        *   Row 1: Col 8, 9
        *   Row 2: Col 8, 9
        *   Row 3: Col 7, 8, 9
        *   Row 4: Col 7, 8, 9
        *   Sunk to bottom: Row 10: Col 8, 9; Row 11: Col 8, 9; Row 12: Col 7, 8, 9; Row 13: Col 7, 8, 9.

**Final Grid Construction:**
*   Rows 0-9: Only pebbles at (1,4), (2,4), (3,4) and (1,6).
*   Row 10: Col 8, 9 (C4), Col 11, 12 (C5).
*   Row 11: Col 8, 9 (C4), Col 11, 12 (C5).
*   Row 12: Col 1, 2 (C1), Col 7, 8, 9 (C4), Col 11, 12 (C5).
*   Row 13: Col 1, 2 (C1), Col 7, 8, 9 (C4), Col 11, 12 (C5).

ANSWER:
O O O O O O O O O O O O O O
O O O O Y O Y O O O O O O O
O O O O Y O O O O O O O O O
O O O O Y O O O O O O O O O
O O O O O O O O O O O O O O
O O O O O O O O O O O O O O
O O O O O O O O O O O O O O
O O O O O O O O

... [180 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.92)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 418: "A naturalist classifies unknown species by the size of their ... [7 chars truncated]" k=1 alts: 14/15 6e82a1ae

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 clusters (connected components) of grey (X) cells against a black (.) background. Each cluster varies in size, meaning the number of cells it contains. Clusters can be any shape — L-shapes, straight lines, squares, etc. — and are scattered across the grid without overlapping.

Do: 1. Identify every connected component of grey (X) cells in the input grid, using 4-connectivity (up, down, left, right — not diagonal). 2. Count the number of cells in each connected component. 3. Recolor each component based on its size: cells belonging to a 2-cell cluster become green (G), cells belonging to a 3-cell cluster become red (R), and cells belonging to a 4-cell cluster become blue (B). 4. All black (.) background cells remain unchanged.

Grid: The grid dimensions match the input exactly (typically 10x10). The background is black (.). The only non-background elements are clusters of grey cells in the input, which become green, red, or blue in the output depending on cluster size. No cells are added or removed; only colors change.

Figurative Descriptions (16 variants)

"A naturalist classifies unknown species by the size of their herds."

gemma-4-31b: k=1

See: Scattered across a dark landscape, small herds of mysterious grey animals huddle together. Some travel in pairs, some in trios, and some in groups of four. Each herd keeps to itself, never touching another.

Do: A naturalist arrives to catalog the wildlife. She identifies each herd by counting its members, then paints them with a tag color revealing their species: the smallest pairs share one color, the middle-sized trios another, and the largest bands of four a third. The empty wilderness stays untouched.

Grid: The dark terrain remains as-is. Every grey animal receives its species tag — a new coat color determined solely by how many companions share its herd. No creatures appear or vanish; only their coats change.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (5168 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Dark Landscape (`.`)**: The background/empty space.
    *   **Grey Animals (`X`)**: The objects to be transformed. They form "herds" (connected components of `X`s).
    *   **Species Tags (Colors)**: The new colors assigned to the `X`s based on the size of their connected component.

2.  **AFFORDANCES**:
    *   The `X` cells can be grouped into connected components (orthogonal adjacency).
    *   The size of each component determines its new color.
    *   The background `.` remains unchanged.

3.  **TRANSFORMATION RULE**:
    *   Identify all connected components of `X`.
    *   Count the number of cells in each component.
    *   Assign colors based on the size (referencing Example 1):
        *   Size 1: Not explicitly defined in Example 1, but looking at the logic:
            *   Example 1: Size 2 $\rightarrow$ Blue (`B`), Size 3 $\rightarrow$ Red (`R`), Size 4 $\rightarrow$ Blue (`B`)? Wait, let's re-examine Example 1.
            *   Example 1 Analysis:
                *   (2,2)-(2,4) is size 3 $\rightarrow$ Red (`R`)
                *   (2,7)-(3,7) is size 2 $\rightarrow$ Green (`G`)? No, (2,7) and (3,7) are `G`.
                *   (5,3)-(5,4) and (6,3) is size 3 $\rightarrow$ Red (`R`)
                *   (7,7) is size 1 $\rightarrow$ Blue (`B`)
                *   (8,1)-(9,2) is size 4 $\rightarrow$ Blue (`B`)
                *   (8,6)-(8,8) is size 3 $\rightarrow$ Blue (`B`)? No, let's look closer.
                *   Example 1 Output:
                    *   (2,2-4): R R R (Size 3)
                    *   (2,7-3,7): G G (Size 2)
                    *   (5,3-6,3): R R R (Size 3)
                    *   (7,7): B (Size 1)
                    *   (8,1-9,2): B B B B (Size 4)
                    *   (8,6-8,8): B B B (Size 3) - *Wait, this contradicts the first size 3.*

    *   **Re-evaluating Example 1**:
        *   Size 1: (7,7) $\rightarrow$ B
        *   Size 2: (2,7-3,7) $\rightarrow$ G
        *   Size 3: (2,2-4) $\rightarrow$ R, (5,3-6,3) $\rightarrow$ R, (8,6-8,8) $\rightarrow$ B? No, (8,6-8,8) is size 3 and is B.
        *   Size 4: (8,1-9,2) $\rightarrow$ B.
        *   Let's look at the colors again:
            *   Size 1: B
            *   Size 2: G
            *   Size 3: R (mostly)
            *   Size 4: B
            *   Wait, (8,6-8,8) is size 3 and is B. (8,1-9,2) is size 4 and is B. (7,7) is size 1 and is B.
            *   Maybe the rule is: Size 1, 4, and some others are B?
            *   Let's look at the "Metaphorical Description": "smallest pairs share one color, the middle-sized trios another, and the largest bands of four a third."
            *   Pairs (2) $\rightarrow$ Color A
            *   Trios (3) $\rightarrow$ Color B
            *   Bands of four (4) $\rightarrow$ Color C
            *   Looking at Example 1 again:
                *   Size 2: (2,7-3,7) $\rightarrow$ G. (Pairs = Green)
                *   Size 3: (2,2-4) $\rightarrow$ R, (5,3-6,3) $\rig

... [2168 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.93)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 430: "Rockets on a launchpad ignite according to their fuel type." k=2 alts: 15/15 72a961c9

Training Examples

Example 1

Input

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Output

Example 2

Input

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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 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."

gemma-4-31b: k=2

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.

gemma-4-31b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (3070 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Night Sky**: The black cells (`.`).
    *   **Launchpad**: The row containing the blue runway (`B`).
    *   **Engines**: The colored cells embedded in the launchpad: Azure (`A`) and Red (`R`).
    *   **Plumes**: The vertical columns of blue (`B`) exhaust trailing up from the engines.
    *   **Flares**: The top-most cell of a plume, which matches the engine's color (`A` or `R`).

2.  **AFFORDANCES**:
    *   The launchpad row remains static.
    *   Engines (`A` and `R`) trigger a vertical growth upwards.
    *   The height of the plume depends on the engine color.

3.  **TRANSFORMATION RULE**:
    *   Locate the row containing the blue runway (`B`).
    *   For every `A` (Azure) engine in that row: Create a plume extending upwards. Based on Example 1, an `A` engine at row 3 (0-indexed) creates a plume reaching row 0. The plume consists of the engine itself, blue cells (`B`) above it, and is capped by an `A` at the top. In Example 1, the engine is at row 3, the plume is at row 1 and 2, and the flare is at row 0. Total height from runway = 3 cells.
    *   For every `R` (Red) engine in that row: Create a plume extending upwards. Based on Example 2, an `R` engine at row 5 creates a plume reaching row 1. The plume consists of the engine itself, blue cells (`B`) above it, and is capped by an `R` at the top. In Example 2, the engine is at row 5, the plume is at rows 2, 3, 4, and the flare is at row 1. Total height from runway = 4 cells.
    *   **Height Summary**:
        *   `A` (Azure) $\rightarrow$ Plume height = 3 cells (including engine).
        *   `R` (Red) $\rightarrow$ Plume height = 4 cells (including engine).
    *   The plumes stop if they hit the top edge of the grid.

### Applying the Rule to Test Input

*   **Grid Dimensions**: 9 rows x 11 columns.
*   **Launchpad Row**: Row 6 (0-indexed).
*   **Engines found at Row 6**:
    *   Col 1: `R` (Red) $\rightarrow$ Height 4. Plume cells: Row 5 (`B`), Row 4 (`B`), Row 3 (`B`), Row 2 (`R`).
    *   Col 3: `A` (Azure) $\rightarrow$ Height 3. Plume cells: Row 5 (`B`), Row 4 (`B`), Row 3 (`A`).
    *   Col 7: `A` (Azure) $\rightarrow$ Height 3. Plume cells: Row 5 (`B`), Row 4 (`B`), Row 3 (`A`).
    *   Col 9: `R` (Red) $\rightarrow$ Height 4. Plume cells: Row 5 (`B`), Row 4 (`B`), Row 3 (`B`), Row 2 (`R`).

**Mapping the coordinates (Row, Col):**
*   Col 1 (R): (5,1)=B, (4,1)=B, (3,1)=B, (2,1)=R
*   Col 3 (A): (5,3)=B, (4,3)=B, (3,3)=A
*   Col 7 (A): (5,7)=B, (4,7)=B, (3,7)=A
*   Col 9 (R): (5,9)=B, (4,9)=B, (3,9)=B, (2,9)=R

**Final Grid Construction:**
Row 0: . . . . . . . . . . .
Row 1: . . . . . . . . . . .
Row 2: . R . . . . . . . R .
Row 3: . B . A . . . A . B .
Row 4: . B . B . . . B . B .
Row 5: . B . B . . . B . B .
Row 6: B R B A B B B A B R B
Row 7: . . . . . . . . . . .
Row 8: . . . . . . . . . . .

ANSWER:
. . . . . . . . . . .
. . . . . . . . . . .
. R . . . . . . . R .
. B . A . . . A . B .
. B . B . . . B . B .
. B . B . . . B .

... [70 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.91)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 433: "Raindrops fall toward a drumhead and splash upward on impact" k=4 alts: 5/15 73c3b0d8

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 a horizontal red line spanning the full width of the grid, a set of yellow dots scattered on the black background (some above the red line, some below it), and otherwise empty black cells.

Do: 1. Shift every yellow dot down by exactly one row. The red line remains fixed in place. 2. After shifting, check each yellow dot that is now positioned exactly one row above the red line. For each such dot, generate a V-shaped bounce pattern: place additional yellow dots along two diagonal paths extending upward from that dot's position — one going up-left (row-1, col-1 per step) and one going up-right (row-1, col+1 per step). Continue each diagonal path until it exits the grid boundary. 3. Yellow dots that are not exactly one row above the red line after shifting (whether above or below the red line) simply remain at their new shifted position with no bounce effect. 4. All other cells remain unchanged.

Grid: The grid dimensions and the position of the red horizontal line vary across instances. The background is black (.). The red line always spans the full width of the grid. Yellow dots may appear anywhere above or below the red line. The coordinate system is row-column with row 0 at the top.

Figurative Descriptions (16 variants)

"Raindrops fall toward a drumhead and splash upward on impact"

gemma-4-31b: k=4

See: Yellow raindrops hang suspended in a dark sky above and below a taut red drumhead stretched across the world. The air is still, everything frozen mid-fall.

Do: Gravity pulls each raindrop one step closer to the earth. The red drumhead is anchored and never moves. Any drop that lands right on the drumhead's edge erupts into a V-shaped splash — twin arcs of yellow spray flying up-left and up-right, each droplet one step further along the diagonal until it escapes the sky. Drops that are still drifting through open air, or that have already passed beneath the drum, simply settle into their new resting place — no splash, no fanfare.

Grid: The dark sky (black) can stretch to any height or width. The red drumhead always runs its full width like a horizon line, dividing above from below. Yellow raindrops may float anywhere in the sky or sit beneath the drum. The world is read top-to-bottom, left-to-right.

gemma-4-31b — MARC valid, solved with 4 examples

Input

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Prediction

vs

Expected

Reasoning (5457 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Yellow (Y)**: Raindrops.
    *   **Red (R)**: The drumhead (a horizontal line acting as a boundary).
    *   **Black (.)**: The sky/void.

2.  **AFFORDANCES**:
    *   **Raindrops (Y)**: Can move downward by one cell.
    *   **Drumhead (R)**: Stationary. Acts as a trigger for a "splash" if a raindrop lands on it.
    *   **Sky (.)**: Space for movement and splash patterns.

3.  **TRANSFORMATION RULE**:
    *   **Gravity**: Every yellow cell `(r, c)` moves to `(r+1, c)`.
    *   **The Splash**: If a raindrop's destination `(r+1, c)` is occupied by a red cell `R`, it triggers a V-shaped splash.
    *   **Splash Pattern**: The splash consists of yellow cells extending diagonally upwards and outwards from the point of impact `(r+1, c)`.
        *   The impact point itself remains `R`.
        *   The spray goes up-left and up-right: `(r, c-1), (r-1, c-2), (r-2, c-3)...` and `(r, c+1), (r-1, c+2), (r-2, c+3)...` until the edge of the grid is reached.
    *   **Non-Impact**: If the destination is black `(.)`, the drop simply moves there. If the drop is already below the red line, it simply moves down one cell.

### Applying the Rule to Test Input

**Input Grid Analysis:**
*   Grid size: 12 rows x 8 columns.
*   Red line (Drumhead): Row 3 (0-indexed).
*   Yellow drops:
    1.  `(0, 4)`
    2.  `(1, 0)`
    3.  `(6, 1)`

**Step-by-Step Transformation:**
1.  **Drop at (0, 4)**: Moves to `(1, 4)`. Destination is `.`. Result: `(1, 4) = Y`.
2.  **Drop at (1, 0)**: Moves to `(2, 0)`. Destination is `.`. Result: `(2, 0) = Y`.
3.  **Drop at (6, 1)**: Moves to `(7, 1)`. Destination is `.`. Result: `(7, 1) = Y`.

**Wait, let's re-examine the "Splash" trigger in the training examples.**
Example 1: Red line at row 9. Drop at (7, 4) moves to (8, 4). No splash.
Example 2: Red line at row 5. Drop at (2, 1) moves to (3, 1). Drop at (3, 4) moves to (4, 4).
Wait, looking at Example 2 output:
Input: `(2, 1)` and `(3, 4)`.
Output: `(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)` and `(3, 0), (3, 2), (3, 4), (3, 6)`.
This suggests a different trigger. Let's re-read: "Any drop that lands right on the drumhead's edge erupts into a V-shaped splash".
In Example 2, the red line is at row 5. A drop at row 4 would land on row 5.
In Example 2, the drops are at `(2, 1)` and `(3, 4)`. Neither is at row 4.
Let's look at Example 4: Red line at row 6. Drop at `(4, 2)`.
Output: `(3, 0), (3, 4), (4, 1), (4, 3), (5, 2)`.
This is a V-shape centered at `(5, 2)`? No, the drop was at `(4, 2)`, it moves to `(5, 2)`. The splash is `(4, 1), (4, 3), (3, 0), (3, 4)`.
The splash happens when the drop *would* land on the red line.
In Example 4, the drop is at `(4, 2)`. It moves to `(5, 2)`. The red line is at `(6, 2)`.
Wait, the rule says "lands right on the drumhead's edge". If the red line is at row 6, a drop at row 5 lands on it.
In Example 4, the drop is at `(4, 2)`. It moves to `(5, 2)`. It hasn't hit the red line yet.
Let's re-read Example 4 again. Inp

... [2460 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.92)

Prediction

Expected

Figurative + 4 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."

gemma-4-31b: 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.

gemma-4-31b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (5361 chars)

### Conceptual Digestion

1.  **The CAST**:
    *   **Dark Riverbank**: The row or column of black cells (`.`).
    *   **Meadow**: The area of orange cells (`O`).
    *   **Azure Saplings**: Azure cells (`A`) located in the two layers closest to the riverbank.
    *   **Young Saplings**: A single `A` cell (depth 1 from the river).
    *   **Full Trees**: Two `A` cells stacked perpendicular to the river (depth 2 from the river).

2.  **The AFFORDANCES**:
    *   **Young Saplings** $\rightarrow$ Grow: They expand by one cell further into the meadow (becoming depth 2).
    *   **Full Trees** $\rightarrow$ Vanish: They are removed from the grid.
    *   **Vanishing Trees** $\rightarrow$ Cast Shadows: For every full tree that vanishes, two black cells (`.`) appear at the farthest opposite shore of the meadow.

3.  **The TRANSFORMATION RULE**:
    *   Identify the riverbank (the line of `.`).
    *   Identify the "soil" (the two rows/columns adjacent to the river).
    *   If a cell at depth 1 is `A` and the cell at depth 2 is `O`, the cell at depth 2 becomes `A` (Growth).
    *   If a cell at depth 1 is `A` and the cell at depth 2 is `A`, both cells become `O` (Death).
    *   For every "Death" event, two cells at the opposite edge of the meadow (farthest from the river) are turned black (`.`).

### Applying the Rule to Test Input

**Input Analysis**:
*   **Riverbank**: Bottom row (Row 7: `. . . . . . . . . . . . . . . .`).
*   **Soil**: Row 6 and Row 5.
*   **Opposite Shore**: Top row (Row 0).

**Evaluating Azure Cells (Columns 0-15)**:
*   Col 0: Row 6=A, Row 5=A $\rightarrow$ **Death**. (Opposite shore: Row 0, Col 0 and Row 0, Col 1 become `.`)
*   Col 1: Row 6=O, Row 5=O $\rightarrow$ No change.
*   Col 2: Row 6=A, Row 5=O $\rightarrow$ **Growth**. (Row 5 becomes A).
*   Col 3: Row 6=O, Row 5=O $\rightarrow$ No change.
*   Col 4: Row 6=A, Row 5=A $\rightarrow$ **Death**. (Opposite shore: Row 0, Col 2 and Row 0, Col 3 become `.`)
*   Col 5: Row 6=O, Row 5=O $\rightarrow$ No change.
*   Col 6: Row 6=A, Row 5=A $\rightarrow$ **Death**. (Opposite shore: Row 0, Col 4 and Row 0, Col 5 become `.`)
*   Col 7: Row 6=O, Row 5=O $\rightarrow$ No change.
*   Col 8: Row 6=A, Row 5=O $\rightarrow$ **Growth**. (Row 5 becomes A).
*   Col 9: Row 6=O, Row 5=O $\rightarrow$ No change.
*   Col 10: Row 6=O, Row 5=O $\rightarrow$ No change.
*   Col 11: Row 6=O, Row 5=O $\rightarrow$ No change.
*   Col 12: Row 6=A, Row 5=O $\rightarrow$ **Growth**. (Row 5 becomes A).
*   Col 13: Row 6=O, Row 5=O $\rightarrow$ No change.
*   Col 14: Row 6=O, Row 5=O $\rightarrow$ No change.
*   Col 15: Row 6=A, Row 5=A $\rightarrow$ **Death**. (Opposite shore: Row 0, Col 6 and Row 0, Col 7 become `.`)

**Final Grid Construction**:
*   Row 0: `. . . . . . . . O O O O O O O O` (Wait, the rule says "two cells at the farthest opposite shore". In Example 1, the shadows were placed at the end of the row. In Example 2, they were placed at the bottom. Let's re-examine Example 1: The river is Co

... [2361 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.80)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 444: "A seed crystal grows into ever-larger reflections of itself, ... [35 chars truncated]" k=1 alts: 3/15 762cd429

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 a single 2x2 colored seed pattern placed somewhere in the grid. The seed contains four colored cells arranged in a 2x2 block (top-left, top-right, bottom-left, bottom-right), where each cell is a non-black color. The seed's four colors define a quadrant pattern.

Do: Starting from the 2x2 seed pattern, generate a series of scaled copies at exponentially increasing sizes, each placed immediately to the right of the previous one and vertically centered on the seed's position. Specifically: Level 0 is the original 2x2 seed (each cell is 1x1). Level 1 doubles the scale: each of the four quadrant colors becomes a 2x2 block, producing a 4x4 region placed directly to the right of level 0 and centered vertically on the seed. Level 2 doubles again: each quadrant color becomes a 4x4 block, producing an 8x8 region placed to the right of level 1, centered on the seed. Continue doubling (level n has cell size 2^n, producing a region of size 2^(n+1) x 2^(n+1)) until the grid's right edge is reached. At every level, the 2x2 quadrant arrangement is preserved: top-left quadrant uses the seed's top-left color, top-right uses the seed's top-right color, bottom-left uses the seed's bottom-left color, bottom-right uses the seed's bottom-right color. Each level's region is vertically centered on the seed's center row. Cells that fall outside the grid boundaries remain black.

Grid: The output grid has the same dimensions as the input grid. The background is black. The seed pattern remains at its original position. The scaled copies expand rightward from the seed, filling the grid toward the right edge. The vertical extent of each level is centered on the seed's vertical midpoint, growing symmetrically upward and downward. No content extends to the left of the seed.

Figurative Descriptions (16 variants)

"A seed crystal grows into ever-larger reflections of itself, each generation dwarfing the last."

gemma-4-31b: k=1

See: In a vast dark field, a tiny 2×2 embryo sits quietly — four colored organs packed into one small heart. Each quadrant holds a different hue, like the four chambers of a beating heart waiting to pump life outward.

Do: The heart begins to beat. With each pulse, it projects a shadow of itself to the right — but each shadow is twice the size of the last, as if viewed through a succession of magnifying glasses lined up in a row. The first echo is a 4×4 ghost, the next an 8×8 phantom, then 16×16, and so on, each one faithfully preserving the four-chambered arrangement of the original heart, just writ larger and larger. The echoes march rightward like Russian nesting dolls laid open in a line, smallest to largest, until they crash against the edge of the world. Each echo is vertically anchored to the heartbeat's center, growing equally above and below like a tree branching symmetrically from its trunk.

Grid: The dark field stays the same size. The original heart never moves. Its echoes only radiate to the right, never to the left. Where an echo would extend beyond the sky or below the earth, it simply doesn't exist — the darkness holds. The four colors in each echo always sit in the same quadrant positions as the original: upper-left stays upper-left, lower-right stays lower-right, like a flag whose design never rotates no matter how large the banner grows.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (3523 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **The Heart (Embryo)**: A 2x2 block of colors located at a specific coordinate in the input grid.
    *   **The Echoes (Shadows)**: Scaled-up versions of the 2x2 heart (4x4, 8x8, 16x16, etc.) that appear to the right of the original.
    *   **The Field**: The background grid (black `.`).

2.  **AFFORDANCES**:
    *   The heart's colors are mapped to quadrants: Top-Left (TL), Top-Right (TR), Bottom-Left (BL), Bottom-Right (BR).
    *   Each echo preserves these quadrants. For a $2n \times 2n$ echo, each quadrant is an $n \times n$ block of the corresponding color.
    *   Echoes are centered vertically relative to the original heart's center.
    *   Echoes are placed sequentially to the right.

3.  **TRANSFORMATION RULE**:
    *   **Identify Heart**: Find the 2x2 block. In the test input, it is at row 7, col 0 (0-indexed).
        *   TL: B, TR: B, BL: A, BR: A. (Wait, looking at the test input: `B B` / `A A`. This means TL=B, TR=B, BL=A, BR=A).
    *   **Center Point**: The center of the 2x2 heart is between row 7/8 and col 0/1.
    *   **Echo 1 (4x4)**:
        *   Size: 4x4.
        *   Vertical range: Centered on the heart. Heart rows are 7, 8. Center is 7.5. A 4x4 block centered at 7.5 spans rows 6, 7, 8, 9.
        *   Horizontal range: Placed to the right. In Example 1, the 2x2 was at (4,0)-(5,1). The 4x4 echo started at col 2. So the 4x4 echo starts immediately after the heart.
        *   Colors: TL=B, TR=B, BL=A, BR=A. (Each quadrant is 2x2).
    *   **Echo 2 (8x8)**:
        *   Size: 8x8.
        *   Vertical range: Centered at 7.5. Spans rows 4, 5, 6, 7, 8, 9, 10, 11.
        *   Horizontal range: Starts after the 4x4 echo (col 6).
        *   Colors: Each quadrant is 4x4.
    *   **Echo 3 (16x16)**:
        *   Size: 16x16.
        *   Vertical range: Centered at 7.5. Spans rows 0 to 15.
        *   Horizontal range: Starts after the 8x8 echo (col 14).
        *   Colors: Each quadrant is 8x8.

### Applying to Test Input
*   **Heart (2x2)**: Rows 7-8, Cols 0-1. Colors: `B B` / `A A`.
*   **Echo 1 (4x4)**: Rows 6-9, Cols 2-5.
    *   Rows 6-7, Cols 2-3: B | Rows 6-7, Cols 4-5: B
    *   Rows 8-9, Cols 2-3: A | Rows 8-9, Cols 4-5: A
*   **Echo 2 (8x8)**: Rows 4-11, Cols 6-13.
    *   Rows 4-7, Cols 6-9: B | Rows 4-7, Cols 10-13: B
    *   Rows 8-11, Cols 6-9: A | Rows 8-11, Cols 10-13: A
*   **Echo 3 (16x16)**: Rows 0-15, Cols 14-29.
    *   Rows 0-7, Cols 14-21: B | Rows 0-7, Cols 22-29: B
    *   Rows 8-15, Cols 14-21: A | Rows 8-15, Cols 22-29: A

ANSWER:
. . . . . . . . . . . . . . B B B B B B B B B B B B B B B B
. . . . . . . . . . . . . . B B B B B B B B B B B B B B B B
. . . . . . . . . . . . . . B B B B B B B B B B B B B B B B
. . . . . . . . . . . . . . B B B B B B B B B B B B B B B B
. . . . . . B B B B B B B B B B B B B B B B B B B B B B B B
. . . . . . B B B B B B B B B B B B B B B B B B B B B B B B
. . B B B B B B B B B B B B B B B B B B B B B B B B B B B B
B B B B B B B B 

... [523 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.93)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 449: "A dam holds back a flood that fills everything below it." k=2 alts: 10/15 782b5218

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 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."

gemma-4-31b: 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.

gemma-4-31b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (5969 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **The Dam**: Red cells (`R`). These act as the boundary/divider.
    *   **Sediment**: Any non-red, non-black cells (e.g., `B` in Example 1, `X` in Example 2, `W` in Test Input).
    *   **Empty Air/Sky**: Black cells (`.`).

2.  **AFFORDANCES**:
    *   The Red cells are immovable; they stay in their exact positions.
    *   The area *above* the dam is cleared (becomes black `.`).
    *   The area *below* the dam is filled with the sediment color found in the input.

3.  **TRANSFORMATION RULE**:
    *   For each column:
    *   Find the **highest** red cell (`R`) in that column.
    *   Every cell **above** that first `R` becomes black (`.`).
    *   The red cell itself stays `R`.
    *   Every cell **below** that first `R` (including other red cells) is filled. However, looking at Example 2, the rule is more nuanced: the dam is the *entire set* of red cells.
    *   **Refined Rule**:
        1.  Identify all `R` cells. They remain `R`.
        2.  For each column, find the **topmost** `R`.
        3.  All cells in that column **above** the topmost `R` become `.`.
        4.  All cells in that column **below** the topmost `R` that are not `R` become the "sediment" color.
        5.  Wait, looking at Example 2 again: The red cells form a "staircase". The area *below* the red boundary is filled with the sediment color (`X`). The red cells themselves are preserved.
        6.  **Final Rule**: For each column, find the row index of the first `R`. All cells above this index become `.`. All cells at or below this index become either `R` (if they were `R` in the input) or the sediment color (if they were anything else).

### Applying to Test Input

**Sediment Color**: Maroon (`W`)

**Input Grid Analysis (Column by Column):**
Col 0: R at row 5. (Rows 0-4 become `.`, Row 5 is `R`, Rows 6-9 become `W`)
Col 1: R at row 4. (Rows 0-3 become `.`, Row 4 is `R`, Row 5 is `R`, Rows 6-9 become `W`)
Col 2: R at row 4. (Rows 0-3 become `.`, Row 4 is `R`, Row 5 is `.`, Rows 6-9 become `W`) -> Wait, Row 5 is `.` in input, but it's below the first `R`, so it becomes `W`.
Col 3: R at row 4. (Rows 0-3 become `.`, Row 4 is `R`, Row 5 is `R`, Rows 6-9 become `W`)
Col 4: R at row 4. (Rows 0-3 become `.`, Row 4 is `.`, Row 5 is `R`, Rows 6-9 become `W`) -> Wait, Col 4 first R is at row 5. (Rows 0-4 become `.`, Row 5 is `R`, Rows 6-9 become `W`)
Col 5: R at row 4. (Rows 0-3 become `.`, Row 4 is `R`, Row 5 is `R`, Rows 6-9 become `W`)
Col 6: R at row 4. (Rows 0-3 become `.`, Row 4 is `R`, Row 5 is `.`, Rows 6-9 become `W`)
Col 7: R at row 4. (Rows 0-3 become `.`, Row 4 is `R`, Row 5 is `R`, Rows 6-9 become `W`)
Col 8: R at row 4. (Rows 0-3 become `.`, Row 4 is `W`, Row 5 is `R`, Rows 6-9 become `W`) -> First R is at row 5. (Rows 0-4 become `.`, Row 5 is `R`, Rows 6-9 become `W`)
Col 9: R at row 4. (Rows 0-3 become `.`, Row 4 is `R`, Row 5 is `R`, Rows 6-9 become `W`)

**Let's re-verify the "Dam" positions (R):**
Row 4: 

... [2978 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.97)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 460: "A stained-glass window reveals its true colors when sunlight ... [24 chars truncated]" k=1 alts: 5/15 7c008303

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 is a 9×9 grid divided into four quadrants by a horizontal row and a vertical column of azure (A) cells that form a cross. One of the four quadrants (6×6) contains a pattern made of green (G) cells on a black (.) background. An adjacent quadrant (2×2, tucked into the corner next to the A-cross) contains exactly four colored cells arranged in a 2×2 block — these are the color key. The remaining two quadrants are empty (all black).

Do: 1. Locate the row and column of A cells; they intersect to divide the grid into four quadrants. 2. Identify the 6×6 quadrant containing the green pattern and the 2×2 quadrant containing the color key. 3. Determine the spatial relationship between the key quadrant and the pattern quadrant: the 2×2 key maps onto the four 3×3 sub-blocks of the 6×6 pattern based on their relative positions (top-left key cell maps to the top-left 3×3 block, top-right key cell to the top-right 3×3 block, bottom-left key cell to the bottom-left 3×3 block, bottom-right key cell to the bottom-right 3×3 block). 4. Produce a 6×6 output grid: for each 3×3 block of the green pattern, replace every green (G) cell with the color from the corresponding position in the 2×2 key, and keep every black (.) cell as black.

Grid: The input grid is always 9×9. The output grid is always 6×6 — it contains only the recolored pattern with no azure dividers. The background color is black (.). The 2×2 color key can appear in any of the three non-pattern quadrants (its exact corner varies across instances), and the green pattern can occupy any of the four quadrants, but it is always the 6×6 one.

Figurative Descriptions (16 variants)

"A stained-glass window reveals its true colors when sunlight passes through a prism."

gemma-4-31b: k=1

See: An azure cross divides the world like the leading of a cathedral window, separating four panes. One large pane holds a pattern traced in plain green glass — a design waiting to be illuminated. Tucked into a nearby corner, a tiny 2×2 prism glows with four jewel-toned colors, each one a secret instruction. The remaining panes are dark, as if the light hasn't reached them yet.

Do: The prism catches the light and casts it onto the green glass. Each of the prism's four facets shines toward the quadrant of the pattern that mirrors its own position — upper-left facet illuminates the upper-left quarter, and so on. Wherever the green glass stands, it absorbs the color of the light falling on it, transforming from plain green into the jewel tone of its corresponding facet. Wherever there is only darkness, no light takes hold. Strip away the leading — the azure framework was only ever scaffolding — and what remains is the stained-glass window in full color.

Grid: The cathedral window is always 9×9 before the leading is removed. The finished stained-glass panel is always 6×6 — the illuminated design without its frame. The darkness is black (.). The prism may sit in any dark corner adjacent to the leading, and the green tracery may fill any of the four panes, but it always occupies the large one.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (3671 chars)

### Conceptual Digestion

**1. Identify the CAST:**
*   **Azure Cross (A):** The "leading" or scaffolding. It divides the 9x9 grid into four 4x4 quadrants (with the center row/column being the dividers).
*   **Green Glass (G):** The pattern to be colored. It exists within one of the 4x4 quadrants.
*   **The Prism (2x2 block of colors):** A small square located in one of the dark quadrants. It contains four colors (one for each quadrant: Top-Left, Top-Right, Bottom-Left, Bottom-Right).
*   **Darkness (.):** Empty space.

**2. Identify the AFFORDANCES:**
*   The **Azure Cross** defines the boundaries.
*   The **Prism** provides the color mapping. The color at position (0,0) of the prism corresponds to the Top-Left quadrant, (0,1) to Top-Right, (1,0) to Bottom-Left, and (1,1) to Bottom-Right.
*   The **Green Glass** acts as a mask; it takes the color assigned to its quadrant.

**3. Identify the TRANSFORMATION RULE:**
1.  Locate the 2x2 prism. In the test input, it is at the bottom right:
    *   Top-Left of prism: `R` (Red)
    *   Top-Right of prism: `B` (Blue)
    *   Bottom-Left of prism: `Y` (Yellow)
    *   Bottom-Right of prism: `O` (Orange)
2.  Identify the quadrant containing the green pattern. In the test input, the green pattern is in the Top-Left quadrant (rows 0-5, cols 0-5, excluding the azure lines).
3.  The Top-Left quadrant of the pattern is mapped to the Top-Left color of the prism.
    *   Top-Left Prism Color = `R` (Red).
4.  Replace all `G` in the Top-Left quadrant with `R`.
5.  Remove the Azure scaffolding (the 7th row and 7th column in the 9x9 grid, though the prompt says the result is 6x6, implying we remove the dividers and the empty padding).
6.  Wait, let's re-examine the grid dimensions. The input is 9x9. The output is 6x6.
    *   Input: 9x9. Azure lines are at index 6 (column) and index 6 (row).
    *   This divides the grid into a 6x6 area and some margins.
    *   Looking at Example 1: Azure is at col 6 and row 2. The output is 6x6.
    *   In Example 1: Prism is at (0,7) to (1,8). Colors: (0,7)=B, (0,8)=R, (1,7)=Y, (1,8)=B.
    *   Pattern is in the bottom-left quadrant (rows 3-8, cols 0-5).
    *   Bottom-Left color of prism is `Y`.
    *   Wait, the example output shows the pattern colored with `B` and `R` and `Y`.
    *   Let's re-read: "Each of the prism's four facets shines toward the quadrant of the pattern that mirrors its own position".
    *   The 6x6 pattern itself is divided into four 3x3 quadrants.
    *   Prism (2x2):
        Top-Left color $\rightarrow$ Top-Left 3x3 of the 6x6 pattern.
        Top-Right color $\rightarrow$ Top-Right 3x3 of the 6x6 pattern.
        Bottom-Left color $\rightarrow$ Bottom-Left 3x3 of the 6x6 pattern.
        Bottom-Right color $\rightarrow$ Bottom-Right 3x3 of the 6x6 pattern.

**Applying to Test Input:**
1.  **Prism (bottom right):**
    (0,0) of prism: `R`
    (0,1) of prism: `B`
    (1,0) of prism: `Y`
    (1,1) of prism: `O`
2.  **Pattern (top left 6x6):**
    Row 0: `.

... [671 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.78)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 494: "A picture frame holds a window, and a wandering puzzle piece ... [27 chars truncated]" k=1 alts: 0/0 846bdb03

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 two distinct structures on a black background. First, a rectangular frame defined by exactly four yellow (Y) corner cells. Between the top and bottom Y corners on the left side, a vertical bar of one color fills the cells; between the top and bottom Y corners on the right side, a vertical bar of a different color fills the cells. The top and bottom edges of the frame (between Y corners) are empty (black). Second, somewhere else on the grid there is a small compact pattern composed of the same two colors used in the frame's side bars. This pattern is an irregular shape occupying a few rows and columns.

Do: 1. Locate the four Y (yellow) cells that form the corners of a rectangle. These define the output grid dimensions (rows from top-Y to bottom-Y inclusive, columns from left-Y to right-Y inclusive). 2. Identify the left-bar color (the color filling cells between the top-left and bottom-left Y corners) and the right-bar color (filling cells between the top-right and bottom-right Y corners). 3. Extract the small pattern found elsewhere on the grid (the cluster of non-black, non-yellow cells not part of the frame). Record it as a 2D array preserving its two colors and black cells. 4. Determine whether the pattern's colors are laterally swapped relative to the frame: check whether the color that appears on the left side of the pattern matches the right-bar color of the frame. If so, reflect the entire pattern horizontally (mirror left-to-right). If the colors already match (left pattern color = left bar color), use the pattern as-is. 5. Construct the output: start with the frame (Y corners, left-bar color filling the left edge between corners, right-bar color filling the right edge, black elsewhere). Place the (possibly reflected) pattern into the interior of the frame, aligning it to the top-left of the interior region (the cells not on the frame border).

Grid: The input is always a 13-row by 13-column grid with a black (.) background. The output grid dimensions are determined by the Y-corner rectangle: its height equals the number of rows spanned by the Y corners and its width equals the number of columns spanned. The output background is black. All cells outside the frame edges and the placed pattern remain black.

Figurative Descriptions (1 variants)

"A picture frame holds a window, and a wandering puzzle piece finds its way home inside."

gemma-4-31b: k=1

See: On a dark stage, four golden corner posts mark the boundaries of a picture frame. Two colored curtains hang along the left and right sides of the frame — each side a different hue. Elsewhere on the stage, a small stained-glass fragment drifts untethered, composed of the same two colors found in the curtains. It is a shard that broke free from the window the frame was meant to hold.

Do: The golden posts call the shard home. But the shard may have tumbled and flipped on its journey — if its colors face the wrong way (its left half wearing the right curtain's color), it must look into a mirror and reverse itself before it can return. Once oriented so that each color faces its matching curtain, the shard nestles into the upper-left corner of the window, filling in the empty space between the curtains. The curtains remain draped along the frame's sides, the golden posts hold their corners, and the rest of the window stays dark — only the returned shard brings additional color to the interior.

Grid: The dark stage is always a 13×13 void. The picture frame's size — determined by the span between the golden corner posts — becomes the finished window you see in the output. The curtains are one cell wide, hanging between corner posts on each side. The top and bottom edges of the frame hold nothing but the posts themselves. The shard is small and irregular, just a few cells of color adrift in the darkness beyond the frame.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (5070 chars)

### Conceptual Digestion

1.  **The CAST**:
    *   **Golden Corner Posts**: Yellow (`Y`) cells. They define the bounding box of the final output grid.
    *   **Curtains**: The vertical lines of color connecting the top and bottom yellow posts. The left curtain has one color, and the right curtain has another.
    *   **The Shard**: A small cluster of colored cells located outside the frame. It consists of the same two colors as the curtains.
    *   **The Dark Stage**: The black (`.`) background.

2.  **The AFFORDANCES**:
    *   The frame (defined by `Y` posts) determines the output dimensions.
    *   The shard can be flipped horizontally (mirrored) if its colors are not aligned with the curtains.
    *   The shard is placed in the upper-left interior of the frame.

3.  **The TRANSFORMATION RULE**:
    *   **Step 1: Define the Frame**. Find the coordinates of the four `Y` cells. The output grid size is the width and height of the rectangle they form.
    *   **Step 2: Identify Curtain Colors**. The color of the cells between the left `Y` posts is the "Left Color". The color of the cells between the right `Y` posts is the "Right Color".
    *   **Step 3: Extract and Orient the Shard**. Find the shard (the cluster of non-black cells outside the frame).
        *   Check the shard's color distribution. If the cells that should be on the left (Left Color) are on the right side of the shard's own bounding box, mirror the shard horizontally.
    *   **Step 4: Assemble the Output**.
        *   Start with the frame: `Y` at corners, Left Color on the left edge, Right Color on the right edge.
        *   Place the oriented shard in the top-left corner of the interior (starting at row 1, col 1, relative to the output grid).
        *   Fill all other interior cells with black (`.`).

### Applying the Rule to Test Input

1.  **Define the Frame**:
    *   Yellow posts are at (1, 1), (1, 8), (6, 1), (6, 8).
    *   Output dimensions: Height = $6-1+1 = 6$; Width = $8-1+1 = 8$.

2.  **Identify Curtain Colors**:
    *   Left curtain (between (1,1) and (6,1)): Red (`R`).
    *   Right curtain (between (1,8) and (6,8)): Azure (`A`).
    *   Left Color = `R`, Right Color = `A`.

3.  **Extract and Orient the Shard**:
    *   Shard cells are at: (9,1)=A, (9,3)=A, (9,4)=R, (10,1)=A, (10,2)=A, (10,3)=A, (10,4)=R, (10,5)=R, (10,6)=R, (11,1)=A, (11,5)=R, (12,1)=A, (12,5)=R, (12,6)=R.
    *   Shard Bounding Box: Rows 9-12, Cols 1-6.
    *   Looking at the shard: The `A` cells are mostly on the left, and `R` cells are mostly on the right.
    *   Wait, the Left Color is `R` and the Right Color is `A`.
    *   Since the shard has `A` on the left and `R` on the right, it is mirrored relative to the curtains.
    *   **Mirror the shard horizontally**:
        *   Original shard (relative to its own 4x6 box):
            Row 0: A . A R . .
            Row 1: A A A R R R
            Row 2: A . . . R .
            Row 3: A . . . R R
        *   Mirrored shard:
            Ro

... [2070 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 506: "A quiet room with tripwires — disturb one spot and the ... [31 chars truncated]" k=2 alts: 0/0 8731374e

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 large axis-aligned rectangle filled almost entirely with a single dominant color (the background color). This rectangle is embedded within a larger grid of random, noisy colors. Inside the rectangle, one or more cells deviate from the background color — these are anomaly cells, all sharing the same non-background color (the marker color).

Do: 1. Locate the largest solid-color rectangle in the input grid. Identify its background color (the color filling the vast majority of its cells) and its bounding coordinates (top row, bottom row, left column, right column). 2. Identify every anomaly cell inside the rectangle — cells whose color differs from the background. Note each anomaly's row and column position relative to the rectangle's top-left corner. All anomalies share the same marker color. 3. Create an output grid with the same dimensions as the rectangle (number of rows × number of columns), filled entirely with the background color. 4. For every row (relative to the rectangle) that contained an anomaly, fill that entire row in the output with the marker color. 5. For every column (relative to the rectangle) that contained an anomaly, fill that entire column in the output with the marker color. The result is a grid where anomaly rows and anomaly columns form full cross-hatch lines of the marker color, and all other cells remain the background color.

Grid: The output grid dimensions equal the dimensions of the embedded rectangle found in the input (rows × columns). The output uses exactly two colors: the rectangle's dominant background color and the marker color of the anomaly cells. Rows and columns containing anomalies become solid lines of the marker color; their intersections are also the marker color. All remaining cells are the background color.

Figurative Descriptions (1 variants)

"A quiet room with tripwires — disturb one spot and the whole row and column light up."

gemma-4-31b: k=2

See: A calm, monochrome lake sits hidden within a chaotic city of clashing neon signs. The lake is almost perfectly still — one uniform color stretching wall to wall — except for a few tiny stones that have been dropped in, each the same foreign color, each sending out silent ripples that no one has yet seen.

Do: Extract the lake from its noisy surroundings. Now awaken the ripples: each dropped stone sends a shockwave racing the full length of its row and the full height of its column, painting every cell it passes through in the stone's color. Where two shockwaves cross, the color intensifies but looks the same. The still water everywhere else remains undisturbed. The city beyond the lake's borders is forgotten entirely.

Grid: The output is the lake alone — same dimensions, same calm background color. The stones themselves vanish into the lines they created: every row a stone touched becomes a solid horizon line of the stone's color, every column becomes a solid vertical beam. The rest of the water keeps its original stillness.

gemma-4-31b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (4665 chars)

**Conceptual Digestion**

1.  **CAST**:
    *   **The Lake**: A rectangular region of uniform background color (the "calm, monochrome lake").
    *   **The Stones**: Cells within the lake that have a different color than the background.
    *   **The City**: All cells outside the boundaries of the lake.
    *   **The Ripples**: The effect of the stones, which paint the entire row and column of the stone's position within the lake's boundaries.

2.  **AFFORDANCES**:
    *   The lake's boundaries are defined by the largest contiguous rectangle of a single color (or a region dominated by one color) that contains "stones."
    *   The background color of the lake is preserved unless overwritten by a ripple.
    *   Stones trigger a "cross" pattern (full row and full column) of their own color.

3.  **TRANSFORMATION RULE**:
    *   **Step 1: Identify the Lake.** Find the rectangular area of the grid that forms the "lake." In the training examples, this is the large block of a single color (Y in Ex 1, B in Ex 2).
    *   **Step 2: Identify the Stones.** Find all cells within that rectangle that differ from the background color.
    *   **Step 3: Apply Ripples.** For every stone found, fill its entire row (within the lake's bounds) and its entire column (within the lake's bounds) with the stone's color.
    *   **Step 4: Final Output.** The output is only the lake's dimensions. The background remains the original lake color; the ripples are the stone colors.

**Applying to Test Input:**

1.  **Identify the Lake**:
    Looking at the test input, there is a large block of 'A' (azure) cells.
    Rows 2 to 11 (0-indexed) and Columns 3 to 11 contain a dense block of 'A's.
    Let's refine the boundaries:
    Row 2: Col 3-10 are 'A'
    Row 3: Col 3-10 are 'A'
    Row 4: Col 3-9 are 'A' (Col 10 is 'B')
    Row 5: Col 3-11 are 'A'
    Row 6: Col 3-11 are 'A'
    Row 7: Col 3-4 are 'A', Col 6-10 are 'A' (Col 5 is 'B')
    Row 8: Col 3-10 are 'A'
    Row 9: Col 3-10 are 'A'
    Row 10: Col 3-10 are 'A'
    Row 11: Col 3-10 are 'A'
    The lake is the rectangle from Row 2 to Row 11 and Column 3 to Column 11.
    Dimensions: 10 rows x 9 columns.
    Background color: A.

2.  **Identify the Stones (cells in R2-11, C3-11 that are not 'A')**:
    *   Row 4, Col 9: 'B' (blue)
    *   Row 7, Col 5: 'B' (blue)
    *   (Checking others: Row 2 Col 11 is 'O', but that's outside the A-block if we define the block as C3-10. Let's check the width. Row 5, 6 have 'A' up to Col 11. Let's assume the lake is C3 to C11).
    *   Wait, let's re-examine the block:
        R2: A A A A A A A A (C3-C10)
        R3: A A A A A A A A (C3-C10)
        R4: A A A A A A B A (C3-C10) -> Stone 'B' at (4, 9)
        R5: A A A A A A A A (C3-C10)
        R6: A A A A A A A A (C3-C10)
        R7: A A B A A A A A (C3-C10) -> Stone 'B' at (7, 5)
        R8: A A A A A A A A (C3-C10)
        R9: A A A A A A A A (C3-C10)
        R10: A A A A A A A A (C3-C10)
        R11: A A A A A A A A (C3-C10)
   

... [1671 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.49)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 520: "Seeds scattered in a field grow into square garden plots arr ... [30 chars truncated]" k=1 alts: 0/0 8abad3cf

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Literal Description

See: The input grid contains several distinct non-background colors scattered across the grid, with O (orange) serving as the background color. Each non-background color appears a number of times that is a perfect square (1, 4, 9, 16, 25, etc.). The spatial arrangement of these colored cells in the input does not matter — only the total count of each color matters.

Do: 1. Identify all non-O colors present in the input grid and count the total number of cells of each color. 2. Each count will be a perfect square. Compute the square root of each count to get the side length of a solid square block for that color. 3. Sort the colors in ascending order by their block side length (smallest to largest). 4. Construct the output by placing these solid square blocks left to right in ascending size order, separated by single-column vertical strips of O. 5. All blocks are bottom-aligned: the bottom row of every block sits on the bottom row of the output grid. 6. The output height equals the side length of the largest block. 7. Fill all remaining cells (above shorter blocks and in the separator columns) with O.

Grid: The output grid's height equals the side length of the largest square block. The output grid's width equals the sum of all block side lengths plus one O-column separator between each adjacent pair of blocks (i.e., number_of_colors - 1 separator columns). O (orange) is the background color for all unfilled space.

Figurative Descriptions (1 variants)

"Seeds scattered in a field grow into square garden plots arranged by size at harvest time."

gemma-4-31b: k=1

See: Scattered across an orange field, seeds of different colors have been tossed carelessly by the wind. Some colors appear as just a single seed, others as small handfuls, others as abundant clusters. The orange soil itself is not a crop — it is merely the earth in which everything grows.

Do: When harvest season arrives, each color of seed reveals its true nature: every scattered seed of a color pulls together and grows into a perfect square garden plot, its side determined by the seed's hidden vitality. The smallest plot sprouts on the left, the largest on the right, lined up along a shared ground like buildings on a street. Between each neighboring garden, a single column of bare orange earth serves as a footpath. Short gardens don't float — they sit firmly on the ground with open sky (orange air) above them.

Grid: The street of gardens is exactly as tall as the tallest plot and as wide as all the plots laid side by side with one dirt footpath between each pair. Every patch of open air and every footpath is filled with the orange of earth and sky.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (3553 chars)

### Conceptual Digestion

**1. Identify the CAST:**
*   **Orange (O):** The background/soil. It remains the background in the output and fills all empty spaces (footpaths and "sky").
*   **Non-Orange Colors (., B, R, G, Y, X, M, A, W):** These are the "seeds." Each unique color represents a different type of garden plot.

**2. Identify the AFFORDANCES:**
*   **Count:** The number of pixels of a specific color in the input determines the "vitality" (area) of the resulting square garden.
*   **Square Root:** Since the gardens are "perfect square plots," the side length of the square is the square root of the count of that color.
*   **Ordering:** The plots are arranged from smallest (left) to largest (right).
*   **Alignment:** All plots are bottom-aligned (sitting on the ground).

**3. Identify the TRANSFORMATION RULE:**
1.  Count the occurrences of every non-orange color in the input grid.
2.  Calculate the side length $S = \sqrt{\text{count}}$ for each color.
3.  Sort the colors by their side length $S$ in ascending order.
4.  Construct a grid where:
    *   The height is equal to the maximum $S$ found.
    *   The width is the sum of all $S$ values plus $(N-1)$ for the orange footpaths (where $N$ is the number of unique colors).
    *   Each color $C$ forms an $S \times S$ square of color $C$ at the bottom of its designated section.
    *   All other areas (above shorter squares and the columns between squares) are filled with Orange (O).

---

### Applying the Rule to Test Input

**Input Grid Analysis:**
*   `O O O . . . O O O Y`
*   `. . O . O . O W O Y`
*   `. . O . . . O O O Y`
*   `O O O O O O O . O Y`
*   `O O O O O . . . O O`

**Step 1: Count non-orange colors**
*   Black (`.`): 8 occurrences
*   Maroon (`W`): 1 occurrence
*   Yellow (`Y`): 4 occurrences

**Step 2: Calculate side lengths ($S = \sqrt{\text{count}}$)**
*   Maroon (`W`): $\sqrt{1} = 1$
*   Yellow (`Y`): $\sqrt{4} = 2$
*   Black (`.`): $\sqrt{8} \approx 2.82$ (Wait, the prompt says "perfect square garden plot". Let's re-count the black dots).

**Re-counting Black (`.`):**
Row 1: col 4, 5, 6 (3)
Row 2: col 1, 2, 4, 6 (4)
Row 3: col 1, 2, 4, 5, 6 (5)
Row 4: col 8 (1)
Row 5: col 6, 7, 8 (3)
Total = $3 + 4 + 5 + 1 + 3 = 16$.
$\sqrt{16} = 4$.

**Step 3: Sort by size**
1.  Maroon (`W`): $S=1$
2.  Yellow (`Y`): $S=2$
3.  Black (`.`): $S=4$

**Step 4: Determine Output Dimensions**
*   Height = Max $S = 4$.
*   Width = $1 (W) + 1 (\text{path}) + 2 (Y) + 1 (\text{path}) + 4 (.) = 9$.

**Step 5: Construct the Grid (Bottom-Up)**
*   **Col 1 (W):** Bottom row is `W`, rows above are `O`.
*   **Col 2 (Path):** All `O`.
*   **Col 3-4 (Y):** Bottom 2 rows are `Y`, top 2 rows are `O`.
*   **Col 5 (Path):** All `O`.
*   **Col 6-9 (.):** All 4 rows are `.`.

**Grid Layout:**
Row 1: `O O O O O . . . .`
Row 2: `O O O O O . . . .`
Row 3: `O O Y Y O . . . .`
Row 4: `W O Y Y O . . . .`

Wait, let's check the alignment again: "Short gardens don't float — they sit firmly on the ground with open 

... [559 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.28)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 554: "A compass rose casts colored shadows diagonally away from it ... [8 chars truncated]" k=2 alts: 0/0 93b581b8

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 2×2 block of four distinctly colored cells. Label the cells by position: top-left (TL), top-right (TR), bottom-left (BL), bottom-right (BR).

Do: 1. Keep the original 2×2 block in place. 2. For each cell in the block, project a 2×2 filled square of the diagonally opposite cell's color into the corresponding corner quadrant adjacent to the block: - The top-left corner region gets a 2×2 square of the BR cell's color. - The top-right corner region gets a 2×2 square of the BL cell's color. - The bottom-left corner region gets a 2×2 square of the TR cell's color. - The bottom-right corner region gets a 2×2 square of the TL cell's color. 3. Each 2×2 projection is placed in the rectangular region diagonally opposite the source cell, immediately adjacent to the block, extending outward toward the grid corner. Specifically, if the block occupies rows r to r+1 and cols c to c+1, the projections fill: top-left at rows r-2 to r-1, cols c-2 to c-1; top-right at rows r-2 to r-1, cols c+2 to c+3; bottom-left at rows r+2 to r+3, cols c-2 to c-1; bottom-right at rows r+2 to r+3, cols c+2 to c+3. 4. Clip any projection that extends beyond the grid boundary (only the in-bounds portion is drawn).

Grid: The grid is 6×6 with a black (.) background. The 2×2 block can appear at any position within the grid. The four corner projection regions may be partially or fully clipped by the grid edges depending on block placement.

Figurative Descriptions (1 variants)

"A compass rose casts colored shadows diagonally away from its heart."

gemma-4-31b: k=2

See: On a dark field sits a tiny jeweled compass rose — four gemstones set in a 2×2 square, each a different color, marking the cardinal corners of its face.

Do: Each gemstone yearns for the corner farthest from itself, so it sends its diagonal opposite's color as a shadow. The top-left gem's shadow doesn't carry its own hue — it carries the color of the gem it faces across the center, the bottom-right stone. These colored shadows land in the diagonal corner regions like reflections thrown into the four quadrants of the night sky. Each shadow is twice the size of the gem that inspired it, a 2×2 echo. The compass rose itself remains unmoved at the center of this exchange — only its reflections radiate outward.

Grid: The dark field is a 6×6 night sky. The compass rose can be mounted anywhere on the field, so some of its diagonal shadow-echoes may fall partly or entirely beyond the edge of the world — only what lands on the sky is visible.

gemma-4-31b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (2779 chars)

### Conceptual Digestion

**1. Identify the CAST:**
*   **The Dark Field:** The 6x6 grid of black cells (`.`).
*   **The Compass Rose:** A 2x2 square of four different colored gemstones located somewhere in the grid.
*   **The Shadows (Echoes):** 2x2 blocks of color that appear in the quadrants diagonal to the gemstones.

**2. Identify the AFFORDANCES:**
*   The Compass Rose acts as the source of color and the anchor for the transformation.
*   The diagonal opposite of each gemstone determines the color of the shadow cast into the opposite quadrant.
*   The grid boundaries act as a clipping mask; any shadow falling outside the 6x6 area is ignored.

**3. Identify the TRANSFORMATION RULE:**
*   Locate the 2x2 Compass Rose. Let its coordinates be $(r, c), (r, c+1), (r+1, c), (r+1, c+1)$.
*   Let the colors be:
    *   Top-Left (TL): $(r, c)$
    *   Top-Right (TR): $(r, c+1)$
    *   Bottom-Left (BL): $(r+1, c)$
    *   Bottom-Right (BR): $(r+1, c+1)$
*   The "shadows" are 2x2 blocks placed in the corners of the grid relative to the center of the rose:
    *   **Top-Left Quadrant:** A 2x2 block of color **BR** is placed starting at $(r-2, c-2)$.
    *   **Top-Right Quadrant:** A 2x2 block of color **BL** is placed starting at $(r-2, c+2)$.
    *   **Bottom-Left Quadrant:** A 2x2 block of color **TR** is placed starting at $(r+2, c-2)$.
    *   **Bottom-Right Quadrant:** A 2x2 block of color **TL** is placed starting at $(r+2, c+2)$.
*   The original 2x2 Compass Rose remains in place.

---

### Applying the Rule to Test Input

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

1.  **Locate Compass Rose:**
    *   TL: (3, 2) = G (Green)
    *   TR: (3, 3) = B (Blue)
    *   BL: (4, 2) = R (Red)
    *   BR: (4, 3) = X (Grey)
    *   (Using 0-indexing: Row 3, Col 2)

2.  **Determine Shadows:**
    *   **Top-Left Shadow (Color BR = X):**
        Starts at $(3-2, 2-2) = (1, 0)$.
        Cells: (1,0), (1,1), (2,0), (2,1) $\rightarrow$ **X**
    *   **Top-Right Shadow (Color BL = R):**
        Starts at $(3-2, 2+2) = (1, 4)$.
        Cells: (1,4), (1,5), (2,4), (2,5) $\rightarrow$ **R**
    *   **Bottom-Left Shadow (Color TR = B):**
        Starts at $(3+2, 2-2) = (5, 0)$.
        Cells: (5,0), (5,1) $\rightarrow$ **B** (Note: Row 6 is out of bounds)
    *   **Bottom-Right Shadow (Color TL = G):**
        Starts at $(3+2, 2+2) = (5, 4)$.
        Cells: (5,4), (5,5) $\rightarrow$ **G** (Note: Row 6 is out of bounds)

3.  **Construct Final Grid:**
    *   Row 0: `. . . . . .`
    *   Row 1: `X X . . R R`
    *   Row 2: `X X . . R R`
    *   Row 3: `. . G B . .`
    *   Row 4: `. . R X . .`
    *   Row 5: `B B . . G G`

ANSWER:
. . . . . .
X X . . R R
X X . . R R
. . G B . .
. . R X . .
B B . . G G

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.61)

Prediction

Expected

Figurative + 2 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: 6/15 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."

gemma-4-31b: 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.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (3227 chars)

### Conceptual Digestion

**1. Identify the CAST:**
*   **Azure (A):** The "figures" or "souls" on the stage.
*   **Black (.):** The "darkness" or "empty ground."
*   **Red (R):** The result of two azure figures mirroring each other (recognition).
*   **Grey (X):** The result of an azure figure mirroring an empty space (loneliness).

**2. Identify the AFFORDANCES:**
*   The grid is $6 \times 6$.
*   The "lake" is a horizontal mirror line running through the middle.
*   A cell at $(row, col)$ mirrors the cell at $(5-row, col)$.
*   Only Azure (A) cells are transformed. Black (.) cells remain Black.

**3. Identify the TRANSFORMATION RULE:**
For every cell $(r, c)$ in the grid:
*   If the cell is Black (.), it remains Black (.).
*   If the cell is Azure (A):
    *   Check the mirrored cell $(5-r, c)$.
    *   If the mirrored cell is also Azure (A), the current cell becomes Red (R).
    *   If the mirrored cell is Black (.), the current cell becomes Grey (X).

---

### Applying the Rule to Test Input

**Test Input:**
Row 0: `. . . A . A`
Row 1: `A A A . A A`
Row 2: `A A A A . A`
Row 3: `A . . . A A`
Row 4: `. A . . . A`
Row 5: `A A A . A A`

**Step-by-step Mirroring:**
*   **Col 0:**
    *   (0,0) is `.` $\rightarrow$ `.`
    *   (1,0) is `A`, (4,0) is `.` $\rightarrow$ `X`
    *   (2,0) is `A`, (3,0) is `A` $\rightarrow$ `R`
    *   (3,0) is `A`, (2,0) is `A` $\rightarrow$ `R`
    *   (4,0) is `.` $\rightarrow$ `.`
    *   (5,0) is `A`, (0,0) is `.` $\rightarrow$ `X`

*   **Col 1:**
    *   (0,1) is `.` $\rightarrow$ `.`
    *   (1,1) is `A`, (4,1) is `A` $\rightarrow$ `R`
    *   (2,1) is `A`, (3,1) is `.` $\rightarrow$ `X`
    *   (3,1) is `.` $\rightarrow$ `.`
    *   (4,1) is `A`, (1,1) is `A` $\rightarrow$ `R`
    *   (5,1) is `A`, (0,1) is `.` $\rightarrow$ `X`

*   **Col 2:**
    *   (0,2) is `.` $\rightarrow$ `.`
    *   (1,2) is `A`, (4,2) is `.` $\rightarrow$ `X`
    *   (2,2) is `A`, (3,2) is `.` $\rightarrow$ `X`
    *   (3,2) is `.` $\rightarrow$ `.`
    *   (4,2) is `.` $\rightarrow$ `.`
    *   (5,2) is `A`, (0,2) is `.` $\rightarrow$ `X`

*   **Col 3:**
    *   (0,3) is `A`, (5,3) is `.` $\rightarrow$ `X`
    *   (1,3) is `.` $\rightarrow$ `.`
    *   (2,3) is `A`, (3,3) is `.` $\rightarrow$ `X`
    *   (3,3) is `.` $\rightarrow$ `.`
    *   (4,3) is `.` $\rightarrow$ `.`
    *   (5,3) is `.` $\rightarrow$ `.`

*   **Col 4:**
    *   (0,4) is `.` $\rightarrow$ `.`
    *   (1,4) is `A`, (4,4) is `.` $\rightarrow$ `X`
    *   (2,4) is `.` $\rightarrow$ `.`
    *   (3,4) is `A`, (2,4) is `.` $\rightarrow$ `X`
    *   (4,4) is `.` $\rightarrow$ `.`
    *   (5,4) is `A`, (0,4) is `.` $\rightarrow$ `X`

*   **Col 5:**
    *   (0,5) is `A`, (5,5) is `A` $\rightarrow$ `R`
    *   (1,5) is `A`, (4,5) is `A` $\rightarrow$ `R`
    *   (2,5) is `A`, (3,5) is `A` $\rightarrow$ `R`
    *   (3,5) is `A`, (2,5) is `A` $\rightarrow$ `R`
    *   (4,5) is `A`, (1,5) is `A` $\rightarrow$ `R`
    *   (5,5) is `A`, (0,5) is `A` $\rightarrow$ `R`

**Final 

... [227 chars truncated]

Test

Test Input

→

Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.14)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 656: "A fortress casts its shadow outward, but the shadow carries ... [40 chars truncated]" k=1 alts: 0/0 aa62e3f4

Training Examples

Example 1

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Output

Example 2

Input

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Output

Literal Description

See: The input grid has a background of azure (A) and contains a single closed shape made of a 'border color' (the most frequent non-background color). This border color forms the outer shell of the shape. Nested inside the border is an 'inner color' — a distinct color occupying one or more cells fully enclosed by the border. There may also be a 'fill color' between the border and the inner color, acting as padding. The shape is compact and roughly symmetric.

Do: 1. Identify the border color (the non-background color forming the outer shell of the shape) and the inner color (the distinct color nested deepest inside the shape). Ignore any fill color between them. 2. Create an output grid of the same dimensions, filled entirely with background (A). 3. For each cell occupied by the border color in the input, examine its four cardinal neighbors (up, down, left, right). For each neighbor that is either background (A) in the input or would be outside the grid boundary, if that neighbor position is within the grid, place the inner color there in the output. 4. All other cells in the output remain background (A). In short: the border projects the inner color one step outward in every direction that faces away from the shape's interior.

Grid: The output grid has the same dimensions as the input grid. The background color is azure (A). The only non-background color in the output is the inner color from the input shape, placed at specific positions adjacent to where the border was. The original shape (border, fill, and inner color) is entirely replaced by background in the output.

Figurative Descriptions (1 variants)

"A fortress casts its shadow outward, but the shadow carries the color of the treasure locked inside."

gemma-4-31b: k=1

See: On a calm azure sea, a fortress sits — its walls built from one color, guarding a hidden jewel of another color deep within. The space between wall and jewel may be filled with mortar, but the jewel is what matters. The fortress is compact, like a closed fist.

Do: The fortress crumbles and vanishes. But as each wall stone falls, it casts the jewel's light outward — a beacon that shines one step into the open sea beyond where each stone stood. The light only escapes through the outer face of the wall, the side that breathed open air. Where the wall faced inward, toward its own halls, no light escapes. The fortress is gone; only its outward glow remains, painted in the color of what it once protected.

Grid: The sea remains the same size. The fortress, its walls, its mortar, its jewel — all dissolve back into azure. What remains are glowing marks in the jewel's color, tracing a halo just outside where the fortress walls once stood. The glow only appears on the seaward side of each former wall stone.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (3389 chars)

### Conceptual Digestion

1.  **The CAST**:
    *   **The Sea**: The background color, which is Azure (`A`).
    *   **The Fortress**: A compact cluster of non-azure cells.
    *   **The Walls/Mortar**: The outer and intermediate layers of the fortress (in the test input, these are Yellow `Y`).
    *   **The Jewel**: A single cell of a different color located inside the fortress (in the test input, this is Green `G`).

2.  **The AFFORDANCES**:
    *   The fortress is identified as the contiguous block of non-`A` cells.
    *   The "Jewel" color is the color of the innermost cell (or the unique color within the cluster).
    *   The "Outer Face" of the wall refers to the boundary where a fortress cell is adjacent to the "Sea" (`A`).

3.  **The TRANSFORMATION RULE**:
    *   **Step 1**: Identify the color of the Jewel (the inner-most distinct color). In the test input, the jewel is Green (`G`).
    *   **Step 2**: Identify all cells that belong to the fortress (non-`A` cells).
    *   **Step 3**: For every cell in the fortress, check its four cardinal neighbors (Up, Down, Left, Right).
    *   **Step 4**: If a neighbor is the "Sea" (`A`), place a mark of the Jewel's color (`G`) in that neighbor's position.
    *   **Step 5**: Clear the entire original fortress (set all non-`A` cells to `A`).
    *   **Step 6**: The final grid consists of the original sea, with the jewel's color marking the "halo" just outside the former fortress walls.

### Applying the Rule to Test Input

**Input Grid:**
(0,0) A (0,1) A (0,2) Y (0,3) A (0,4) A
(1,0) A (1,1) A (1,2) Y (1,3) Y (1,4) A
(2,0) A (2,1) Y (2,2) Y (2,3) Y (2,4) A
(3,0) A (3,1) Y (3,2) G (3,3) Y (3,4) A
(4,0) A (4,1) Y (4,2) Y (4,3) Y (4,4) A

1.  **Jewel Color**: Green (`G`).
2.  **Fortress Cells**: (0,2), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (4,1), (4,2), (4,3).
3.  **Finding the Halo (Neighbors of Fortress that are 'A')**:
    *   (0,2) is Y: Neighbors are (0,1)A, (0,3)A, (1,2)Y. $\rightarrow$ Halo at **(0,1), (0,3)**.
    *   (1,2) is Y: Neighbors are (0,2)Y, (2,2)Y, (1,1)A, (1,3)Y. $\rightarrow$ Halo at **(1,1)**.
    *   (1,3) is Y: Neighbors are (0,3)A, (2,3)Y, (1,2)Y, (1,4)A. $\rightarrow$ Halo at **(0,3), (1,4)**.
    *   (2,1) is Y: Neighbors are (1,1)A, (3,1)Y, (2,0)A, (2,2)Y. $\rightarrow$ Halo at **(1,1), (2,0)**.
    *   (2,2) is Y: Neighbors are (1,2)Y, (3,2)G, (2,1)Y, (2,3)Y. $\rightarrow$ No A neighbors.
    *   (2,3) is Y: Neighbors are (1,3)Y, (3,3)Y, (2,2)Y, (2,4)A. $\rightarrow$ Halo at **(2,4)**.
    *   (3,1) is Y: Neighbors are (2,1)Y, (4,1)Y, (3,0)A, (3,2)G. $\rightarrow$ Halo at **(3,0)**.
    *   (3,2) is G: Neighbors are (2,2)Y, (4,2)Y, (3,1)Y, (3,3)Y. $\rightarrow$ No A neighbors.
    *   (3,3) is Y: Neighbors are (2,3)Y, (4,3)Y, (3,2)G, (3,4)A. $\rightarrow$ Halo at **(3,4)**.
    *   (4,1) is Y: Neighbors are (3,1)Y, (4,0)A, (4,2)Y. $\rightarrow$ Halo at **(4,0)**.
    *   (4,2) is Y: Neighbors are (3,2)G, (4,1)Y, (4,3)Y. $\rightarrow$ No A neighbors (botto

... [389 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.16)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 660: "A pebble dropped in a still pond sends out rings of color." k=1 alts: 13/15 aaef0977

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Literal Description

See: The input is an 8×8 grid filled entirely with orange (O) cells except for exactly one cell that has a different color — the 'seed.' The seed can be any of the nine non-orange colors: black (.), blue (B), red (R), green (G), yellow (Y), grey (X), magenta (M), orange is excluded as it is the background, azure (A), or maroon (W).

Do: 1. Locate the single non-orange cell in the input. Record its color C and its position (r, c) using zero-indexed row and column coordinates. 2. Use the fixed 9-color cycle in this order: G, Y, ., X, R, A, W, M, B (indices 0 through 8). 3. Determine the index of the seed color C within this cycle. Call it i. 4. For every cell (row, col) in the output grid, compute the Manhattan distance d = |row − r| + |col − c|. 5. Assign that cell the color at position (i + d) mod 9 in the cycle. 6. Fill the entire grid this way. The result is a diamond-shaped ripple of colors radiating outward from the seed position.

Grid: The grid is always 8×8. The input uses orange (O) as the uniform background with exactly one non-orange seed cell. The output grid has the same 8×8 dimensions but contains no orange — every cell is replaced by a color from the 9-color cycle determined by its Manhattan distance from the seed.

Figurative Descriptions (16 variants)

"A pebble dropped in a still pond sends out rings of color."

gemma-4-31b: k=1

See: A calm, uniform orange lake stretches across the grid — perfectly still, without a single ripple. Somewhere in this lake, a single colored pebble rests just beneath the surface, waiting to disturb the peace.

Do: The pebble drops. From the point of impact, concentric diamond-shaped waves radiate outward, each ring shifting to the next color in an endless chromatic heartbeat — a prayer wheel of nine hues spinning forever forward. The closer a spot is to where the stone fell, the younger its ripple; the farther away, the more the wave has aged and cycled through the spectrum. The particular color of the pebble determines which note the melody begins on, and every ring thereafter follows the same ancient song in order.

Grid: The once-tranquil orange lake is completely transformed — no trace of stillness remains. Every point on the water now shimmers with the color of whichever ripple has reached it, painting a diamond-shaped mandala centered on the point of impact. The lake keeps its original shores but is reborn entirely in the nine sacred colors of the wave.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (4895 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **The Lake**: The background grid of orange (`O`) cells.
    *   **The Pebble**: A single cell of a different color (the "seed") located within the orange lake.
    *   **The Waves**: Concentric diamond-shaped rings radiating from the pebble.

2.  **AFFORDANCES**:
    *   The position of the pebble $(r, c)$ serves as the center of the transformation.
    *   The color of the pebble determines the starting color of the sequence.
    *   The distance from the center determines which color in the sequence is applied.

3.  **TRANSFORMATION RULE**:
    *   **Distance Metric**: The "diamond-shaped waves" indicate the use of **Manhattan Distance**: $dist = |r - r_{pebble}| + |c - c_{pebble}|$.
    *   **Color Sequence**: The "prayer wheel of nine hues" refers to a specific cyclic order of the colors provided in the key. Looking at Example 1:
        *   Pebble is Green (`G`) at (0, 6).
        *   At $dist=0$, color is `G`.
        *   At $dist=1$, color is `Y`.
        *   At $dist=2$, color is `.`.
        *   At $dist=3$, color is `X`.
        *   At $dist=4$, color is `R`.
        *   At $dist=5$, color is `A`.
        *   At $dist=6$, color is `W`.
        *   At $dist=7$, color is `M`.
        *   At $dist=8$, color is `B`.
        *   Sequence: `G` $\rightarrow$ `Y` $\rightarrow$ `.` $\rightarrow$ `X` $\rightarrow$ `R` $\rightarrow$ `A` $\rightarrow$ `W` $\rightarrow$ `M` $\rightarrow$ `B` $\rightarrow$ (back to `G`).
    *   **The Master Sequence**: Based on the order provided in the color key (`. B R G Y X M O A W`), but adjusted to match the example's cycle:
        The sequence in Example 1 is: `G` (Green) $\rightarrow$ `Y` (Yellow) $\rightarrow$ `.` (Black) $\rightarrow$ `X` (Grey) $\rightarrow$ `R` (Red) $\rightarrow$ `A` (Azure) $\rightarrow$ `W` (Maroon) $\rightarrow$ `M` (Magenta) $\rightarrow$ `B` (Blue).
        Let's verify the sequence: `G, Y, ., X, R, A, W, M, B`.
        This is a cycle of 9 colors.

### Applying to Test Input

*   **Pebble Position**: (2, 1) - Row 2, Col 1 (0-indexed).
*   **Pebble Color**: `.` (Black).
*   **Sequence starting from `.`**: `.` $\rightarrow$ `X` $\rightarrow$ `R` $\rightarrow$ `A` $\rightarrow$ `W` $\rightarrow$ `M` $\rightarrow$ `B` $\rightarrow$ `G` $\rightarrow$ `Y` $\rightarrow$ (back to `.`).

**Distance Map and Color Assignment**:
*   $dist=0$: `.`
*   $dist=1$: `X`
*   $dist=2$: `R`
*   $dist=3$: `A`
*   $dist=4$: `W`
*   $dist=5$: `M`
*   $dist=6$: `B`
*   $dist=7$: `G`
*   $dist=8$: `Y`
*   $dist=9$: `.`
*   $dist=10$: `X`
*   $dist=11$: `R`
*   $dist=12$: `A`
*   $dist=13$: `W`

**Calculating for each cell (r, c)**:
Row 0:
(0,0): dist=3 $\rightarrow$ A | (0,1): dist=2 $\rightarrow$ R | (0,2): dist=3 $\rightarrow$ A | (0,3): dist=4 $\rightarrow$ W | (0,4): dist=5 $\rightarrow$ M | (0,5): dist=6 $\rightarrow$ B | (0,6): dist=7 $\rightarrow$ G | (0,7): dist=8 $\rightarrow$ Y
Row 1:
(1,0): dist=2 $\rightarrow$ R | (1,1): dist=1 $\rightarrow$ X | 

... [1895 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.14)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 664: "Tree rings reveal the age of the world, each colored seed gr ... [33 chars truncated]" k=1 alts: 0/0 ac0c2ac3

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 an orange (O) background with several non-orange colored cells scattered across it. Each non-orange cell is a single pixel of a distinct color. The number of non-orange cells equals the number of concentric square rings needed to tile the entire output grid (including the center pixel). The cells are located at varying distances from the center of the grid.

Do: 1. Identify all non-orange cells in the input grid and record each cell's color and position. 2. Compute the center of the grid (row = (height-1)/2, col = (width-1)/2). 3. Calculate the Euclidean distance from each non-orange cell to the grid center. 4. Sort the non-orange cells by distance from the grid center, nearest first. 5. Assign each cell to a concentric square ring: the nearest cell is ring 0 (the single center pixel), the next nearest is ring 1 (the 3×3 frame around the center), the next is ring 2 (the 5×5 frame), and so on outward. The outermost cell fills the border ring. 6. Construct the output grid (same dimensions as input) by filling each ring with its assigned color. Ring 0 is one pixel at the center; ring k fills all positions whose Chebyshev distance (max of absolute row and column offsets) from the center equals k.

Grid: The output grid has the same dimensions as the input grid. The grid has odd height and odd width, ensuring a unique center pixel. The entire grid is tiled by concentric square rings emanating from the center, with no gaps or overlap. The number of rings equals the number of non-orange cells in the input, which also equals max(ceil(height/2), ceil(width/2)) for a square or near-square grid.

Figurative Descriptions (1 variants)

"Tree rings reveal the age of the world, each colored seed growing outward from the heartwood."

gemma-4-31b: k=1

See: A vast orange field lies fallow, but scattered across it are colored seeds — each a different hue, each planted at a different distance from the heart of the field. The number of seeds matches the number of rings a great tree would need to fill the entire land.

Do: The seeds awaken and compete to become rings of the world-tree. The seed closest to the heart takes root first, becoming the single heartwood pixel at the center. The next closest seed grows into the first ring of bark around it. Each successive seed, moving outward by proximity to the heart, wraps itself as the next layer of bark around all inner layers — like a nesting doll assembling itself from the inside out. The outermost seed becomes the skin of the tree, touching every edge of the world.

Grid: When the tree is fully grown, its cross-section fills the entire grid — every cell belongs to exactly one ring of bark. The heartwood is a single pixel at the center; each ring of bark forms a square frame one layer thicker than the last. No orange field remains; the tree has consumed the whole world.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (2303 chars)

### Conceptual Digestion

**1. Identify the CAST:**
*   **Orange (O):** The "fallow field" (background). It is completely replaced in the output.
*   **Colored Pixels (Seeds):** The specific colors (B, R, G, Y, X, A, etc.) scattered in the input.
*   **The Heart:** The center of the grid. For a $13 \times 13$ grid, the center is at row 6, column 6 (0-indexed).

**2. Identify the AFFORDANCES:**
*   The seeds are sorted by their distance from the center.
*   The distance is measured as the Chebyshev distance: $\max(|x_1 - x_2|, |y_1 - y_2|)$.
*   The sorted seeds determine the order of the concentric square rings.

**3. Identify the TRANSFORMATION RULE:**
*   **Step 1: Find the center.** For a $13 \times 13$ grid, the center is $(6, 6)$.
*   **Step 2: Identify and sort seeds.** Find all non-orange pixels and calculate their distance from $(6, 6)$.
    *   R: $(6, 6) \rightarrow \text{dist} = 0$
    *   X: $(5, 5) \rightarrow \text{dist} = \max(|5-6|, |5-6|) = 1$
    *   A: $(4, 8) \rightarrow \text{dist} = \max(|4-6|, |8-6|) = 2$
    *   B: $(3, 8) \rightarrow \text{dist} = \max(|3-6|, |8-6|) = 3$
    *   G: $(10, 5) \rightarrow \text{dist} = \max(|10-6|, |5-6|) = 4$
    *   Y: $(11, 1) \rightarrow \text{dist} = \max(|11-6|, |1-6|) = 5$
    *   .: $(0, 12) \rightarrow \text{dist} = \max(|0-6|, |12-6|) = 6$
*   **Step 3: Map to rings.**
    *   Ring 0 (Center pixel): R
    *   Ring 1 (Square frame at dist 1): X
    *   Ring 2 (Square frame at dist 2): A
    *   Ring 3 (Square frame at dist 3): B
    *   Ring 4 (Square frame at dist 4): G
    *   Ring 5 (Square frame at dist 5): Y
    *   Ring 6 (Square frame at dist 6): .

### Applying the Rule to Test Input

The output is a series of concentric squares filling the $13 \times 13$ grid.
*   Center (6,6): R
*   Layer 1 (5,5 to 7,7): X
*   Layer 2 (4,4 to 8,8): A
*   Layer 3 (3,3 to 9,9): B
*   Layer 4 (2,2 to 10,10): G
*   Layer 5 (1,1 to 11,11): Y
*   Layer 6 (0,0 to 12,12): .

ANSWER:
. . . . . . . . . . . . .
. Y Y Y Y Y Y Y Y Y Y Y .
. Y G G G G G G G G G Y .
. Y G B B B B B B B G Y .
. Y G B A A A A A B G Y .
. Y G B A X X X A B G Y .
. Y G B A X R X A B G Y .
. Y G B A X X X A B G Y .
. Y G B A A A A A B G Y .
. Y G B B B B B B B G Y .
. Y G G G G G G G G G Y .
. Y Y Y Y Y Y Y Y Y Y Y .
. . . . . . . . . . . . .

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.48)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 674: "Loyal pets hear their owner's whistle and come running home." k=1 alts: 7/15 ae3edfdc

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 'center' pixels — one blue (B) and one red (R) — placed on a black background. Scattered around the grid are 'satellite' pixels: orange (O) pixels that share a row or column with the blue center, and green (G) pixels that share a row or column with the red center. Each satellite is aligned with its center in one of the four cardinal directions (directly above, below, left, or right), separated by some distance of black cells. There may also be stray colored pixels that do not align cardinally with either center; these are noise.

Do: 1. Identify the two center pixels: blue (B) and red (R). Note their positions. 2. For each center, find its associated satellites — orange (O) for blue, green (G) for red — that lie in the same row or same column as that center (i.e., directly above, below, left, or right of it at any distance). 3. For each satellite, determine its cardinal direction relative to its center (up, down, left, or right). 4. Clear the entire grid to black. 5. Place each center pixel back at its original position. 6. Place each satellite in the cell immediately adjacent to its center in the same cardinal direction it originally occupied. That is, if a satellite was anywhere above its center, place it one cell above; if it was to the left, place it one cell to the left; and so on.

Grid: The grid is 15 rows by 15 columns. The background is black (.). The output grid has the same dimensions. Only the center pixels and their collapsed satellites appear in the output; all other cells are black.

Figurative Descriptions (16 variants)

"Loyal pets hear their owner's whistle and come running home."

gemma-4-31b: k=1

See: Two homeowners live on a vast dark field — one in a blue house, one in a red house. Each owner has pets of a signature color: the blue owner keeps orange cats, and the red owner keeps green dogs. The pets have wandered off along the roads (rows and columns) leading away from home, some near, some far. A few stray animals roam the field too, but they belong to nobody.

Do: Each owner stands on the porch and calls their pets home. Every pet hears the whistle and bolts straight back along the road it wandered down, not stopping until it reaches the yard — curling up in the very first patch of grass next to the front door, on whichever side it came running from. The strays, hearing no familiar voice, simply vanish into the night. When morning comes, each home stands with its faithful companions huddled as close as possible, one on each side they returned from.

Grid: The dark field is 15 plots by 15 plots. Two homes — blue and red — anchor the scene. After the calling, only the homes and their returned pets remain; the rest of the field is empty darkness.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (2619 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Homes**: Blue (B) and Red (R).
    *   **Blue Owner's Pets**: Orange (O).
    *   **Red Owner's Pets**: Green (G).
    *   **Strays**: Any other colored pixels (though not present in the test input, they are ignored).
    *   **Field**: Black (.).

2.  **AFFORDANCES**:
    *   Pets move along the row or column they are currently in toward the home of their corresponding color.
    *   A pet "returns home" if it shares the same row or the same column as its home.
    *   The destination is the cell immediately adjacent to the home (up, down, left, or right).

3.  **TRANSFORMATION RULE**:
    *   **Identify Home Positions**: Find the coordinates of B and R.
    *   **Process Blue Pets (O)**: For every O at $(r, c)$:
        *   If $r = r_B$, it moves to $(r_B, c_B \pm 1)$ depending on whether $c < c_B$ or $c > c_B$.
        *   If $c = c_B$, it moves to $(r_B \pm 1, c_B)$ depending on whether $r < r_B$ or $r > r_B$.
        *   If neither, it is a stray and vanishes.
    *   **Process Red Pets (G)**: For every G at $(r, c)$:
        *   If $r = r_R$, it moves to $(r_R, c_R \pm 1)$ depending on whether $c < c_R$ or $c > c_R$.
        *   If $c = c_R$, it moves to $(r_R \pm 1, c_R)$ depending on whether $r < r_R$ or $r > r_R$.
        *   If neither, it is a stray and vanishes.
    *   **Final State**: Only the homes and the pets that successfully moved to the adjacent cells remain.

### Applying the Rule to Test Input

**1. Home Positions:**
*   Blue (B): Row 6, Col 5 (0-indexed)
*   Red (R): Row 3, Col 11 (0-indexed)

**2. Blue Pets (O):**
*   O at (6, 0): Same row as B (6). $0 < 5$, so it moves to (6, 4).
*   O at (6, 14): Same row as B (6). $14 > 5$, so it moves to (6, 6).

**3. Red Pets (G):**
*   G at (0, 11): Same column as R (11). $0 < 3$, so it moves to (2, 11).
*   G at (3, 0): Same row as R (3). $0 < 11$, so it moves to (3, 10).
*   G at (12, 11): Same column as R (11). $12 > 3$, so it moves to (4, 11).

**4. Final Grid Construction:**
*   B at (6, 5)
*   O at (6, 4) and (6, 6)
*   R at (3, 11)
*   G at (2, 11), (3, 10), and (4, 11)
*   All other cells are black (.).

ANSWER:
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . G . . .
. . . . . . . . . . G R . . .
. . . . . . . . . . . G . . .
. . . . . . . . . . . . . . .
. . . . O B O . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.99)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 706: "A single drop of dye falls into water and stains whatever cl ... [24 chars truncated]" k=1 alts: 1/15 b7256dcd

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 an orange (O) background containing one or more connected components (4-connected) made of magenta (M) cells. Scattered across the grid are single cells of other non-orange, non-magenta colors (e.g., yellow, blue, green, azure, maroon, grey). Each of these colored cells may or may not be 4-adjacent (sharing an edge) to a magenta connected component.

Do: 1. Identify every connected component of magenta (M) cells using 4-connectivity (up, down, left, right). 2. For each non-orange, non-magenta colored cell in the grid, check whether it is 4-adjacent to any cell belonging to a magenta connected component. 3. If the colored cell is adjacent to a magenta component, replace every magenta cell in that component with the colored cell's color. Then replace the colored cell itself with orange (O). 4. If the colored cell is NOT adjacent to any magenta component, simply replace it with orange (O) — it disappears. 5. Any magenta component that has no adjacent colored marker remains magenta. 6. The result is the transformed grid.

Grid: The output grid has the same dimensions as the input grid. The background color is orange (O). All non-orange, non-magenta marker cells from the input are removed (set to orange). Magenta shapes that were painted are replaced entirely by the color of their adjacent marker; unpainted magenta shapes remain as magenta.

Figurative Descriptions (16 variants)

"A single drop of dye falls into water and stains whatever clay sculpture it touches."

gemma-4-31b: k=1

See: An orange lake stretches across the grid. Rising from the water are sculptures made of magenta clay, their cells fused together in connected formations. Floating on the surface nearby are single droplets of vivid color — green, yellow, blue — each one a potent dye waiting to be absorbed.

Do: Each dye droplet reaches out to whatever it touches. If a droplet is brushing against a clay sculpture, the sculpture drinks in the color completely — every cell of connected clay transforms to match the dye. The droplet, spent, dissolves back into the orange water and vanishes. Droplets that float alone, touching no sculpture, simply sink and disappear without a trace. Any sculpture that no droplet touched remains its original magenta clay.

Grid: The lake remains the same size. The orange water fills every space it did before. All the little dye droplets are gone — absorbed or dissolved. Where magenta sculptures once stood, you may now see shapes dyed a new color, or sculptures still wearing their original magenta if no dye ever reached them.

gemma-4-31b — MARC valid, solved with 1 example

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Prediction

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Reasoning (4326 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Orange Lake (`O`)**: The background/environment. It remains unchanged.
    *   **Magenta Clay (`M`)**: Sculptures. These are connected components of `M` cells. They are the targets of the transformation.
    *   **Dye Droplets (`G`, `Y`, `B`, `A`, etc.)**: Single cells of colors other than `O` or `M`. These are the agents of change.
    *   **Other colors (`X`, etc.)**: Based on the description, these are treated as part of the environment or potential dyes.

2.  **AFFORDANCES**:
    *   A **Dye Droplet** can "touch" (be orthogonally adjacent to) a **Magenta Sculpture**.
    *   If a droplet touches a sculpture, the entire connected component of `M` cells is recolored to the droplet's color.
    *   The droplet itself always disappears (becomes `O`).
    *   If a droplet touches nothing (or only `O`), it disappears.
    *   If a sculpture is not touched by any droplet, it remains `M`.

3.  **TRANSFORMATION RULE**:
    1.  Identify all connected components of `M` (magenta sculptures).
    2.  Identify all single-cell "dye" droplets (any color that is not `O` or `M`).
    3.  For each dye droplet:
        *   Check its 4-neighbors (up, down, left, right).
        *   If a neighbor is part of a magenta sculpture, that entire sculpture changes to the dye's color.
        *   If a sculpture is touched by multiple different dyes, the rule doesn't explicitly state priority, but typically the first encountered or a specific order applies. However, in these puzzles, usually, one sculpture is touched by one dye.
    4.  Remove all dye droplets (replace with `O`).
    5.  The background `O` remains `O`.

---

### Applying the Rule to Test Input

**Input Grid:**
Row 0: Y O M O O O X
Row 1: M M M O O O O
Row 2: O O M O B O O
Row 3: O O O O M M O
Row 4: O O O O M M O
Row 5: M M A O O O O
Row 6: O M O O O O O

**Step 1: Identify Magenta Sculptures (Connected Components of M)**
*   **Sculpture 1**: (0,2), (1,0), (1,1), (1,2), (2,2)
*   **Sculpture 2**: (3,4), (3,5), (4,4), (4,5)
*   **Sculpture 3**: (5,0), (5,1), (6,1)

**Step 2: Identify Dye Droplets**
*   (0,0): Yellow (`Y`)
*   (0,6): Grey (`X`)
*   (2,4): Blue (`B`)
*   (5,2): Azure (`A`)

**Step 3: Check for Adjacency**
*   **Yellow (0,0)**: Neighbors are (0,1) `O` and (1,0) `M`. It touches **Sculpture 1**.
    *   Sculpture 1 becomes Yellow (`Y`).
*   **Grey (0,6)**: Neighbors are (0,5) `O` and (1,6) `O`. Touches nothing.
    *   Dissolves.
*   **Blue (2,4)**: Neighbors are (1,4) `O`, (3,4) `M`, (2,3) `O`, (2,5) `O`. It touches **Sculpture 2**.
    *   Sculpture 2 becomes Blue (`B`).
*   **Azure (5,2)**: Neighbors are (4,2) `O`, (6,2) `O`, (5,1) `M`, (5,3) `O`. It touches **Sculpture 3**.
    *   Sculpture 3 becomes Azure (`A`).

**Step 4: Final Assembly**
*   Background `O` stays `O`.
*   Sculpture 1 $\rightarrow$ `Y`
*   Sculpture 2 $\rightarrow$ `B`
*   Sculpture 3 $\rightarrow$ `A`
*   All dye droplets $\rightarrow$ `O`

**Mapping to Grid:**
(0,0): Y $\

... [1326 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.92)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 715: "A stone dropped in a walled pond sends out ripples that alte ... [28 chars truncated]" k=1 alts: 0/0 b7fb29bc

Training Examples

Example 1

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Example 2

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Example 3

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Output

Literal Description

See: A rectangular green (G) border encloses an interior region of empty (black) cells. Exactly one cell inside the border contains a green (G) dot — a seed point. All other interior cells are black.

Do: For each empty interior cell, compute the Chebyshev distance to the green seed dot: max(|row_diff|, |col_diff|). Color the cell based on this distance: distance 0 remains green (G), odd distances (1, 3, 5, …) become yellow (Y), even distances (2, 4, 6, …) become red (R). This produces concentric rectangular rings alternating yellow and red radiating outward from the seed.

Grid: The grid is 15×15 with a black background. A green rectangular border (9×9 outer dimensions) is positioned within it. The interior of the border is 7×7 cells. The grid exterior remains unchanged; only the interior cells are filled.

Figurative Descriptions (1 variants)

"A stone dropped in a walled pond sends out ripples that alternate between warm and cool."

gemma-4-31b: k=1

See: A green fortress wall encloses a still, dark pond. Somewhere on the pond's surface, a single green pebble rests — the point of impact, frozen in the instant before the splash.

Do: Drop the pebble. Ripples spread outward in concentric squares, lapping against the fortress walls. The first ripple glows yellow like sunlight on water, the next turns red like a reflection of sunset, then yellow again, red again — alternating warmth as they radiate from the splash point. The pebble itself stays green, unmoved at the center of the disturbance. Each ripple reaches as far as it can before the walls contain it.

Grid: The fortress sits within a larger dark expanse — a night sky surrounding the pond. The walls form a green rectangle, and the pond inside is seven cells across. Beyond the walls, the darkness is undisturbed — only the water inside responds to the stone.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Reasoning (5149 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Fortress Wall**: The green (`G`) rectangle. It acts as a boundary.
    *   **Pond**: The black (`.`) area inside the green rectangle.
    *   **Pebble**: The single green (`G`) cell located inside the pond. This is the center of the transformation.
    *   **Ripples**: Concentric squares of alternating colors (`Y` for yellow, `R` for red) expanding from the pebble.
    *   **Night Sky**: The black (`.`) area outside the green rectangle.

2.  **AFFORDANCES**:
    *   The pebble's coordinates $(r, c)$ serve as the origin for the ripples.
    *   The ripples expand outward: distance $d=1$ is yellow, $d=2$ is red, $d=3$ is yellow, etc.
    *   The distance $d$ is measured as the Chebyshev distance: $d = \max(|r - r_i|, |c - c_i|)$.
    *   Ripples only fill cells that are inside the green boundary and are not the pebble itself.
    *   The green boundary (`G`) and the exterior black area (`.`) remain unchanged.

3.  **TRANSFORMATION RULE**:
    1.  Locate the green pebble $(r, c)$ inside the green rectangle.
    2.  For every cell $(i, j)$ inside the green rectangle:
        *   Calculate $d = \max(|r - i|, |c - j|)$.
        *   If $d = 0$, the cell remains `G` (the pebble).
        *   If $d > 0$:
            *   If $d$ is odd, the cell becomes `Y` (Yellow).
            *   If $d$ is even, the cell becomes `R` (Red).
    3.  Cells outside the green rectangle or forming the green rectangle boundary remain unchanged.

### Applying the Rule to Test Input

*   **Green Boundary**: Rows 2 to 10, Columns 3 to 11.
*   **Pebble Location**: Row 5, Column 4 (0-indexed: Row 5, Col 4).
    *   Wait, let's re-count:
        Row 0: . . . . . . . . . . . . . . .
        Row 1: . . . . . . . . . . . . . . .
        Row 2: . . . G G G G G G G G G . . .
        Row 3: . . . G . . . . . . . G . . .
        Row 4: . . . G . . . . . . . G . . .
        Row 5: . . . G G . . . . . . G . . .  <- Pebble is at (5, 4)
        Row 6: . . . G . . . . . . . G . . .
        Row 7: . . . G . . . . . . . G . . .
        Row 8: . . . G . . . . . . . G . . .
        Row 9: . . . G . . . . . . . G . . .
        Row 10: . . . G G G G G G G G G . . .
*   **Pebble Coordinates**: $(5, 4)$.
*   **Ripples**:
    *   $d=1$ (Yellow): $(4,3)-(6,5)$ range, excluding boundary and pebble.
    *   $d=2$ (Red): $(3,2)-(7,6)$ range.
    *   $d=3$ (Yellow): $(2,1)-(8,7)$ range.
    *   $d=4$ (Red): $(1,0)-(9,8)$ range.
    *   $d=5$ (Yellow): $(0,-1)-(10,9)$ range.
    *   $d=6$ (Red): $( -1,-2)-(11,10)$ range.

Let's map the interior (Rows 3-9, Cols 4-10):
Row 3: $d=\max(|5-3|, |4-c|) = \max(2, |4-c|)$.
- Col 4: $\max(2,0)=2 \rightarrow R$
- Col 5: $\max(2,1)=2 \rightarrow R$
- Col 6: $\max(2,2)=2 \rightarrow R$
- Col 7: $\max(2,3)=3 \rightarrow Y$
- Col 8: $\max(2,4)=4 \rightarrow R$
- Col 9: $\max(2,5)=5 \rightarrow Y$
- Col 10: $\max(2,6)=6 \rightarrow R$

Row 4: $d=\max(|5-4|, |4-c|) = \max(1, |4-c|)$.
- Col 4: $\max(1,0)=1 \rightarrow Y$
-

... [2155 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.84)

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=1 alts: 0/15 bbb1b8b6

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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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."

gemma-4-31b: k=1

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.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Reasoning (2106 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Grey Wall (`X`)**: A vertical divider separating the grid into two halves (left and right).
    *   **Vault Door (`B` and `.`)**: Located on the left side. `B` (blue) represents the door structure, and `.` (black) represents the "keyholes" or gaps.
    *   **Key (Single Color, e.g., `R`, `M`)**: Located on the right side. The shape formed by the colored pixels represents the "teeth" of the key.

2.  **AFFORDANCES**:
    *   The gaps (`.`) in the blue door on the left can be filled by the colored pixels of the key on the right.
    *   The key's shape must be an exact match for the gaps' shape.

3.  **TRANSFORMATION RULE**:
    *   **Step 1**: Isolate the shape of the gaps (`.`) in the left room (relative to the blue door's bounding box) and the shape of the key in the right room.
    *   **Step 2**: Compare the two shapes.
        *   If the key's shape is identical to the gaps' shape (same number of pixels in the same relative positions), the key "fits."
        *   If the key fits, replace all `.` (gaps) in the left room with the key's color.
        *   If the key does not fit (extra pixels or missing pixels), the left room remains unchanged.
    *   **Step 3**: The output grid consists only of the left room (the vault door area), removing the grey wall and the right room.

### Applying the Rule to Test Input

**Input Analysis:**
Left Room (Vault Door):
Row 0: `B B B B`
Row 1: `. B B .`
Row 2: `. B B .`
Row 3: `. . . .`
Gaps (`.`) are at: (1,0), (1,3), (2,0), (2,3), (3,0), (3,1), (3,2), (3,3).

Right Room (Key):
Row 0: `R . . .`
Row 1: `R R R R`
Row 2: `R . . .`
Row 3: `. . . .`
Key pixels (`R`) are at: (0,0), (1,0), (1,1), (1,2), (1,3), (2,0).

**Comparison:**
*   Gaps shape: A "C" or "U" like frame around the blue center.
*   Key shape: A "T" or "cross" like shape.
*   The shapes do not match. The key does not fit the lock.

**Result:**
Since the key does not match the lock, the vault stays sealed and unchanged. The output is the left room exactly as it appeared in the input.

ANSWER:
B B B B
. B B .
. B B .
. . . .

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 796: "Fountains erupt through broken aqueducts, each geyser painti ... [58 chars truncated]" k=1 alts: 0/0 cf133acc

Training Examples

Example 1

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Example 2

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Example 3

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Output

Literal Description

See: The input grid contains two types of colored elements on a black background: (1) Horizontal bars — rows that are mostly filled with a single color but contain exactly one gap (a black cell). Multiple horizontal bars appear at various rows, each a different color. (2) Vertical seeds — short vertical columns of a single color at the bottom of the grid, each occupying one column. Each vertical seed sits in a column that corresponds to the gap position of one of the horizontal bars. The horizontal bars and vertical seeds together form two independent vertical chains (one per gap column), where the bars are like rungs and the seeds are starting points at the bottom.

Do: For each vertical seed at the bottom of the grid: (1) Identify which column the seed occupies. (2) Trace upward from the seed through that column. The seed's own color fills the cells from the seed's position downward to the bottom edge. (3) Moving upward from the seed, find the nearest horizontal bar that has its gap in this column. Fill the gap cell in that bar with the bar's own color (completing the bar). Fill all black cells in this column between the seed and this bar with the color of the bar directly below (the seed's color for the first segment). (4) Now treat this bar's color as the new propagating color. Continue upward from this bar to find the next horizontal bar with its gap in this column. Fill all cells in this column between the two bars with the current propagating color. Fill the gap in the newly reached bar with that bar's own color. (5) Repeat: adopt the latest bar's color and continue upward. When no more horizontal bars remain above, fill the remaining cells in this column up to the top edge with the color of the last bar encountered. (6) All cells outside these gap columns remain unchanged.

Grid: The grid is 15 rows by 15 columns. The background is black (.). The grid dimensions remain the same between input and output. Horizontal bars span most or all of a row and always contain exactly one black gap cell. Vertical seeds are short contiguous columns of a single color positioned at the bottom of the grid. Each gap column is shared by multiple horizontal bars, creating a vertical chain.

Figurative Descriptions (1 variants)

"Fountains erupt through broken aqueducts, each geyser painting the sky with the colors of the pipes it bursts through."

gemma-4-31b: k=1

See: Across a dark landscape, ancient aqueducts stretch horizontally — colored pipelines that are nearly complete but each has one broken joint, a single missing segment. At the ground level, small geysers of color bubble up, each one positioned directly beneath one of these broken joints. The aqueducts and geysers form two vertical shafts of potential energy, like elevator columns running through a building's floors.

Do: Each geyser erupts upward with tremendous pressure, shooting a column of water toward the sky. As the rising column hits the first broken aqueduct above it, it seals the crack — the pipe repairs itself with its own native color. But the geyser doesn't stop; it takes on the color of each aqueduct it passes through, like light filtering through stained glass. Between each aqueduct, the column glows with the color of the pipe it most recently burst through. When it clears the highest aqueduct, the fountain keeps spraying that final color all the way to the heavens. The geyser's own original color stains everything below the first pipe it reaches, down into the earth.

Grid: The landscape is a 15-by-15 dark canvas. The aqueducts are horizontal streaks of color, each missing exactly one brick. The geysers are short vertical pulses of color rooted near the bottom. Two vertical shafts run through the scene, each threading through its own set of aqueducts. Everything outside these two shafts remains untouched darkness.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (3741 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Aqueducts**: Horizontal lines of a single color with one missing segment (a gap).
    *   **Geysers**: Vertical segments of color located at the bottom of the grid, positioned exactly in the column of a gap in an aqueduct.
    *   **Shafts**: The vertical columns defined by the geysers.

2.  **AFFORDANCES**:
    *   The geyser acts as a source of color that "shoots" upward.
    *   The gap in the aqueduct is a "broken joint" that gets filled by the rising column.
    *   The rising column changes color as it passes through each aqueduct.

3.  **TRANSFORMATION RULE**:
    *   Identify the two vertical shafts (columns) where geysers are located.
    *   For each shaft:
        *   From the bottom up to the first aqueduct encountered, the column is filled with the **geyser's original color**.
        *   When the column hits an aqueduct, the gap in that aqueduct is filled with the **aqueduct's color**.
        *   The column then continues upward, maintaining the color of the **most recently passed aqueduct**.
        *   This process repeats for every aqueduct in that shaft.
        *   Once the column passes the highest aqueduct in that shaft, it continues to the top of the grid (row 0) in the color of the **final (highest) aqueduct**.

### Applying the Rule to Test Input

**Shaft 1 (Column 3):**
*   Geyser color: `M` (Magenta) at (13,3) and (14,3).
*   Aqueducts in Column 3:
    1.  Row 11: `Y` (Yellow) - Gap at (11,3).
    2.  Row 6: `G` (Green) - Gap at (6,3).
    3.  Row 2: `R` (Red) - Gap at (2,3).
*   **Filling Column 3**:
    *   Rows 14 down to 12: `M` (Geyser color).
    *   Row 11: `Y` (Fills gap, column becomes `Y`).
    *   Rows 10 down to 7: `Y` (Previous aqueduct color).
    *   Row 6: `G` (Fills gap, column becomes `G`).
    *   Rows 5 down to 3: `G` (Previous aqueduct color).
    *   Row 2: `R` (Fills gap, column becomes `R`).
    *   Rows 1 down to 0: `R` (Final aqueduct color).

**Shaft 2 (Column 8):**
*   Geyser color: `A` (Azure) at (14,8).
*   Aqueducts in Column 8:
    1.  Row 11: `Y` (Yellow) - Gap at (11,8).
    2.  Row 8: `W` (Maroon) - Gap at (8,8).
    3.  Row 3: `X` (Grey) - Gap at (3,8).
*   **Filling Column 8**:
    *   Rows 14 down to 12: `A` (Geyser color).
    *   Row 11: `Y` (Fills gap, column becomes `Y`).
    *   Rows 10 down to 9: `Y` (Previous aqueduct color).
    *   Row 8: `W` (Fills gap, column becomes `W`).
    *   Rows 7 down to 4: `W` (Previous aqueduct color).
    *   Row 3: `X` (Fills gap, column becomes `X`).
    *   Rows 2 down to 0: `X` (Final aqueduct color).

### Final Grid Construction

*   Row 0: `. . . R . . . . X . . . . . .`
*   Row 1: `. . . R . . . . X . . . . . .`
*   Row 2: `R R R R R R . . X . . . . . .`
*   Row 3: `. . . G . . X X X X X X X X X`
*   Row 4: `. . . G . . . . W . . . . . .`
*   Row 5: `. . . G . . . . W . . . . . .`
*   Row 6: `G G G G G G G . W . . . . . .`
*   Row 7: `. . . Y . . . . W . . . . . .`
*   Row 8: `. . . Y . .

... [741 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.90)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 820: "A mirror reveals what's missing and what's imagined — ... [40 chars truncated]" k=2 alts: 0/0 d47aa2ff

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 10x21 grid containing a vertical column of grey (X) cells at column 10, dividing the grid into two 10x10 subgrids: the Left grid (columns 0-9) and the Right grid (columns 11-20). Both subgrids contain scattered colored cells (such as Y, W, O, A, G, M) on a black (.) background. The two subgrids are nearly identical, but they differ at a small number of positions: some colored cells appear in the Left grid but not the Right, and some appear in the Right grid but not the Left.

Do: 1. Separate the input into the Left grid (columns 0-9) and the Right grid (columns 11-20), discarding the grey divider column. 2. Compare the two grids cell by cell. 3. Start with a copy of the Left grid as the output. 4. For each position where the grids differ: (a) If the Left grid has a colored cell and the Right grid has black at that position, replace that cell in the output with red (R). (b) If the Left grid has black and the Right grid has a colored cell at that position, replace that cell in the output with blue (B). 5. All positions where the Left and Right grids match remain unchanged in the output.

Grid: The input grid is 10 rows by 21 columns. A vertical grey (X) divider at column 10 splits it into two 10x10 subgrids. The output grid is 10x10, the same dimensions as each subgrid. The background color is black (.).

Figurative Descriptions (1 variants)

"A mirror reveals what's missing and what's imagined — ghosts glow blue, and memories burn red."

gemma-4-31b: k=2

See: A grey curtain hangs down the center of a stage, dividing two nearly identical scenes. Actors in colorful costumes perform on both sides, but a few have quietly slipped away from one side, and a few uninvited guests have appeared on the other. The curtain hides these small betrayals from the audience.

Do: Tear down the curtain and hold the two scenes up to the light together. Where an actor stood on the left but their shadow is missing on the right, they were never real — paint them red, the color of fading memory. Where the right stage conjured someone the left never knew, mark their empty chair blue, the color of longing. Everyone who appears faithfully on both sides stays exactly as they are — they were always true.

Grid: The stage is ten rows deep and twenty-one seats wide, split by a single grey curtain column. Each half is a ten-by-ten scene of scattered colored performers against darkness. The final performance — after the curtain falls — is a single ten-by-ten scene where truth is preserved and discrepancies are dyed in red and blue.

gemma-4-31b — MARC valid, solved with 2 examples

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Prediction

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Reasoning (4170 chars)

### Conceptual Digestion

1.  **The CAST**:
    *   **The Stage**: A 10x21 grid.
    *   **The Curtain**: The central column (index 10) consisting of grey 'X' characters.
    *   **The Scenes**: Two 10x10 grids (Left: columns 0-9, Right: columns 11-20).
    *   **The Actors**: Colored characters (Y, W, O, etc.) representing objects at specific coordinates.
    *   **The Void**: Black '.' characters.

2.  **The AFFORDANCES**:
    *   The grid is split into two halves.
    *   Each cell $(r, c)$ in the left half corresponds to cell $(r, c+11)$ in the right half.
    *   Colors can be compared between these corresponding positions.

3.  **The TRANSFORMATION RULE**:
    *   Compare the left scene ($L$) and the right scene ($R$).
    *   If $L(r, c) = R(r, c)$ and both are colors (or both are black), the output $O(r, c) = L(r, c)$.
    *   If $L(r, c)$ is a color but $R(r, c)$ is black (actor missing on the right), the output $O(r, c) = \text{Red (R)}$.
    *   If $L(r, c)$ is black but $R(r, c)$ is a color (uninvited guest on the right), the output $O(r, c) = \text{Blue (B)}$.
    *   If both are different colors (though not seen in examples), the logic suggests they are both "untrue," but based on the metaphor, we focus on presence vs. absence.

### Applying the Rule to Test Input

**Left Scene (L) vs Right Scene (R):**
- Row 0: L(0,4)=Y, R(0,4)=. $\rightarrow$ **R**
- Row 1: L(1,1)=W, R(1,1)=W (True); L(1,17)=Y $\rightarrow$ **B** at (1,7) [Wait, R(1,17) is col 6 of right scene: $17-11=6$]. Let's re-index.

**Correct Indexing (Right side col $j$ is $j-11$):**
- Row 0: L(0,4)=Y; R(0,4)=. $\rightarrow$ **R** at (0,4)
- Row 1: L(1,1)=W; R(1,1)=W (True); R(1,6)=Y $\rightarrow$ **B** at (1,6)
- Row 2: L(2,3)=Y; R(2,3)=Y (True); L(2,7)=W; R(2,7)=. $\rightarrow$ **R** at (2,7); R(2,8)=W $\rightarrow$ **B** at (2,8)
- Row 3: All black.
- Row 4: L(4,3)=W; R(4,3)=W (True); L(4,6)=O; R(4,6)=. $\rightarrow$ **R** at (4,6)
- Row 5: L(5,x)=.; R(5,5)=O $\rightarrow$ **B** at (5,5)
- Row 6: L(6,0)=Y; R(6,0)=Y (True)
- Row 7: All black.
- Row 8: L(8,4)=O; R(8,4)=O (True); L(8,7)=Y; R(8,7)=Y (True)
- Row 9: L(9,0)=W; R(9,0)=W (True)

**Wait, let's re-verify Row 1 and 2 carefully.**
Test Input:
Row 0: `. . . . Y . . . . .` | `X` | `. . . . . . . . . .` $\rightarrow$ L(0,4)=Y, R(0,4)=. $\rightarrow$ **R**
Row 1: `. W . . . . . . . .` | `X` | `. W . . . . Y . . .` $\rightarrow$ L(1,1)=W, R(1,1)=W; R(1,6)=Y $\rightarrow$ **B**
Row 2: `. . . Y . . . W . .` | `X` | `. . . Y . . . W . .` $\rightarrow$ L(2,3)=Y, R(2,3)=Y; L(2,7)=W, R(2,7)=W. (Wait, looking closer at test input: ` . . . Y . . . W . . X . . . Y . . . W . .`)
Let's re-count Row 2:
L: `. . . Y . . . W . .` (Y at 3, W at 7)
R: `. . . Y . . . W . .` (Y at 3, W at 7)
Wait, the test input string is: `. . . Y . . . W . . X . . . Y . . . W . .`
Right side: `. . . Y . . . W . .`
Col 0: .
Col 1: .
Col 2: .
Col 3: Y
Col 4: .
Col 5: .
Col 6: .
Col 7: W
Col 8: .
Col 9: .
They are identical.

Row 4: `. . . W . . O . . . X 

... [1170 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 852: "Rain falls until it finds a bucket that can hold it." k=1 alts: 0/0 db7260a4

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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Example 5

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Output

Literal Description

See: The input grid contains one blue dot and one or more red shapes on a black background. Each red shape is a container formed by two vertical walls (left and right columns of red cells) connected by a horizontal bottom bar of red cells. The bottom bar may be complete (spanning the full width between the walls) or incomplete (having one or more gaps). The blue dot is always positioned above the red shapes, in the top few rows of the grid.

Do: 1. Locate the single blue dot and note its column position. 2. Remove the blue dot from its original position (replace with black). 3. Trace a path straight downward from the blue dot's column through the grid. 4. When the path encounters a red container, check whether that container's bottom bar is complete (no gaps between the two vertical walls) or incomplete (has at least one gap). 5. If the container is CLOSED (complete bottom bar), fill the entire interior of that container with blue. The interior is defined as all cells that are bounded by the left wall, right wall, and bottom bar, above the bottom bar and between the walls, that are currently black. Then stop. 6. If the container is OPEN (incomplete bottom bar with a gap), the blue passes through — do not fill that container. Continue tracing downward to the next container below. 7. If the blue passes through all containers without finding a closed one, fill the entire bottom row of the grid with blue.

Grid: The grid is rectangular (typically 10x10 but may vary). The background is black (.). Red cells (R) form container shapes. There is exactly one blue cell (B) in the input. The output grid has the same dimensions as the input.

Figurative Descriptions (1 variants)

"Rain falls until it finds a bucket that can hold it."

gemma-4-31b: k=1

See: A single blue raindrop hovers in the sky above a landscape of red buckets. Each bucket is made of two tall walls with a floor stretched between them — but some floors have cracks or missing planks, leaving holes where water would drain right through.

Do: The raindrop falls straight down from where it hangs in the sky. When it reaches a bucket, it checks the floor: if the floor is solid and unbroken, the rain pools inside, filling the bucket to the brim with blue water. But if the floor has gaps, the water slips through the cracks and keeps falling. If no bucket can hold the rain, it splashes across the entire ground, painting the bottom of the world blue.

Grid: The sky is black and empty except for one blue raindrop. The buckets are built from red walls and red floors. Water that pools turns the empty black space inside a bucket blue. A raindrop that reaches the ground floods the lowest row entirely.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (4638 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Blue Raindrop (B)**: The starting point of the water.
    *   **Red Walls/Floors (R)**: The structure of the "buckets".
    *   **Black Space (.)**: Empty air or the interior of a bucket.
    *   **Ground**: The bottom-most row of the grid.

2.  **AFFORDANCES**:
    *   The raindrop moves vertically downward (same column).
    *   A "bucket" is defined as a region enclosed by red walls on the left and right, with a red floor at the bottom.
    *   If the raindrop hits a red floor (R) that is continuous between two red walls, the space above that floor (within the walls) fills with blue (B).
    *   If the raindrop hits a gap (black space) where a floor should be, it continues falling.
    *   If the raindrop reaches the bottom row without being caught by a solid bucket, the entire bottom row turns blue (B).

3.  **TRANSFORMATION RULE**:
    1.  Locate the column of the blue raindrop (B).
    2.  Trace a path straight down from that column.
    3.  Identify the first "bucket" encountered. A bucket is a set of red walls (R) with a solid red floor (R) spanning the width between the walls.
    4.  If the raindrop's column passes through a gap in the floor (a '.' where the floor should be), it ignores that bucket and continues falling.
    5.  If it hits a solid red floor, fill the interior of that specific bucket (the area between the walls and above the floor) with blue (B).
    6.  If it reaches the bottom of the grid without being caught, fill the entire last row with blue (B).

### Applying the Rule to Test Input

*   **Raindrop Position**: Column 8 (0-indexed: 0 1 2 3 4 5 6 7 **8** 9).
*   **Path Down Column 8**:
    *   Row 0: B (Start)
    *   Row 1: .
    *   Row 2: .
    *   Row 3: .
    *   Row 4: R (Wall/Floor part)
    *   Row 5: . (Gap!)
    *   Row 6: R (Wall)
    *   Row 7: R (Wall)
    *   Row 8: R (Floor)
    *   Row 9: . (Ground)

*   **Analysis**:
    *   At Row 4, there is a red structure, but looking at the "bucket" logic: the raindrop is at Col 8. In Row 4, Col 8 is 'R'. However, looking at Row 5, Col 8 is '.', meaning there is a hole in the floor of any bucket that would have been at Row 4.
    *   The raindrop continues falling through Row 5.
    *   It then encounters the structure at the bottom. In Row 8, Col 8 is 'R'. This is part of a floor spanning from Col 2 to Col 8.
    *   The walls for this bottom bucket are at Col 2 and Col 8.
    *   The floor is at Row 8, from Col 2 to Col 8.
    *   The interior of this bucket (Rows 6 and 7, between Col 2 and Col 8) should be filled with blue.
    *   Wait, let's re-examine the "bucket" definition: "two tall walls with a floor stretched between them".
    *   Bucket 1 (Top): Walls at Col 5 and Col 9. Floor at Row 4 (Col 7, 8, 9). Raindrop is at Col 8. It hits the floor at Row 4. But is the floor solid? Row 4, Col 7=R, 8=R, 9=R. Yes. However, the description says "if the floor has gaps, the water slips through". In the test input, 

... [1638 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.80)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 860: "Scattered birds return to roost on a single wire at dusk" k=3 alts: 0/0 dce56571

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 azure (A) background with a cluster of non-azure colored pixels forming an irregular shape. All non-background pixels are the same color (e.g., maroon, green, red, or grey).

Do: 1. Count the total number of non-azure pixels (N) and note their color (C). 2. Clear the entire grid to azure. 3. Find the vertical center row of the grid (for H rows, this is row H÷2 rounded down, using zero-indexed rows). 4. Place a horizontal line of N pixels of color C on that center row, centered horizontally. To center: compute the left starting column as (W−N)÷2 where W is the grid width, then fill N consecutive cells with color C.

Grid: The output grid has the same dimensions as the input. The background is entirely azure (A) except for a single horizontal line of colored pixels centered both vertically and horizontally.

Figurative Descriptions (1 variants)

"Scattered birds return to roost on a single wire at dusk"

gemma-4-31b: k=3

See: Against a vast azure sky, a flock of same-colored birds has scattered in a chaotic cluster — some huddled together, others drifting apart — as if startled mid-flight.

Do: As evening falls, the sky clears and the birds find their calm. They gather themselves and glide down to a single telephone wire stretched across the exact heart of the sky. Each bird that was aloft claims one perch on the wire, settling side by side until the whole flock forms one neat row, balanced perfectly at the center of the horizon.

Grid: The sky returns to pure, unbroken azure. The only feature is a single wire of birds — every last one accounted for — perched in a tidy line at the vertical middle, centered left-to-right so the row hangs symmetrically in the open air.

gemma-4-31b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (2426 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Azure (A)**: The background (the sky).
    *   **Non-Azure colors (W, G, R, X)**: The "birds" (the flock).

2.  **AFFORDANCES**:
    *   The birds can be counted.
    *   The grid has a vertical center (middle row) and a horizontal center (middle column).

3.  **TRANSFORMATION RULE**:
    *   **Count**: Count the total number of non-azure pixels in the input grid.
    *   **Clear**: Set the entire output grid to azure (A).
    *   **Position**: Place the counted number of pixels in a single horizontal row.
    *   **Alignment**:
        *   The row must be placed at the **vertical center** of the grid.
        *   The row must be **centered horizontally** (left-to-right).
    *   **Color**: The birds maintain their original color (all birds in the examples are the same color).

### Applying the Rule to Test Input

1.  **Count the birds (X)**:
    *   Row 1: 0
    *   Row 2: 1 (col 8)
    *   Row 3: 4 (col 7, 9, 10, 11)
    *   Row 4: 3 (col 8, 10, 11)
    *   Row 5: 2 (col 7, 12)
    *   Row 6: 1 (col 12)
    *   Row 7: 1 (col 11)
    *   Row 8: 1 (col 12)
    *   Row 9: 1 (col 12)
    *   Row 10: 0
    *   Row 11: 0
    *   **Total Count = 1 + 4 + 3 + 2 + 1 + 1 + 1 + 1 = 14**

2.  **Grid Dimensions**:
    *   Height: 11 rows.
    *   Width: 28 columns.

3.  **Determine Position**:
    *   **Vertical Center**: Row index $\lfloor 11 / 2 \rfloor = 5$ (the 6th row).
    *   **Horizontal Centering**:
        *   Total width = 28.
        *   Bird count = 14.
        *   Remaining space = $28 - 14 = 14$.
        *   Left padding = $14 / 2 = 7$.
        *   The birds occupy columns 8 through 21 (indices 7 to 20).

4.  **Construct Output**:
    *   Rows 1-5: All A.
    *   Row 6: 7 A's, 14 X's, 7 A's.
    *   Rows 7-11: All A.

ANSWER:
A A A A A A A A A A A A A A A A A A A A A A A A A A A A
A A A A A A A A A A A A A A A A A A A A A A A A A A A A
A A A A A A A A A A A A A A A A A A A A A A A A A A A A
A A A A A A A A A A A A A A A A A A A A A A A A A A A A
A A A A A A A A A A A A A A A A A A A A A A A A A A A A
A A A A A A A X X X X X X X X X X X X X X X A A A A A A A
A A A A A A A A A A A A A A A A A A A A A A A A A A A A
A A A A A A A A A A A A A A A A A A A A A A A A A A A A
A A A A A A A A A A A A A A A A A A A A A A A A A A A A
A A A A A A A A A A A A A A A A A A A A A A A A A A A A
A A A A A A A A A A A A A A A A A A A A A A A A A A A A

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 875: "A wanted poster leads bounty hunters to fence in the fugitiv ... [2 chars truncated]" k=1 alts: 3/15 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."

gemma-4-31b: k=1

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.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (3050 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **The Jailhouse**: The top-left 4x4 area. The grey bars (X) at row 4 (index 3) and column 4 (index 3) define the boundary.
    *   **The Mugshot**: The 3x3 grid of colors located at (0,0) to (2,2). These are the "suspects".
    *   **The Fugitives**: A matching 3x3 block of colors located elsewhere in the 15x15 grid.
    *   **The Fence**: A 5x5 perimeter of grey (X) cells that will be drawn around the fugitives.

2.  **AFFORDANCES**:
    *   The mugshot provides the pattern to search for.
    *   The rest of the grid is the search area.
    *   The output is the original grid with the added 5x5 perimeter of X's around the matching 3x3 block.

3.  **TRANSFORMATION RULE**:
    *   **Step 1**: Extract the 3x3 pattern from the top-left corner (rows 0-2, cols 0-2).
    *   **Step 2**: Scan the grid (excluding the jailhouse area) for an identical 3x3 pattern.
    *   **Step 3**: Once found at top-left coordinate $(r, c)$, create a 5x5 boundary of 'X's from row $r-1$ to $r+3$ and column $c-1$ to $c+3$.
    *   **Step 4**: The interior 3x3 block (the fugitives) remains unchanged.

### Applying the Rule to Test Input

1.  **Identify Mugshot (0,0 to 2,2)**:
    Row 0: `. O G`
    Row 1: `B . G`
    Row 2: `B . .`

2.  **Search for Pattern in Grid**:
    Scanning the grid for `. O G` / `B . G` / `B . .`:
    *   Looking at row 7, col 1: `. O .` (No)
    *   Looking at row 11, col 1: `. R R` (No)
    *   Looking at row 12, col 2: `X R R` (No)
    *   Looking at row 13, col 2: `G . .` (No)
    *   Looking at row 11, col 10: `B . G` (Wait, let's check the block starting at row 11, col 10)
        Row 11: `B . G` (Matches Row 1 of mugshot? No, mugshot Row 0 is `. O G`)
    *   Looking at row 12, col 10: `B . .` (Matches Row 2 of mugshot)
    *   Looking at row 11, col 10: `B . G` (Matches Row 1 of mugshot)
    *   Looking at row 10, col 10: `. O G` (Matches Row 0 of mugshot)
    
    **Found it!** The fugitives are at:
    Row 10: `. O G` (cols 10, 11, 12)
    Row 11: `B . G` (cols 10, 11, 12)
    Row 12: `B . .` (cols 10, 11, 12)
    Top-left corner of fugitives: $(10, 10)$.

3.  **Erect the Fence**:
    The 3x3 block is at $(10, 10)$ to $(12, 12)$.
    The 5x5 perimeter is from row $10-1=9$ to $10+3=13$ and col $10-1=9$ to $10+3=13$.
    
    Fence coordinates (X):
    Row 9: cols 9, 10, 11, 12, 13
    Row 10: cols 9 and 13
    Row 11: cols 9 and 13
    Row 12: cols 9 and 13
    Row 13: cols 9, 10, 11, 12, 13

4.  **Final Grid Construction**:
    Update the test input with the X's at the specified coordinates.

ANSWER:
. O G X . . . . . . . G X Y .
B . G X R . B . . . . A . . .
B . . X M . . W W . X . . . W
X X X X . . R B . . G . . . .
G . . G B A X . X R . . X . .
Y . W R . . B . R . . . . . .
. . R . . . W X Y . A . . X X
. O . . . X X O . . B . . . B
. . . G . O G O . . . . O . .
. . . . . . . W . X X X X X .
. . . . G . . . G X . O G X R
. R R . . . . . . X B . G X .
. . X R R R . . . X B . . X .
. . G . .

... [50 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: N/A)

No grid

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 893: "The hottest ember escapes the dying campfires" k=3 alts: 14/15 e50d258f

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 two or three rectangular blocks of non-background cells, separated by borders of black (.) cells. Each block is composed of azure (A) cells forming a background within the block, with a small number of blue (B) and red (R) cells scattered among them.

Do: 1. Identify all distinct rectangular blocks of non-dot cells in the input grid. Blocks are separated from each other by rows or columns of dot cells. 2. For each block, count the number of red (R) cells it contains. 3. Select the block with the highest red cell count. 4. Extract that block exactly as it appears and output it.

Grid: The input grid is approximately 10x10 with black (.) cells serving as background and separators between blocks. Each block is a contiguous rectangle of non-dot cells. The output grid has the exact dimensions of the selected block, containing only the cells from that block with no surrounding dots.

Figurative Descriptions (16 variants)

"The hottest ember escapes the dying campfires"

gemma-4-31b: k=3

See: Scattered across the darkness like campfires in a valley, you see several glowing hearths — each a patch of pale azure coals with sparks of red flame and blue smoke drifting among them. The darkness between them is cold night air.

Do: Each campfire burns with a different intensity. Count the red-hot embers in each hearth — they are the true measure of its heat. The fire burning hottest, the one with the most living flame, refuses to die. Rescue it from the night and carry it forward whole.

Grid: The valley floor is dark (black). Each campfire is a compact rectangular bed of azure coals speckled with red embers and blue cinders. You must lift the hottest fire out intact — every coal, ember, and cinder in its exact arrangement — leaving the cold night behind.

gemma-4-31b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (2273 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Darkness (Black `.`)**: The background/void.
    *   **Campfires (Azure `A`, Blue `B`, Red `R`)**: Compact rectangular blocks of colors.
    *   **Embers (Red `R`)**: The specific color used to determine the "heat" or intensity of a campfire.
    *   **Coals/Cinders (Azure `A`, Blue `B`)**: The other components of the campfire block.

2.  **AFFORDANCES**:
    *   The grid contains multiple isolated rectangular clusters of non-black cells.
    *   Each cluster can be analyzed for the count of red cells (`R`).
    *   The cluster with the highest count of `R` is selected.

3.  **TRANSFORMATION RULE**:
    *   Identify all contiguous rectangular blocks of non-black cells.
    *   For each block, count the number of red cells (`R`).
    *   Find the block with the maximum number of red cells.
    *   Extract that specific rectangular block in its entirety (preserving all `A`, `B`, and `R` cells) and output it as the final grid.

### Applying the Rule to Test Input

**Step 1: Identify the blocks.**
*   **Block 1 (Top-Left):**
    Rows 0-3, Cols 0-3.
    `R A A A`
    `A A B A`
    `B R A B`
    `A A A A`
    Red count: 2 (`R` at 0,0 and 2,1).

*   **Block 2 (Top-Right):**
    Rows 1-3, Cols 6-9.
    `R A B .` (Wait, let's check boundaries)
    Row 1: `R A B .` (Col 6-8)
    Row 2: `A A A .` (Col 6-8)
    Row 3: `R B A .` (Col 6-8)
    Wait, looking closer at the test input:
    Row 1: `R A B .` (Cols 6,7,8)
    Row 2: `A A A .` (Cols 6,7,8)
    Row 3: `R B A .` (Cols 6,7,8)
    Row 4: `A A R .` (Cols 6,7,8)
    Row 5: `R A B .` (Cols 6,7,8)
    Row 6: `B A A .` (Cols 6,7,8)
    This is a block from Row 1 to Row 6, Cols 6 to 8.
    Content:
    `R A B`
    `A A A`
    `R B A`
    `A A R`
    `R A B`
    `B A A`
    Red count: 4 (`R` at 1,6; 3,6; 4,8; 5,6).

*   **Block 3 (Bottom-Left):**
    Rows 6-8, Cols 1-4.
    `B R A R`
    `A A B A`
    `B R A B`
    Red count: 3 (`R` at 6,2; 6,4; 8,2).

**Step 2: Compare Red Counts.**
*   Block 1: 2
*   Block 2: 4
*   Block 3: 3

**Step 3: Extract the winner.**
Block 2 has the most red cells (4).

**Block 2 Content:**
Row 1: `R A B`
Row 2: `A A A`
Row 3: `R B A`
Row 4: `A A R`
Row 5: `R A B`
Row 6: `B A A`

ANSWER:
R A B
A A A
R B A
A A R
R A B
B A A

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.32)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 895: "A green laser beam bounces off prisms in a dark room" k=4 alts: 0/0 e5790162

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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Output

Literal Description

See: The input grid contains a black background with three types of colored cells: exactly one green (G) cell, and one or more magenta (M) and azure (A) cells scattered across the grid. These colored cells act as a source and deflectors for a path that will be drawn.

Do: Starting from the green (G) cell, emit a path of green cells moving RIGHT. The path travels one cell at a time in its current direction. When the path reaches the cell that is exactly one step before a magenta (M) or azure (A) cell (i.e., adjacent to it along the direction of travel), it stops and makes a turn: if the deflector is magenta (M), turn CLOCKWISE 90 degrees (right becomes down, down becomes left, left becomes up, up becomes right); if the deflector is azure (A), turn COUNTER-CLOCKWISE 90 degrees (right becomes up, up becomes left, left becomes down, down becomes right). After turning, the path continues in the new direction from the cell where it stopped. The deflector cells themselves are NOT overwritten — the path stops one cell before each deflector. This process repeats, bouncing off deflectors in sequence, until the path exits the grid boundary. All cells the path passes through are colored green. The original G, M, and A cells remain unchanged.

Grid: The grid has a black (.) background. Dimensions vary across instances. The coordinate system is row-column with (0,0) at the top-left corner. The grid boundaries act as the termination condition for the path — once the path would move outside the grid, it stops. The original colored cells (G, M, A) are preserved in place; only the path cells are added as green.

Figurative Descriptions (1 variants)

"A green laser beam bounces off prisms in a dark room"

gemma-4-31b: k=4

See: In a pitch-black chamber, a green laser emitter sits waiting. Scattered throughout the room are crystal prisms — some glow magenta, others shimmer azure. Each prism has a unique way of bending light that passes near it.

Do: The laser fires its green beam to the right. The beam streaks through the darkness, painting every tile it crosses in vivid green. When the beam reaches a prism, it refracts — magenta prisms twist the light clockwise, like turning a steering wheel right, while azure prisms bend it the opposite way, like a left turn. The beam never shatters the prisms; it kisses the tile just before each one and veers off in its new direction. The light keeps bouncing from prism to prism, zigzagging through the chamber, until it finally escapes through a wall and vanishes into the night.

Grid: The dark chamber is a grid of black (.) tiles. The green (G) emitter, magenta (M) prisms, and azure (A) prisms all remain intact and unaltered — only the beam's trail is painted green across the floor.

gemma-4-31b — MARC valid, solved with 4 examples

Input

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Prediction

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Expected

Reasoning (7962 chars)

### Conceptual Digestion

1.  **CAST**:
    *   `G` (Green Emitter): The starting point of the laser beam.
    *   `M` (Magenta Prism): A clockwise (CW) reflector.
    *   `A` (Azure Prism): A counter-clockwise (CCW) reflector.
    *   `.` (Black Tile): Empty space that can be painted green.

2.  **AFFORDANCES**:
    *   The laser beam moves in a straight line (Right, Down, Left, or Up).
    *   When the beam hits a tile *adjacent* to a prism, it changes direction *before* entering the prism's tile.
    *   **Magenta (M)**:
        *   Right $\rightarrow$ Down
        *   Down $\rightarrow$ Left
        *   Left $\rightarrow$ Up
        *   Up $\rightarrow$ Right
    *   **Azure (A)**:
        *   Right $\rightarrow$ Up
        *   Up $\rightarrow$ Left
        *   Left $\rightarrow$ Down
        *   Down $\rightarrow$ Right

3.  **TRANSFORMATION RULE**:
    *   Start at `G`, moving **Right**.
    *   Paint every tile `G` until a prism is encountered.
    *   The tile containing the prism remains its original color (`M` or `A`).
    *   Change direction based on the prism type and continue painting.
    *   Stop when the beam exits the grid boundaries.

### Step-by-Step Execution for Test Input

**Grid Dimensions**: 10 rows x 12 columns.
**Start**: `G` at (7, 0). Direction: **Right**.

1.  **Path 1**: From (7, 0) moving Right.
    *   Tiles: (7, 0), (7, 1), (7, 2).
    *   At (7, 3), there is an `A` (Azure).
    *   Beam stops at (7, 2).
    *   **Refraction at A (7, 3)**: Right $\rightarrow$ **Up**.

2.  **Path 2**: From (7, 3) moving Up.
    *   Tiles: (6, 3), (5, 3), (4, 3), (3, 3).
    *   At (3, 2), there is an `M` (Magenta), but the beam is at column 3.
    *   Wait, let's check for prisms in column 3: (3, 2) is M, (7, 3) is A.
    *   Moving Up from (7, 3): (6, 3), (5, 3), (4, 3), (3, 3), (2, 3), (1, 3), (0, 3).
    *   Are there any prisms in column 3?
        *   Row 0: .
        *   Row 1: .
        *   Row 2: .
        *   Row 3: . (M is at 3, 2)
        *   Row 4: .
        *   Row 5: .
        *   Row 6: .
    *   The beam continues Up until it exits the grid at (0, 3).

**Wait, let me re-verify the prism coordinates for the Test Input:**
- (0, 9): M
- (1, 6): M
- (2, 10): A
- (3, 2): M
- (4, 7): A
- (7, 3): A
- (7, 0): G

**Re-tracing Path:**
1.  Start (7, 0) $\rightarrow$ Right.
2.  Hits `A` at (7, 3). Beam paints (7, 0), (7, 1), (7, 2).
3.  Refracts at `A` (7, 3): Right $\rightarrow$ **Up**.
4.  Moves Up from (7, 3): (6, 3), (5, 3), (4, 3), (3, 3), (2, 3), (1, 3), (0, 3).
5.  Check for prisms in column 3:
    - (3, 2) is M (Wrong column)
    - (7, 3) is A (Starting point of this leg)
    - No other prisms in column 3.
6.  Beam exits at (0, 3).

**Wait, let me double-check the "kisses the tile just before" rule.**
Example 1: G at (2,0), A at (2,4). Output: G G G G A. (Beam paints 0, 1, 2, 3).
Example 2: G at (3,0), M at (3,4). Output: G G G G M. Then Down from (3,4) to (5,4), then Right from (5,4) to (5,5).
Wait, in Example 2:
Inpu

... [4962 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.81)

Prediction

Expected

Figurative + 4 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 899: "Scattered breadcrumbs召 home the lost puzzle pieces th ... [13 chars truncated]" k=3 alts: 0/0 e6721834

Training Examples

Example 1

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Output

Example 2

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Example 3

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Literal Description

See: The input grid is divided into two rectangular regions distinguished by their background colors (e.g., yellow vs red, magenta vs blue, azure vs black). One region is the 'canvas' and the other is the 'template bank.' The template bank contains one or more rectangular blocks filled with a secondary color (e.g., azure/A) that stand out against the bank's background. Embedded within each block are a few marker cells of a distinct color (e.g., blue/B). The canvas region, on its own uniform background, contains scattered individual marker cells of that same color. These scattered markers form small clusters, and each cluster's spatial arrangement matches the relative positions of the markers inside exactly one template block.

Do: 1. Identify the two regions by their uniform background colors. The region containing rectangular multi-cell blocks (filled with a color different from either background) is the template bank; the other region is the canvas. 2. In the template bank, isolate each rectangular block. For each block, record its full extent (bounding box of the non-background-of-bank fill color) and the relative positions of the special marker cells within it. 3. In the canvas region, find all marker cells (same color as the markers in the templates). Group them into clusters based on proximity. 4. For each cluster of scattered markers, compare their relative spatial pattern to the marker patterns inside each template block. Find the matching template. 5. Overlay the matched template block onto the canvas so that its internal marker positions align exactly with the scattered marker positions. The block's fill color and marker cells replace the canvas background at those locations. 6. The output is the canvas region alone, with all matched templates placed and the rest remaining as the canvas background color.

Grid: The output grid has the dimensions of the canvas region (one of the two background-color regions in the input). Its background is the canvas region's uniform color. The placed template blocks appear as rectangular patches of a different fill color with embedded marker cells, positioned where the scattered markers were. The template bank region is discarded entirely.

Figurative Descriptions (1 variants)

"Scattered breadcrumbs召 home the lost puzzle pieces they fell from."

gemma-4-31b: k=3

See: The world is split in two: a quiet homeland on one side, and a museum of shapes on the other. The museum displays precious artifacts — colored tiles arranged in neat rectangular frames, each hiding a few distinctive gems within. Across the border in the homeland, someone has dropped lone gems onto the empty ground — tiny clues left like breadcrumbs, each cluster secretly whispering the name of the artifact it once belonged to.

Do: Read the breadcrumbs. Each scattered cluster of gems in the homeland is calling out to its matching artifact across the border — the one whose hidden gems share the same constellation. When a cluster recognizes its artifact, the entire framed piece flies across the divide and settles over the breadcrumbs, fitting perfectly like a key into a lock. The gems align, the frame fills in around them, and the artifact is home. The museum wall is then torn down and forgotten.

Grid: Only the homeland remains. Where it was once bare ground dotted with lonely gems, now the retrieved artifacts sit proudly in place — rectangular patches of their museum framing with gems embedded, surrounded by the homeland's unchanged quiet ground. The museum side vanishes entirely, as if it never existed.

gemma-4-31b — MARC valid, solved with 3 examples

Input

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Prediction

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Reasoning (5089 chars)

**Conceptual Digestion**

1.  **CAST**:
    *   **Homeland**: The region of the grid containing scattered "breadcrumbs" (lone colored pixels) on a background color. In the test input, this is the top half (rows 0-11) with a yellow (Y) background.
    *   **Museum**: The region containing "artifacts" (rectangular frames of a specific color containing a pattern of gems). In the test input, this is the bottom half (rows 12-23) with a red (R) background.
    *   **Breadcrumbs**: Small clusters of colored pixels in the homeland.
    *   **Artifacts**: Rectangular blocks of a different background color (e.g., Azure 'A') containing a specific arrangement of colored pixels.

2.  **AFFORDANCES**:
    *   The breadcrumbs act as "keys" or "signatures."
    *   The artifacts are "locks" that match the signature of the breadcrumbs.
    *   The transformation involves moving the artifact from the museum to the homeland, centering it on the breadcrumbs.

3.  **TRANSFORMATION RULE**:
    *   Identify the background color of the homeland (Y).
    *   Identify the background color of the museum (R).
    *   Locate clusters of non-background pixels in the homeland.
    *   For each cluster, find the artifact in the museum whose internal non-frame pixels match the relative positions of the breadcrumbs.
    *   Replace the homeland's background at the artifact's location with the artifact's frame and internal pixels.
    *   The final output grid size is the size of the homeland (rows 0-11, cols 0-11).

**Applying the rule to Test Input:**

*   **Homeland (Rows 0-11)**: Background = Y.
    *   Cluster 1: (3, 7) = B, (4, 8) = B. (Relative: (0,0) and (1,1)).
    *   Cluster 2: (6, 3) = B, (7, 1) = B, (8, 3) = B. (Relative: (0,2), (1,0), (2,2) - wait, let's re-check).
        *   (6, 3) = B
        *   (7, 1) = B
        *   (8, 3) = B
        *   Relative to top-left (6,1): (0, 2), (1, 0), (2, 2).

*   **Museum (Rows 12-23)**: Background = R.
    *   Artifact 1: Rows 15-17, Cols 3-7. Frame = A.
        *   Internal pixels: (16, 6) = B, (17, 7) = B.
        *   Relative to top-left (15, 3): (1, 3) and (2, 4).
        *   Wait, let's check the breadcrumbs again.
        *   Cluster 1: (3, 7) and (4, 8). Relative: (0, 0) and (1, 1).
        *   Artifact 1 internal: (16, 6) and (17, 7). Relative to (16, 6): (0, 0) and (1, 1).
        *   The artifact is the block from (15, 3) to (17, 7). Size: 3x5.
        *   The "gems" are at (16, 6) and (17, 7).
        *   Matching Cluster 1: (3, 7) and (4, 8).
        *   The artifact (3x5) will be placed such that (16, 6) aligns with (3, 7) and (17, 7) aligns with (4, 8).
        *   Top-left of artifact in homeland: (15-1, 3-3) = (14, 0)? No.
        *   If (16, 6) -> (3, 7), then offset is (-13, 1).
        *   Artifact top-left (15, 3) becomes (15-13, 3+1) = (2, 4).
        *   Artifact range: Rows 2-4, Cols 4-8.

    *   Artifact 2: Rows 20-22, Cols 1-11 (approx). Frame = A.
        *   Internal pixels: (20, 1) = B, (21, 6) = 

... [2101 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.09)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 908: "Three surveyors plant flags and a fence rises to enclose the ... [9 chars truncated]" k=2 alts: 0/0 e7639916

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 three azure (A) pixels on a black (.) background. These three points define the corners and edge midpoints of an axis-aligned rectangle. Each A pixel sits on a different edge of the bounding rectangle formed by the three points.

Do: 1. Identify the three azure (A) pixels and note their (row, column) coordinates. 2. Compute the bounding rectangle of these three points: top edge = minimum row, bottom edge = maximum row, left edge = minimum column, right edge = maximum column. 3. Draw the entire border (perimeter) of this bounding rectangle using blue (B) pixels. This means fill every cell along the top row, bottom row, left column, and right column of the rectangle with B. 4. Restore each of the three original azure (A) pixels to their original positions on the border, overwriting the blue at those locations. The interior of the rectangle and all cells outside the rectangle remain black.

Grid: The grid dimensions match the input exactly (no resizing). The background is black (.). The only non-background colors are azure (A) for the three anchor points and blue (B) for the rectangle border. The coordinate system is row-major with (0,0) at the top-left corner.

Figurative Descriptions (1 variants)

"Three surveyors plant flags and a fence rises to enclose their claim."

gemma-4-31b: k=2

See: Three azure surveyors stand alone in a dark, empty frontier. They have staked their flags at different edges of an invisible plot of land, each one marking a different side of the territory they intend to claim.

Do: The surveyors call for a fence. Blue timber rises from the earth, tracing the smallest rectangle that honors all three claims — running along every edge of the property boundary. Where a surveyor already stands, no fence post is needed; the surveyor herself serves as the corner post, her azure flag flying above the blue timberline. The land inside the fence and the wilderness beyond it remain untouched darkness.

Grid: The frontier keeps its original dimensions. The darkness is empty prairie. Azure flags mark the surveyors who called the fence into being. Blue timber forms the property line connecting them. Nothing grows inside the fence nor beyond it — only the boundary itself is built.

gemma-4-31b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (2666 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Azure (A)**: The "surveyors." These are the seed points that define the boundaries of the rectangle.
    *   **Blue (B)**: The "timber." This forms the perimeter of the smallest bounding box containing all Azure points.
    *   **Black (.)**: The "darkness/frontier." The background and the interior of the rectangle.

2.  **AFFORDANCES**:
    *   The Azure points act as anchors.
    *   The Blue points act as connectors, filling in the edges of the rectangle defined by the minimum and maximum x and y coordinates of the Azure points.

3.  **TRANSFORMATION RULE**:
    *   Find the coordinates $(r, c)$ of all Azure (A) points.
    *   Determine the bounding box:
        *   $r_{min} = \min(\text{rows of A})$
        *   $r_{max} = \max(\text{rows of A})$
        *   $c_{min} = \min(\text{cols of A})$
        *   $c_{max} = \max(\text{cols of A})$
    *   Draw the perimeter of this rectangle using Blue (B).
    *   **Constraint**: If a cell is already Azure (A), it remains Azure (A) and is not replaced by Blue (B).
    *   The interior of the rectangle and the exterior area remain Black (.).

### Applying the Rule to Test Input

**Test Input Coordinates (A):**
1.  Row 3, Col 3 (0-indexed: (3, 3))
2.  Row 5, Col 11 (0-indexed: (5, 11))
3.  Row 12, Col 8 (0-indexed: (12, 8))

**Bounding Box Calculation:**
*   $r_{min} = 3$
*   $r_{max} = 12$
*   $c_{min} = 3$
*   $c_{max} = 11$

**Perimeter Construction:**
*   **Top edge (Row 3):** From Col 3 to 11. (3,3) is A, (3,4) to (3,11) are B.
*   **Bottom edge (Row 12):** From Col 3 to 11. (12,3) to (12,7) are B, (12,8) is A, (12,9) to (12,11) are B.
*   **Left edge (Col 3):** From Row 3 to 12. (3,3) is A, (4,3) to (12,3) are B.
*   **Right edge (Col 11):** From Row 3 to 12. (3,11) is B, (4,11) is B, (5,11) is A, (6,11) to (12,11) are B.

**Final Grid Construction:**
*   Rows 0-2: All .
*   Row 3: . . . A B B B B B B B B .
*   Row 4: . . . B . . . . . . . B .
*   Row 5: . . . B . . . . . . . A .
*   Row 6: . . . B . . . . . . . B .
*   Row 7: . . . B . . . . . . . B .
*   Row 8: . . . B . . . . . . . B .
*   Row 9: . . . B . . . . . . . B .
*   Row 10: . . . B . . . . . . . B .
*   Row 11: . . . B . . . . . . . B .
*   Row 12: . . . B B B B B A B B B .
*   Row 13: All .

ANSWER:
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . A B B B B B B B B .
. . . B . . . . . . . B .
. . . B . . . . . . . A .
. . . B . . . . . . . B .
. . . B . . . . . . . B .
. . . B . . . . . . . B .
. . . B . . . . . . . B .
. . . B . . . . . . . B .
. . . B . . . . . . . B .
. . . B B B B B A B B B .
. . . . . . . . . . . . .

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.93)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 910: "A dance troupe passes choreography down the line at each reh ... [59 chars truncated]" k=1 alts: 9/15 e78887d1

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 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."

gemma-4-31b: k=1

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.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (3220 chars)

### Conceptual Digestion

**1. Identify the CAST:**
*   **Dancers:** The colored 3x3 blocks (R, G, B, X).
*   **Choreography:** The specific pattern of colored pixels within each 3x3 block.
*   **Stage:** The grid.
*   **Blackout Curtains:** The rows of black pixels (`.`) separating the rehearsal rounds.
*   **Rehearsal Rounds:** The vertical repetitions of the dancer lineup.

**2. Identify the AFFORDANCES:**
*   The grid is divided into 3x3 blocks separated by a single column of black pixels.
*   The blocks shift their internal patterns (choreography) from one round to the next.
*   The pattern shifts to the left (the dancer at index $i$ takes the pattern of the dancer at $i+1$).

**3. Identify the TRANSFORMATION RULE:**
*   **Input Analysis:** The input contains multiple "rehearsal rounds" (3x3 blocks separated by black rows).
*   **The Pattern Shift:** In each round, the patterns shift. The metaphor states: "each dancer has learned the moves of the neighbor to their right... the dancer on the far right loops back to mimic the one on the far left."
*   **The Final Step:** The "Opening Night" (output) requires taking the patterns from the **final rehearsal round** and shifting them one more time to the left.
*   **The Output Format:** A single 3-row grid containing the shifted patterns, maintaining the original colors of the dancers' positions but using the patterns of their right-hand neighbors.
*   **Wait, Correction on Color:** The metaphor says "each dancer steps forward wearing their own color but performing the choreography that belonged to the dancer one step to their right." This means the *shape* moves, but the *color* of the shape is determined by the dancer who now owns that shape.
*   **Refined Rule:** 
    1. Identify the 3x3 patterns in the last rehearsal round.
    2. Shift these patterns one position to the left (the pattern at index 0 moves to the last position, index 1 moves to 0, etc.).
    3. The color of the pattern in the output is the color of the dancer at that position in the original lineup.

### Applying the Rule to Test Input

**Step 1: Identify the last rehearsal round (bottom 3x3 blocks).**
Dancer 1 (R):
`R R .`
`. . R`
`R R .`

Dancer 2 (G):
`G . G`
`G . G`
`G . G`

Dancer 3 (B):
`. B .`
`B B B`
`. B .`

Dancer 4 (X):
`X X .`
`. X .`
`X X X`

**Step 2: Shift patterns one to the left.**
*   Position 1 (R) gets Pattern 2 (G):
    `G . G`
    `G . G`
    `G . G` $\rightarrow$ Change color to R:
    `R . R`
    `R . R`
    `R . R`

*   Position 2 (G) gets Pattern 3 (B):
    `. B .`
    `B B B`
    `. B .` $\rightarrow$ Change color to G:
    `. G .`
    `G G G`
    `. G .`

*   Position 3 (B) gets Pattern 4 (X):
    `X X .`
    `. X .`
    `X X X` $\rightarrow$ Change color to B:
    `B B .`
    `. B .`
    `B B B`

*   Position 4 (X) gets Pattern 1 (R):
    `R R .`
    `. . R`
    `R R .` $\rightarrow$ Change color to X:
    `X X .`
    `. . X`
    `X X .`

**Step 3: Assemble the final grid (with black columns between

... [220 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.64)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 914: "A hall of mirrors where one mirror has smudges — clean ... [43 chars truncated]" k=1 alts: 0/0 e84fef15

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 large grid divided into a 5×5 arrangement of identical 5×5 tiles, separated by green (G) lines. The green lines form a regular grid of separators: full rows of G and full columns of G every 6th position (every 5 content cells plus 1 separator). All tiles are copies of a single base pattern — except exactly one tile, which has been altered by replacing some of its non-azure (non-A) cells with azure (A).

Do: 1. Parse the green (G) separator rows and columns to extract the 5×5 arrangement of 5×5 tiles. 2. Determine the base tile: the tile pattern shared by the majority of tiles (all but one). 3. Find the single anomalous tile that differs from the base pattern. 4. Compare the anomalous tile to the base tile cell by cell. Every position where the base tile has a non-azure value but the anomalous tile has azure (A) is a 'erased' position. 5. Produce the output by copying the base tile, then replacing each erased position with blue (B).

Grid: The input grid is 29×29 (five 5×5 tiles separated by single-cell-wide green lines in both dimensions). The output grid is 5×5, matching the dimensions of a single tile. Azure (A) serves as the background/default color within tiles. Green (G) is used exclusively as a separator and does not appear in the output.

Figurative Descriptions (1 variants)

"A hall of mirrors where one mirror has smudges — clean the glass and mark where the smudges were."

gemma-4-31b: k=1

See: Imagine a grand hall tiled with identical mosaic panels, each separated by green grout lines. Every panel is a perfect copy of the master design — except one panel has been vandalized: someone has smeared azure paint over parts of the original pattern, erasing the colorful details beneath.

Do: Find the defaced panel among its identical siblings. Hold it up against any pristine copy and wherever the vandal's azure paint covers what should have been a colorful tile, mark that spot in blue — like placing a restoration flag where the damage occurred. The output is the master panel with blue flags showing every wound.

Grid: The hall is a 5×5 arrangement of mosaic panels, each 5 cells square, with green grout forming the borders between them. Azure is the background clay of each panel — the 'blank' space between decorative elements. The output is a single restored panel where blue marks reveal the vandal's handiwork.

gemma-4-31b — MARC valid, solved with 1 example

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Reasoning (2909 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Mosaic Panels**: 5x5 grids of cells.
    *   **Grout Lines**: Green (G) cells that separate the panels.
    *   **Master Design**: The pattern shared by the "pristine" panels.
    *   **Vandalized Panel**: The one panel that differs from the others.
    *   **Azure (A)**: The background color of the panels.
    *   **Colorful Tiles**: Any non-azure, non-green cells (e.g., R, Y, M, .).
    *   **Vandalism**: When a colorful tile in the master design is replaced by Azure (A) in the vandalized panel.
    *   **Restoration Flag (B)**: Blue cells used in the output to mark where a colorful tile was replaced by Azure.

2.  **AFFORDANCES**:
    *   The grid is a 5x5 arrangement of 5x5 panels.
    *   We can compare panels to find the one that is "missing" colors (replaced by Azure).
    *   The output is a single 5x5 grid representing the master design, but with Blue (B) replacing the colors that were erased in the vandalized panel.

3.  **TRANSFORMATION RULE**:
    *   Identify the master 5x5 pattern by looking at the majority of the panels.
    *   Identify the vandalized panel (the one where some colorful cells are now Azure).
    *   Compare the vandalized panel to the master panel.
    *   If the master panel has a color (not Azure) and the vandalized panel has Azure at that same coordinate, the output cell is Blue (B).
    *   Otherwise, the output cell is the color from the master panel.

### Applying the Rule to Test Input

1.  **Identify Master Panel**:
    Looking at the panels (separated by G):
    Row 0-4, Col 0-4: `R A R A A / A . . A M / A A A A A / A A Y A A / R A A A Y`
    Row 0-4, Col 6-10: `R A R A A / A . . A M / A A A A A / A A Y A A / R A A A Y`
    ...and so on.
    The master pattern is:
    R A R A A
    A . . A M
    A A A A A
    A A Y A A
    R A A A Y

2.  **Identify Vandalized Panel**:
    Check the panels for differences:
    Panel (0,0): Matches master.
    Panel (0,1): Matches master.
    Panel (1,3): Row 1 is `A A A A A` instead of `A . . A M`.
    Wait, let's check Panel (1,3) coordinates:
    Row 7 (index 6+1), Col 18-22 (index 6*3 to 6*3+4).
    Input Row 7: `A . . A M G A . . A M G A . . A M G A A A A A G A . . A M`
    The 4th panel in the 2nd row of panels is `A A A A A`.
    Comparing `A A A A A` (vandalized) to `A . . A M` (master):
    - Col 1: `A` vs `.` -> B
    - Col 2: `A` vs `.` -> B
    - Col 4: `A` vs `M` -> B

3.  **Construct Output**:
    Start with Master:
    R A R A A
    A . . A M
    A A A A A
    A A Y A A
    R A A A Y

    Apply restoration flags (B) where the vandalized panel had Azure instead of the master's color:
    Row 1, Col 1: `.` becomes `B`
    Row 1, Col 2: `.` becomes `B`
    Row 1, Col 4: `M` becomes `B`

    Result:
    R A R A A
    A B B A B
    A A A A A
    A A Y A A
    R A A A Y

ANSWER:
R A R A A
A B B A B
A A A A A
A A Y A A
R A A A Y

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.96)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 915: "A doctor diagnoses dark wounds on grey skin — their co ... [47 chars truncated]" k=2 alts: 0/0 e8593010

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 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."

gemma-4-31b: k=2

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.

gemma-4-31b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (3126 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Grey (X)**: Healthy skin. It remains unchanged.
    *   **Black (.)**: Wounds/Infections. These are the targets for transformation.
    *   **Clusters**: Groups of connected black cells (connected edge-to-edge/orthogonally).

2.  **AFFORDANCES**:
    *   Black cells can be grouped into clusters of size 1, 2, or 3.
    *   Each cluster is replaced by a specific color based on its size.

3.  **TRANSFORMATION RULE**:
    *   **Cluster Size 1** (lone pinprick) $\rightarrow$ **Green (G)**.
    *   **Cluster Size 2** (spread to one neighbor) $\rightarrow$ **Red (R)**.
    *   **Cluster Size 3** (deepest infection) $\rightarrow$ **Blue (B)**.
    *   **Grey (X)** $\rightarrow$ **Grey (X)**.

---

### Step-by-Step Application to Test Input

**Input Grid Analysis:**
Row 0: `. X X X X X . . X X` -> (0,0) is `.`, (0,6)(0,7) are `.`
Row 1: `X X X . X X . X . X` -> (1,3) is `.`, (1,6) is `.`, (1,8) is `.`
Row 2: `X X . X X X X X . X` -> (2,2) is `.`, (2,8) is `.`
Row 3: `X . . X X X X X X X` -> (3,1)(3,2) are `.`
Row 4: `. X X X X X . X X X` -> (4,0) is `.`, (4,6) is `.`
Row 5: `. X X . X X . X . .` -> (5,0) is `.`, (5,3) is `.`, (5,6) is `.`, (5,8)(5,9) are `.`
Row 6: `X X . X X X X X . X` -> (6,2) is `.`, (6,8) is `.`
Row 7: `X X . X X X X X X .` -> (7,2) is `.`, (7,9) is `.`
Row 8: `. . X X X X . X X X` -> (8,0)(8,1) are `.`, (8,6) is `.`
Row 9: `X X X X . X . . X .` -> (9,4) is `.`, (9,6)(9,7) are `.`, (9,9) is `.`

**Cluster Identification:**
1.  (0,0): Size 1 $\rightarrow$ **G**
2.  (0,6), (0,7), (1,6): Size 3 $\rightarrow$ **B**
3.  (1,3): Size 1 $\rightarrow$ **G**
4.  (1,8), (2,8): Size 2 $\rightarrow$ **R**
5.  (2,2), (3,2), (3,1): Size 3 $\rightarrow$ **B**
6.  (4,0), (5,0): Size 2 $\rightarrow$ **R**
7.  (4,6), (5,6): Size 2 $\rightarrow$ **R**
8.  (5,3): Size 1 $\rightarrow$ **G**
9.  (5,8), (5,9), (6,8): Size 3 $\rightarrow$ **B** (Wait, check (6,8) and (7,9) and (5,9). (5,8)-(5,9) and (5,9)-(6,9) is not possible as (6,9) is X. (5,8)-(5,9) and (5,8)-(6,8) is not possible. (5,9) is adjacent to (5,8) and (6,9). (6,8) is adjacent to (5,8) and (7,8). Let's re-examine.)
    *   (5,8), (5,9) are adjacent.
    *   (6,8) is adjacent to (5,8).
    *   Cluster: {(5,8), (5,9), (6,8)}. Size 3 $\rightarrow$ **B**.
10. (6,2), (7,2): Size 2 $\rightarrow$ **R**
11. (7,9), (8,9) - No, (8,9) is X. (7,9) is adjacent to (6,9)X and (8,9)X and (7,8)X. (7,9) is Size 1 $\rightarrow$ **G**.
12. (8,0), (8,1): Size 2 $\rightarrow$ **R**
13. (8,6), (9,6), (9,7): Size 3 $\rightarrow$ **B**
14. (9,4): Size 1 $\rightarrow$ **G**
15. (9,9): Size 1 $\rightarrow$ **G**

**Final Mapping:**
(0,0): G
(0,6): B, (0,7): B, (1,6): B
(1,3): G
(1,8): R, (2,8): R
(2,2): B, (3,1): B, (3,2): B
(4,0): R, (5,0): R
(4,6): R, (5,6): R
(5,3): G
(5,8): B, (5,9): B, (6,8): B
(6,2): R, (7,2): R
(7,9): G
(8,0): R, (8,1): R
(8,6): B, (9,6): B, (9,7): B
(9,4): G
(9,9): G

ANSWER:
G X X X X X B B X X
X X X G X X B X R X
X X

... [156 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.75)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 941: "A talent scout watches a parade from a balcony, then reports ... [32 chars truncated]" k=1 alts: 8/15 edcc2ff0

Training Examples

Example 1

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Output

Example 2

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Example 3

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Literal Description

See: The grid is divided into two regions by a solid horizontal row of a single color at row 7. Above that divider (rows 0–6) is a mostly black section with exactly three single-pixel colored indicators placed in column 0 at rows 1, 3, and 5. Below (rows 7–19) is a rectangular grid whose background color matches the divider row; scattered across this lower grid are small connected shapes in various colors, some matching the indicator colors and some not.

Do: 1. Identify the three indicator colors from column 0 at rows 1, 3, and 5 in the top section. These are the 'kept' colors. 2. Identify the background color of the lower grid (the color filling the solid divider at row 7). 3. In the lower grid (rows 7–19), find all connected components of each kept color (4-connected adjacency). Count how many distinct components exist for each kept color. 4. Update the top section: for each indicator at row r, extend that color rightward from column 0 so the total number of filled cells in that row equals the component count for that color. If the count is 0, clear the indicator entirely (replace with black). All other cells in the top section remain black. 5. In the lower grid, remove every shape whose color is NOT one of the three kept colors by replacing those cells with the background color. Shapes in kept colors remain unchanged.

Grid: The grid is always 10 columns wide and 20 rows tall. Row 7 is a solid horizontal divider whose color defines the background of the lower 13-row region (rows 7–19). The upper 7 rows (0–6) use black as background, with indicator pixels only at (row 1, col 0), (row 3, col 0), and (row 5, col 0). Odd rows in the top section hold indicators; even rows are entirely black.

Figurative Descriptions (16 variants)

"A talent scout watches a parade from a balcony, then reports how popular each act really is."

gemma-4-31b: k=1

See: A balcony overlooks a grand plaza. Three scouts sit stacked along the left railing, each wearing a distinctive color sash. Below, a bustling plaza paved in a single uniform color hosts a fair — small booths and troupes scattered about, each group wearing matching costumes of various colors. Some troupe colors match a scout's sash; others are uninvited performers who snuck in.

Do: Each scout leans over the railing and counts how many separate troupes in the plaza share their sash color — not the number of performers, but the number of distinct groups. The scout then unfurls a banner along the balcony railing, stretching it one tile for each troupe counted. A scout who finds no matching troupes pulls their banner down entirely and disappears. Meanwhile, down in the plaza, security sweeps through and escorts out every uninvited troupe — any group whose costume color doesn't match any scout's sash is absorbed back into the plaza floor, leaving only the scouted acts standing.

Grid: The balcony fills the upper floors (the top seven rows), a quiet black space where scouts sit only on the odd-numbered landings along the leftmost pillar. A solid colored cornice separates balcony from plaza. The plaza stretches below — thirteen rows paved in the cornice's color, with small clustered acts dotted throughout.

gemma-4-31b — MARC valid, solved with 1 example

Input

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Prediction

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Reasoning (3767 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Scouts**: The colored pixels located at (1,0), (3,0), and (5,0) (0-indexed).
    *   **Balcony**: The top 7 rows (0-6).
    *   **Cornice/Plaza Floor**: The color of the row at index 7 (and the subsequent 13 rows).
    *   **Troupes**: Contiguous blocks of the same color (excluding the plaza floor color) within the plaza (rows 8-20).

2.  **AFFORDANCES**:
    *   **Scouts** can "count" troupes of their own color in the plaza.
    *   **Banners** are created by extending the scout's color horizontally to the right in the balcony.
    *   **Security** removes any troupe whose color does not match any of the three scouts.

3.  **TRANSFORMATION RULE**:
    *   **Step 1 (Counting)**: For each scout at (1,0), (3,0), and (5,0), identify its color. Count how many distinct contiguous groups (troupes) of that same color exist in the plaza (rows 8-20).
    *   **Step 2 (Banners)**: In the balcony, replace the scout's row with a line of that scout's color starting from column 0, with a length equal to the count of troupes found. If the count is 0, the scout (and any banner) disappears (becomes black '.').
    *   **Step 3 (Security Sweep)**: In the plaza, any troupe whose color is not one of the three scout colors is changed to the plaza floor color.

### Applying the Rule to Test Input

**1. Identify Scouts and Plaza Floor:**
*   Scout 1 (1,0): **R** (Red)
*   Scout 2 (3,0): **A** (Azure)
*   Scout 3 (5,0): **G** (Green)
*   Plaza Floor Color: **Y** (Yellow)

**2. Count Troupes in Plaza (Rows 8-20):**
*   **Red (R)**:
    1. (8, 1-3)
    2. (11, 6-7) and (12, 6-7) -> One group
    3. (13, 8) and (14, 8) and (15, 8) -> One group
    4. (18, 1-2)
    5. (19, 6-7)
    *   Total Red Troupes = **5**
*   **Azure (A)**:
    *   None found in the plaza.
    *   Total Azure Troupes = **0**
*   **Green (G)**:
    1. (8, 6-7)
    2. (12, 1-2) and (13, 1-2) -> One group
    *   Total Green Troupes = **2**

**3. Determine Banners:**
*   Red Scout (Row 1): Count 5 $\rightarrow$ `R R R R R . . . . .`
*   Azure Scout (Row 3): Count 0 $\rightarrow$ `. . . . . . . . . .`
*   Green Scout (Row 5): Count 2 $\rightarrow$ `G G . . . . . . . .`

**4. Security Sweep (Plaza):**
*   Keep: Red (R), Azure (A), Green (G).
*   Remove: Orange (O), Grey (X).
*   (11, 1-2) Orange $\rightarrow$ Yellow
*   (14, 4-5) and (15, 4-5) Grey $\rightarrow$ Yellow

### Final Grid Construction

Rows 0-6:
0: `. . . . . . . . . .`
1: `R R R R R . . . . .`
2: `. . . . . . . . . .`
3: `. . . . . . . . . .`
4: `. . . . . . . . . .`
5: `G G . . . . . . . .`
6: `. . . . . . . . . .`

Rows 7-20:
7: `Y Y Y Y Y Y Y Y Y Y`
8: `Y R R R Y Y G G Y Y`
9: `Y Y Y Y Y Y Y Y Y Y`
10: `Y Y Y Y Y Y Y Y Y Y` (O replaced by Y)
11: `Y Y Y Y Y Y R R Y Y`
12: `Y G G Y Y Y R R Y Y`
13: `Y G G Y Y Y Y Y R Y`
14: `Y Y Y Y Y Y Y Y R Y` (X replaced by Y)
15: `Y Y Y Y Y Y Y Y R Y` (X replaced by Y)
16: `Y Y Y Y Y Y Y Y Y Y`
17: `Y R R Y Y Y Y Y Y Y`
18: `Y R R Y Y Y R R Y Y`


... [776 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.90)

Prediction

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=1 alts: 6/15 f9012d9b

Training Examples

Example 1

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Example 2

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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."

gemma-4-31b: k=1

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.

gemma-4-31b — MARC valid, solved with 1 example

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Prediction

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Expected

Reasoning (5380 chars)

**Conceptual Digestion**

1.  **CAST:**
    *   **The Tapestry:** The overall grid containing colored cells.
    *   **The Refrain (Motif):** A small rectangular block of colors that repeats infinitely in both horizontal and vertical directions to create the pattern.
    *   **The Moth-eaten Hole:** A rectangular area of black cells (`.`) that represents missing data.
    *   **The Repair Patch:** The output grid, which consists of the colors that should replace the black cells based on the repeating motif.

2.  **AFFORDANCES:**
    *   The existing colored cells provide the key to identifying the period (width and height) of the repeating motif.
    *   The position of the black cells relative to the rest of the grid determines which specific parts of the motif must be extracted for the output.

3.  **TRANSFORMATION RULE:**
    *   Analyze the provided colored cells to find the smallest repeating unit (the motif) that tiles the grid.
    *   Identify the coordinates of the black cells (the hole).
    *   Determine the color that would occupy each black cell's position if the motif were tiled across the entire grid.
    *   The output is a grid of the same dimensions as the hole, containing these predicted colors.

**Applying the Rule to Test Input**

1.  **Analyze the Input Grid:**
    Row 0: A B A A . . .
    Row 1: B A A B . . .
    Row 2: A A B A . . .
    Row 3: A B A A B A A
    Row 4: B A A B A A B
    Row 5: A A B A A B A
    Row 6: A B A A B A A

2.  **Find the Motif:**
    Looking at the rows:
    Row 3: `A B A A B A A` (Wait, let's check the sequence: A, B, A, A, B, A, A...)
    Row 4: `B A A B A A B`
    Row 5: `A A B A A B A`
    Row 6: `A B A A B A A`

    Let's check the horizontal period:
    Row 3: `A B A A` | `B A A` ... the sequence is `A B A A` repeating? No.
    Let's look at the sequence: `A B A A` (4 chars).
    If the motif width is 4:
    Row 3: `A B A A` | `B A A` (The 5th char is B, which matches the 2nd char. The 6th is A, which matches the 3rd. The 7th is A, which matches the 4th).
    Wait, if the motif is `A B A A`, the sequence is:
    Pos 0: A
    Pos 1: B
    Pos 2: A
    Pos 3: A
    Pos 4: A (should be) -> But it is B.
    Let's re-examine: `A B A A B A A`
    The sequence is `A B A A`? No.
    Look at the sequence: `A B A A` ... `B A A` ...
    Actually, look at the sequence: `A B A A` is not it.
    Look at: `A B A A` (4) vs `B A A B` (4).
    Let's look at the columns:
    Col 0: A B A A B A A
    Col 1: B A A B A A B
    Col 2: A A B A A B A
    Col 3: A B A A B A A
    The columns are identical to the rows.
    The sequence is: `A, B, A, A, B, A, A...`
    Wait, the sequence is `A, B, A, A`? No.
    Let's look at the indices:
    0: A
    1: B
    2: A
    3: A
    4: B
    5: A
    6: A
    The pattern is `A B A A`? No, that's 4.
    The pattern is `B A A` starting from index 1.
    Index 0: A
    Index 1: B
    Index 2: A
    Index 3: A
    Index 4: B
    Index 5: A
    Index 6: A
    The repeating un

... [2410 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.44)

Prediction

Expected

Figurative + 1 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: 6/15 fbf15a0b

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 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."

gemma-4-31b: 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.

gemma-4-31b — MARC valid, solved with 3 examples

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Prediction

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Expected

Reasoning (2274 chars)

**Conceptual Digestion**

1.  **Identify the CAST:**
    *   **Azure (A):** The background canvas.
    *   **Grey (X):** The "pins" that mark the cutting line.
    *   **Other Colors (B, O, G, W):** The "tapestry patterns" that are part of the image.

2.  **Identify the AFFORDANCES:**
    *   The grey pins (X) always appear in pairs.
    *   If the pins are in the same column (different rows), they define a horizontal cut.
    *   If the pins are in the same row (different columns), they define a vertical cut.
    *   The cut divides the grid exactly in half.
    *   The half containing the pins is kept; the other half is discarded.
    *   The pins themselves are replaced with the background color (Azure - A).

3.  **Identify the TRANSFORMATION RULE:**
    *   Locate the two grey pins (X).
    *   Determine the axis of the cut:
        *   If pins are at `(r1, c)` and `(r2, c)`, the cut is horizontal. The grid is split into top and bottom halves.
        *   If pins are at `(r, c1)` and `(r, c2)`, the cut is vertical. The grid is split into left and right halves.
    *   Keep the half that contains the pins.
    *   Replace all `X` values in the kept half with `A`.

**Applying the rule to the Test Input:**
*   **Input Grid Size:** 4 rows x 8 columns.
*   **Pin Locations:** `(0, 5)` and `(0, 7)`.
*   **Analysis:** Both pins are in row 0. This indicates a vertical cut.
*   **Cut Line:** The grid is 8 columns wide, so the cut is at column 4.
*   **Kept Half:** The pins are in columns 5 and 7 (the right half). Therefore, we keep the right half (columns 4 through 7) and discard the left half (columns 0 through 3).
*   **Cleanup:** Replace the pins at `(0, 5)` and `(0, 7)` with `A`.

**Processing the right half (Columns 4-7):**
Row 0: `A X A X` $\rightarrow$ `A A A A`
Row 1: `A A A A` $\rightarrow$ `A A A A`
Row 2: `W A W A` $\rightarrow$ `W A W A` (Wait, let's re-check the input)

**Test Input Grid:**
Row 0: `A W A W A X A X` (Cols 0-7)
Row 1: `A A A A A A A A`
Row 2: `A W A W A W A W`
Row 3: `A A A A A A A A`

**Right Half (Cols 4-7):**
Row 0: `A X A X` $\rightarrow$ `A A A A`
Row 1: `A A A A` $\rightarrow$ `A A A A`
Row 2: `A W A W` $\rightarrow$ `A W A W`
Row 3: `A A A A` $\rightarrow$ `A A A A`

ANSWER:
A A A A
A A A A
A W A W
A A A A

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.70)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 987: "A castle's walls absorb the color of the invading army's ban ... [5 chars truncated]" k=1 alts: 13/15 fcb5c309

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 two hollow rectangles outlined in the same color (e.g., blue, red, or green), one larger and one smaller. Their borders are drawn as single-cell-thick lines of that color. Scattered across the grid, both outside and inside the rectangles, are dots of a second, different color. The rest of the grid is black (background). The interior dots inside the larger rectangle occupy specific positions within its interior.

Do: 1. Identify the two hollow rectangles in the grid. They share the same border color. One is larger than the other. 2. Identify the second color — the color of the scattered dots found outside the rectangles. 3. Extract the larger rectangle (including its border and interior). 4. Replace every cell that uses the rectangle's border color with the scattered-dot color. Interior cells that are black remain black; interior cells that already contain the scattered-dot color remain that color. 5. Output the resulting rectangle as the answer grid.

Grid: The output grid has the same dimensions as the larger rectangle found in the input (height and width matching its bounding box, inclusive of borders). The border of the output is entirely the scattered-dot color. Interior cells are either black (.) or the scattered-dot color, preserving the positions of any dots that appeared inside the larger rectangle in the input.

Figurative Descriptions (16 variants)

"A castle's walls absorb the color of the invading army's banners."

gemma-4-31b: k=1

See: Two fortresses stand on a dark battlefield, their walls built from the same stone color. One fortress is grand, the other modest. Scattered across the battlefield like campfires are sparks of a rival color — an invading force that has spread its banners everywhere, even slipping agents inside the fortress walls.

Do: The invaders conquer the larger fortress. Their banners replace every stone in its walls, claiming it entirely. The spies already inside hold their positions. Empty rooms remain empty — the conquest changes the flag, not the furniture. The smaller fortress is forgotten, lost to history.

Grid: The conquered fortress stands alone as the output — same shape, same size, but now every wall stone flies the invader's color. Inside, rooms that were empty stay dark, and any invader agents who had already infiltrated remain where they stood. The fortress's silhouette is unchanged, but its allegiance has shifted completely.

gemma-4-31b — MARC valid, solved with 1 example

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Prediction

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Reasoning (2776 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Fortresses**: Rectangular outlines (walls) made of a single color. In the test input, there are two blue (B) fortresses.
    *   **Invaders**: A different color scattered across the grid. In the test input, the invader color is azure (A).
    *   **Empty Rooms**: Black cells (.) inside the fortress walls.
    *   **Spies**: Invader-colored cells (A) already located inside the fortress walls.

2.  **AFFORDANCES**:
    *   The larger fortress is the target of the transformation.
    *   The smaller fortress is discarded.
    *   The walls of the larger fortress change from their original color (B) to the invader color (A).
    *   The interior of the larger fortress remains unchanged (empty rooms stay black, spies stay azure).

3.  **TRANSFORMATION RULE**:
    *   Identify all "fortresses" (closed rectangular loops of the same color).
    *   Compare their sizes (area/perimeter).
    *   Select the larger fortress.
    *   Crop the grid to the dimensions of this larger fortress.
    *   Replace all wall cells (B) with the invader color (A).
    *   Keep all interior cells as they were ('.' remains '.', 'A' remains 'A').

### Applying the Rule to Test Input

1.  **Identify Fortresses**:
    *   Fortress 1: Top-left/center. Walls at rows 1-8, cols 4-11.
        *   Top wall: row 1, cols 4-11 (8 cells)
        *   Bottom wall: row 8, cols 4-11 (8 cells)
        *   Left wall: rows 1-8, col 4 (8 cells)
        *   Right wall: rows 1-8, col 11 (8 cells)
        *   Dimensions: 8 rows x 8 columns.
    *   Fortress 2: Bottom-right. Walls at rows 11-15, cols 10-15.
        *   Top wall: row 11, cols 10-15 (6 cells)
        *   Bottom wall: row 15, cols 10-15 (6 cells)
        *   Left wall: rows 11-15, col 10 (5 cells)
        *   Right wall: rows 11-15, col 15 (5 cells)
        *   Dimensions: 5 rows x 6 columns.

2.  **Select Larger Fortress**:
    *   Fortress 1 (8x8) is larger than Fortress 2 (5x6).

3.  **Transform Fortress 1**:
    *   Original walls (B) $\rightarrow$ Azure (A).
    *   Interior cells:
        *   Row 2: `. A . A . .` (cols 5-10)
        *   Row 3: `. . . . . .` (cols 5-10)
        *   Row 4: `. . . . . .` (cols 5-10)
        *   Row 5: `. . . . . .` (cols 5-10)
        *   Row 6: `. A . . . .` (cols 5-10)
        *   Row 7: `. . . . A .` (cols 5-10)

4.  **Construct Output Grid (8x8)**:
    *   Row 1: A A A A A A A A
    *   Row 2: A . A . A . . A
    *   Row 3: A . . . . . . A
    *   Row 4: A . . . . . . A
    *   Row 5: A . . . . . . A
    *   Row 6: A . A . . . . A
    *   Row 7: A . . . . A . A
    *   Row 8: A A A A A A A A

ANSWER:
A A A A A A A A
A . A . A . . A
A . . . . . . A
A . . . . . . A
A . . . . . . A
A . A . . . . A
A . . . . A . A
A A A A A A A A

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.94)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 995: "A shooting star streaks across the night sky, its colored fr ... [27 chars truncated]" k=5 alts: 6/15 feca6190

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 single row of 5 cells. Some cells are black (background) and some are non-black (colored). The non-black cells form a pattern embedded within the row, with black cells acting as spacers between or around them.

Do: 1. Count the number of non-black cells in the input row. Call this number N. 2. Create a square output grid of size (5×N) by (5×N), filled entirely with black cells. 3. Place the input row as the bottom row of the output grid, left-aligned (occupying the first 5 columns, with the remaining columns filled with black). 4. For each row above the bottom, shift the entire 5-cell input pattern one column to the right compared to the row below it. Cells that shift beyond the right edge of the output grid are discarded. Cells vacated on the left become black. 5. Continue this diagonal shifting upward until the top row, where the pattern has been shifted right by (5×N − 1) positions. Only the non-black cells that still fall within the grid bounds are drawn; all other cells remain black.

Grid: The output grid is always square. Its side length equals 5 times the number of non-black cells in the input row (e.g., 2 non-black cells → 10×10, 4 non-black cells → 20×20). The background color is black. The input's 5-cell pattern traces a diagonal stripe from the bottom-left area to the top-right corner, with each row offset one column to the right from the row below.

Figurative Descriptions (16 variants)

"A shooting star streaks across the night sky, its colored fragments trailing behind it."

gemma-4-31b: k=5

See: A handful of colored sparks sit loaded in a launch rail at the bottom of a dark night sky. The black cells are empty sky; the colored cells are the glowing fragments of a firework about to be launched diagonally upward.

Do: Light the fuse. The colored sparks launch from the bottom-left and streak toward the upper-right corner, leaving a diagonal trail across the darkness. Each moment the cluster of sparks drifts one step higher and one step to the right, painting a luminous streak across the sky. The brighter the firework — the more colored sparks it carries — the bigger the sky it needs to cross.

Grid: The night sky is a square canvas whose size grows with the brilliance of the firework — more sparks demand a grander stage. The streak runs from the bottom-left corner to the upper-right, a single glowing diagonal ribbon of color against a field of pure darkness.

gemma-4-31b — MARC valid, solved with 5 examples

Input

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Prediction

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Expected

Reasoning (5064 chars)

### Conceptual Digestion

1.  **CAST**:
    *   **Input Grid**: A single row of cells containing colored "sparks" (non-black cells) and empty space (black cells `.`).
    *   **Output Grid**: A square grid representing the "night sky."
    *   **Colored Cells**: The "firework" fragments that leave a trail.

2.  **AFFORDANCES**:
    *   The input row acts as a pattern that is repeated diagonally.
    *   The number of colored sparks determines the size of the output grid.
    *   The pattern shifts one cell up and one cell right in each subsequent row (from bottom to top).

3.  **TRANSFORMATION RULE**:
    *   **Grid Size**: Let $N$ be the number of colored cells in the input row. The output grid is a square of size $S \times S$. Looking at the examples:
        *   Ex 1: 3 colors (W, A, Y) $\rightarrow 15 \times 15$ grid.
        *   Ex 2: 1 color (R) $\rightarrow 5 \times 5$ grid.
        *   Ex 3: 3 colors (Y, M, A) $\rightarrow 15 \times 15$ grid.
        *   Ex 4: 1 color (Y) $\rightarrow 5 \times 5$ grid.
        *   Ex 5: 2 colors (B, O) $\rightarrow 10 \times 10$ grid.
        *   Rule: $S = N \times 5$.
    *   **Pattern Placement**: The input row is placed at the bottom row of the output grid.
    *   **Diagonal Streak**: For every row moving upwards, the input pattern shifts one position to the right.
    *   **Wait, let's refine the shift**:
        *   Bottom row (Row $S-1$): Input pattern as is.
        *   Row $S-2$: Input pattern shifted right by 1.
        *   Row $S-3$: Input pattern shifted right by 2.
        *   ...
        *   Top row (Row 0): Input pattern shifted right by $S-1$.
    *   **Wait, let's re-examine Example 1**:
        Input: `. W . A Y` (Length 5). Colors: W, A, Y (3 colors). Output size: $15 \times 15$.
        Bottom row: `. W . A Y . . . . . . . . . .` (Wait, the example shows `. W . A Y` at the start of the bottom row).
        Let's look closer at Example 1 output:
        Row 14 (bottom): `. W . A Y . . . . . . . . . .`
        Row 13: `. . W . A Y . . . . . . . . .`
        Row 12: `. . . W . A Y . . . . . . . .`
        This is a diagonal shift. The input row is treated as a sequence of length 5, and it is shifted right by 1 for each row we go up.

### Applying to Test Input
Input: `. M O A W`
1.  **Count colors**: M, O, A, W (4 colors).
2.  **Grid Size**: $4 \times 5 = 20$. The output grid is $20 \times 20$.
3.  **Pattern**: `. M O A W`
4.  **Construction**:
    *   Row 19 (bottom): `. M O A W . . . . . . . . . . . . . . .`
    *   Row 18: `. . M O A W . . . . . . . . . . . . . .`
    *   Row 17: `. . . M O A W . . . . . . . . . . . . .`
    *   ...
    *   Row 0 (top): `. . . . . . . . . . . . . . . . . M O A W` (Wait, the shift is 19, so the pattern starts at index 19? No, the pattern is 5 wide. If it shifts 19 times, the first char `.` is at index 19, and the rest are off-grid).
    *   Let's re-verify the shift:
        Example 1: $S=15$. Row 14: shift 0. Row 0: shift 14.
        Input `. W . A Y`

... [2064 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.47)

Prediction

Expected

Figurative + 5 ex PASS (acc: 1.00)

Prediction

Expected

MARC2 Puzzle Inspector March 26, 2026

▶ Task 14: "Each star casts a shadow of everything it is not." k=1 alts: 0/0 0692e18c

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=3 alts: 11/15 0f63c0b9

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 90: "A compass rose unfurls its cardinal and diagonal beams from ... [64 chars truncated]" k=1 alts: 0/0 1d398264

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 100: "Finding the one bird that stayed with its flock while all ot ... [26 chars truncated]" k=1 alts: 3/15 1f85a75f

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 108: "A painter's palette holds swatches above a workbench, and sc ... [62 chars truncated]" k=1 alts: 0/0 20fb2937

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 114: "Green footsteps leave echoes that scatter like reflections i ... [20 chars truncated]" k=3 alts: 0/0 22233c11

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 142: "A stained-glass window template is filled with light filtere ... [31 chars truncated]" k=1 alts: 0/0 278e5215

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 151: "Lightning rods on a rooftop attract bolts from storms on the ... [9 chars truncated]" k=2 alts: 9/15 29700607

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 181: "A stained-glass window reveals the hidden garden beneath the ... [7 chars truncated]" k=2 alts: 0/0 32597951

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 184: "A river runs through a canyon, and the colored rock strata f ... [56 chars truncated]" k=1 alts: 0/0 332202d5

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 202: "A scale weighs azure ice against red fire, and the balance t ... [16 chars truncated]" k=1 alts: 0/0 37ce87bb

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 206: "A gemstone is cut open, and its internal layers spill out li ... [25 chars truncated]" k=2 alts: 0/0 3979b1a8

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 227: "Russian nesting dolls carved from colored sticks" k=1 alts: 3/15 3ee1011a

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 245: "A book falls open and its pages splay apart from the spine." k=2 alts: 8/15 4364c1c4