MARC2 Puzzle Inspector

▶ Task 69: "Two teams combine their footprints to map everywhere anyone ... [10 chars truncated]" k=3 alts: 0/0 195ba7dc

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

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

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

Figurative Descriptions (1 variants)

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

qwen3.5-122b: k=3

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

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

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

qwen3.5-122b — MARC valid, solved with 3 examples

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Prediction

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Reasoning (9196 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A red curtain hangs down the center of a stage.
*   **Elements:**
    *   Red curtain: Separates two sides.
    *   Orange footprints: Mark where dancers stepped.
    *   Black tiles: Untouched floor.
*   **Action:** Raise the curtain.
*   **Result:** The two halves overlay into a single floor plan.
*   **Logic:**
    *   "Wherever either troupe — or both — left an orange footprint, the tile glows blue with the memory of movement." -> If a cell is Orange on the left OR Orange on the right, it becomes Blue.
    *   "Only tiles that neither troupe ever touched remain dark and silent." -> If a cell is Black on the left AND Black on the right, it remains Black (or becomes Black).
    *   "The stage is split evenly by the curtain." -> The input grid has a central column of Red (R) acting as the curtain. The left side and right side are the two troupes.
    *   "Once it lifts, the two halves overlay into a single floor plan." -> The output grid should be the size of one half (excluding the curtain). The transformation is an OR operation between the left half and the right half.
    *   Input colors: Orange (O), Black (.), Red (R).
    *   Output colors: Blue (B), Black (.).

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input dimensions: 5 rows, 13 columns.
    *   Center column (index 6, 0-indexed) is 'R'.
    *   Left side: Columns 0-5 (6 columns).
    *   Right side: Columns 7-12 (6 columns).
    *   Output dimensions: 5 rows, 6 columns.
    *   Logic check:
        *   Row 0: Left `O . O O . O`, Right `O O . . . .`
            *   Col 0: O | O -> B
            *   Col 1: . | O -> B
            *   Col 2: O | . -> B
            *   Col 3: O | . -> B
            *   Col 4: . | . -> .
            *   Col 5: O | . -> B
            *   Result: `B B B B . B`. Matches output.
        *   Row 1: Left `O . . O . .`, Right `. . . O . .`
            *   Col 0: O | . -> B
            *   Col 1: . | . -> .
            *   Col 2: . | . -> .
            *   Col 3: O | O -> B
            *   Col 4: . | . -> .
            *   Col 5: . | . -> .
            *   Result: `B . . B . .`. Matches output.
    *   Transformation Rule: Split grid at the central 'R' column. Compare Left[i][j] and Right[i][j]. If either is 'O', Output[i][j] = 'B'. Else Output[i][j] = '.'.

*   **Example 2:**
    *   Input dimensions: 5 rows, 13 columns.
    *   Center column is 'R'.
    *   Left side: 6 cols. Right side: 6 cols.
    *   Output dimensions: 5 rows, 6 columns.
    *   Logic check:
        *   Row 0: Left `. O O O . O`, Right `O O . O . O`
            *   0: . | O -> B
            *   1: O | O -> B
            *   2: O | . -> B
            *   3: O | O -> B
            *   4: . | . -> .
            *   5: O | O -&g

... [6490 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.12)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 82: "Two monarchs divide a kingdom, each stamping their seal upon ... [22 chars truncated]" k=2 alts: 0/0 1bfc4729

Training Examples

Example 1

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Example 2

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Literal Description

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

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

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

Figurative Descriptions (1 variants)

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

qwen3.5-122b: k=2

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

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

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

qwen3.5-122b — MARC valid, solved with 2 examples

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Reasoning (11346 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Setting:** A 10x10 grid of darkness (black dots `.`).
*   **Elements:** Two "monarchs" represented by single colored banners (pixels) in the input grid. One is in the "northern provinces" (top half), one in the "southern territories" (bottom half).
*   **Action:** Each monarch claims their half and builds fortress walls in their color.
*   **Northern Ruler's Style:** "Crown-like fortification — solid battlements at the top, open corridors, then another solid wall, trailing down to simple flanking towers."
    *   Looking at Example 1 (Blue `B` in top half):
        *   Row 0: `B B B B B B B B B B` (Solid top)
        *   Row 1: `B . . . . . . . . B` (Walls on sides)
        *   Row 2: `B B B B B B B B B B` (Solid middle)
        *   Row 3: `B . . . . . . . . B` (Walls on sides)
        *   Row 4: `B . . . . . . . . B` (Walls on sides)
        *   Wait, let's look closer at the split.
        *   The grid is 10x10.
        *   Example 1 Input: `B` at (2, 6) (0-indexed row, col). `Y` at (7, 5).
        *   Example 1 Output:
            *   Rows 0-4 seem to be Blue `B`.
            *   Rows 5-9 seem to be Yellow `Y`.
            *   Let's check the pattern for Blue (North):
                *   Row 0: `B B B B B B B B B B`
                *   Row 1: `B . . . . . . . . B`
                *   Row 2: `B B B B B B B B B B`
                *   Row 3: `B . . . . . . . . B`
                *   Row 4: `B . . . . . . . . B`
            *   Let's check the pattern for Yellow (South):
                *   Row 5: `Y . . . . . . . . Y`
                *   Row 6: `Y . . . . . . . . Y`
                *   Row 7: `Y Y Y Y Y Y Y Y Y Y`
                *   Row 8: `Y . . . . . . . . Y`
                *   Row 9: `Y Y Y Y Y Y Y Y Y Y`
    *   Wait, the description says "The kingdom is a 10x10 realm... It splits into two equal fiefdoms — north and south."
    *   Usually, a 10x10 split means rows 0-4 are North and rows 5-9 are South.
    *   Let's verify the split point.
    *   Example 1: `B` is at row 2. `Y` is at row 7.
    *   Output Rows 0-4 are Blue. Output Rows 5-9 are Yellow.
    *   So the split is indeed horizontal at the middle (Row 5 starts the South half).
    *   Northern Pattern (Rows 0-4):
        *   Row 0: Full line of color.
        *   Row 1: Color at edges (col 0, col 9).
        *   Row 2: Full line of color.
        *   Row 3: Color at edges.
        *   Row 4: Color at edges.
        *   Wait, looking at Example 1 Output again:
            *   R0: `B B B B B B B B B B`
            *   R1: `B . . . . . . . . B`
            *   R2: `B B B B B B B B B B`
            *   R3: `B . . . . . . . . B`
            *   R4: `B . . . . . . . . B`
        *   This matches "solid battlements at the top (R0), open corridors (R1), then another solid wall (R2), trailing down to simple flank

... [8364 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.48)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 136: "Musical chairs at a costume party — everyone moves one ... [43 chars truncated]" k=1 alts: 1/15 2601afb7

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 a single non-orange color occupy every other column (odd-indexed columns: 1, 3, 5, 7, 9, …). Each bar is anchored to the bottom row and extends upward for some height. Different bars have different colors and different heights. Even-indexed columns (0, 2, 4, …) are entirely orange and serve as separators.

Do: 1. Identify all vertical bars on odd-indexed columns. For each bar, record its color and its height (number of consecutive non-orange cells from the bottom up). 2. List the bars in order from left to right. 3. Rotate the sequence of colors one position to the RIGHT (the rightmost bar's color wraps around to become the leftmost bar's color). 4. Simultaneously rotate the sequence of heights one position to the LEFT (the leftmost bar's height wraps around to become the rightmost bar's height). 5. Redraw the grid: assign each bar position its new color and new height, filling from the bottom up, with all remaining cells orange.

Grid: The grid dimensions match the input exactly (same number of rows and columns). The background color is orange (O). Bars exist only on odd-indexed columns (1, 3, 5, …), and even-indexed columns remain entirely orange. Each bar is a contiguous vertical stripe of one color anchored to the bottom edge.

Figurative Descriptions (16 variants)

"Musical chairs at a costume party — everyone moves one seat right but leaves their shadow behind."

qwen3.5-122b: k=1

See: Against a sunset-orange ballroom floor, costumed dancers stand in evenly spaced lanes, each wearing a single vivid color. Some dancers are tall, some short — their heights tell you how long they've been dancing. They stand rooted to the floor's edge, stretching upward like flames of different lengths, separated by empty aisles of orange light.

Do: The music stops and the dancers play a strange double game. Each dancer strips off their costume and tosses it one partner to the right — the dancer at the far end throws theirs all the way to the front of the line, like a boomerang. But their shadows — the silhouettes they cast on the wall — slide the opposite way, each shadow stretching to fill the space one partner to the left, with the frontmost shadow wrapping to the back. When the music resumes, each lane now wears a borrowed costume at a borrowed height: someone else's color, someone else's stature.

Grid: The ballroom keeps its exact dimensions. The orange floor fills every even lane and all the empty air above the dancers. The dancers only ever stand in the odd lanes, rooted to the bottom edge, rising upward in solid columns of color. After the swap, every lane still has exactly one costumed figure — but the colors and heights have been reshuffled as if the party spun like a carousel.

qwen3.5-122b — MARC valid, solved with 1 example

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Prediction

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Reasoning (9561 chars)

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

**1. Analyze the Metaphorical Description:**

*   **Scene:** A ballroom floor (orange background).
*   **Elements:**
    *   "Costumed dancers": These are colored pixels standing in "lanes".
    *   "Lanes": The description says "evenly spaced lanes". Looking at the examples, the grid seems to be composed of columns.
    *   "Heights": The dancers have different heights (number of pixels in a column).
    *   "Rooted to the floor's edge": They stand at the bottom.
    *   "Empty aisles of orange light": The background is Orange (O).
    *   "Odd lanes": Dancers stand in odd lanes (1st, 3rd, 5th... if 1-indexed, or 0, 2, 4... if 0-indexed). Let's check the examples.
    *   "Even lanes": Filled with orange floor.
*   **Transformation:**
    *   "Music stops... strange double game."
    *   "Costume swap": Each dancer strips off their costume and tosses it one partner to the right. The dancer at the far end throws theirs to the front (wrap around).
        *   This implies the *color* of the column moves to the right.
    *   "Shadows slide opposite way": Shadows slide one partner to the left. The frontmost shadow wraps to the back.
        *   This implies the *height* (or the shape of the column) moves to the left.
    *   "Result": Each lane has a borrowed costume (color) and a borrowed height (stature).
    *   "Orange floor fills every even lane and all the empty air above the dancers."
    *   "Dancers only ever stand in the odd lanes".

**2. Analyze the Training Examples:**

**Example 1:**
Input Grid (9x9):
Row 0: O O O O O O O O O
Row 1: O O O O O M O O O
Row 2: O O O O O M O O O
Row 3: O O O O O M O O O
Row 4: O O O O O M O O O
Row 5: O O O O O M O O O
Row 6: O O O A O M O B O
Row 7: O W O A O M O B O
Row 8: O W O A O M O B O

Let's look at the columns (0-indexed).
Col 0: All O.
Col 1: O, O, O, O, O, O, O, W, W. (Height 2, Color W)
Col 2: All O.
Col 3: O, O, O, O, O, O, A, A, A. (Height 3, Color A)
Col 4: All O.
Col 5: M, M, M, M, M, M, M, M, M. (Height 9, Color M)
Col 6: All O.
Col 7: O, O, O, O, O, O, B, B, B. (Height 3, Color B)
Col 8: All O.

Wait, looking at the input:
Row 0: O O O O O O O O O
Row 1: O O O O O M O O O
...
Row 6: O O O A O M O B O
Row 7: O W O A O M O B O
Row 8: O W O A O M O B O

Columns with non-Orange content:
Col 1: W at rows 7, 8. (Height 2)
Col 3: A at rows 6, 7, 8. (Height 3)
Col 5: M at rows 1-8. (Height 8? Wait, Row 0 is O. So rows 1-8 is 8 pixels).
Col 7: B at rows 6, 7, 8. (Height 3)

Let's check the Output Grid (9x9):
Row 0: O O O O O O O O O
Row 1: O O O W O O O O O
Row 2: O O O W O O O O O
Row 3: O O O W O O O O O
Row 4: O O O W O O O O O
Row 5: O O O W O O O O O
Row 6: O B O W O A O O O
Row 7: O B O W O A O M O
Row 8: O B O W O A O M O

Columns with non-Orange content in Output:
Col 1: B at rows 6, 7, 8. (Height 3, Color B)
Col 3: W at rows 1-8. (Height 8, Color W)
Col 5: A at rows 6, 7, 8.

... [6600 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.26)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 174: "The largest kingdom claims the throne." k=3 alts: 0/0 3194b014

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 (typically 20×20) filled with a noisy background composed of two or three common colors (such as black, white, and orange). Embedded within this background are several distinct colored 'blob' regions — contiguous or near-contiguous clusters of cells in colors that stand out from the background. Each blob is a single color not shared by any other blob, and the blobs vary in size (total number of cells).

Do: 1. Identify all colors present in the grid. Separate them into 'background' colors (those scattered widely and irregularly across the grid) and 'blob' colors (those forming distinct, localized clusters). 2. For each blob color, count the total number of cells of that color in the entire grid. 3. Determine which blob color has the largest cell count. 4. Produce a 3×3 output grid filled entirely with that color.

Grid: The output is always a 3×3 grid filled uniformly with a single color — the color of the largest blob found in the input. The input grid is typically 20×20 with no fixed coordinate system relevance; only the total cell counts of the blob colors matter.

Figurative Descriptions (1 variants)

"The largest kingdom claims the throne."

qwen3.5-122b: k=3

See: A vast, war-torn landscape is scattered with the dust and debris of common earth — dull colors blown everywhere like sand in a storm. But within this chaos, several kingdoms have staked their territory, each flying a unique banner color and occupying a patch of land they've claimed as their own.

Do: The kingdoms are vying for dominance. Count the lands each kingdom holds — every cell under its banner. The kingdom with the greatest territory wins the war and earns the right to sit upon the throne. Crown the victor.

Grid: The throne is a small 3×3 seat of power, draped entirely in the banner color of the largest kingdom. No other color touches it — the victor rules alone.

qwen3.5-122b — MARC valid, solved with 3 examples

Input

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Prediction

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Expected

Reasoning (11385 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Context:** A "war-torn landscape" with "dust and debris" (dull colors) and "kingdoms" (unique banner colors).
*   **Action:** Count the lands each kingdom holds (cells under its banner).
*   **Goal:** Find the kingdom with the greatest territory (most cells).
*   **Output:** A 3x3 grid ("throne") filled entirely with the color of the winning kingdom.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input: A 20x20 grid with various colors (A, B, X, W, G, Y, etc.).
    *   Output: A 3x3 grid of 'G's.
    *   Task: Count the occurrences of each color in the input.
        *   Let's check the counts roughly.
        *   'G' appears in a block in the middle-right area.
        *   'Y' appears in a block at the bottom-left.
        *   'X' appears in a block in the middle-right.
        *   'W' appears in a block in the middle-left.
        *   'A' and 'B' are scattered everywhere (the "dust and debris").
        *   The "kingdoms" seem to be the contiguous blocks of specific colors, or perhaps just the total count of a specific color.
        *   Let's count 'G' cells in Example 1 Input:
            *   Row 7: G G (2)
            *   Row 8: G G G (3)
            *   Row 9: G G G G G (5)
            *   Row 10: G G G G G (5)
            *   Row 11: G G G G G (5)
            *   Row 12: G G G G G (5)
            *   Row 13: G G (2)
            *   Total G: 2+3+5+5+5+5+2 = 27.
        *   Let's count 'Y' cells:
            *   Row 16: Y Y Y Y Y (5)
            *   Row 17: Y Y Y Y Y Y Y (7)
            *   Row 18: Y Y Y Y Y (5)
            *   Total Y: 17.
        *   Let's count 'X' cells:
            *   Row 2: X X X X X (5)
            *   Row 3: X X X X X (5)
            *   Row 4: X X X X X (5)
            *   Row 5: X X X X X (5)
            *   Total X: 20.
        *   Let's count 'W' cells:
            *   Row 5: W W W W (4)
            *   Row 6: W W W W (4)
            *   Row 7: W W W W (4)
            *   Total W: 12.
        *   'A' and 'B' are scattered. Let's assume they are the "dust". The prompt says "dull colors blown everywhere like sand". 'A' (azure) and 'B' (blue) are quite frequent.
        *   The winner is 'G' (Green). The output is a 3x3 grid of 'G'.
        *   Hypothesis: Identify the color that forms the largest contiguous block or simply has the highest count among the "kingdom" colors (excluding the background/dust colors). Or simply the color with the absolute highest count?
        *   Let's check 'A' count in Ex 1. It's very high. 'B' is also very high.
        *   If 'A' and 'B' are "dust", how do we distinguish them from "kingdoms"?
        *   The description says: "dull colors blown everywhere like sand... several kingdoms have staked their territory... unique banner color".
        *   Usually in these puzzles, "background" is often bla

... [8409 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 194: "A curtain divides two dancers, and the spotlight finds whoev ... [16 chars truncated]" k=1 alts: 6/15 34b99a2b

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Literal Description

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

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

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

Figurative Descriptions (16 variants)

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

qwen3.5-122b: k=1

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

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

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

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (11200 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A golden curtain hangs down the center, splitting the stage into two wings (left and right).
*   **Left Wing:** Azure performers (A) among empty squares (black/dots).
*   **Right Wing:** Grey performers (X) mirroring the layout.
*   **Black Squares:** Darkness/Empty stage floor.
*   **Action:** Raise the curtain, wings collapse into one stage.
*   **Transformation Logic:**
    *   Compare the left wing and the right wing.
    *   "Wherever a performer on one side finds only darkness across from them — no partner, no mirror — a red spotlight ignites on that square, marking the lonesome dancer."
    *   "But where two performers lock eyes across the divide, or where darkness meets darkness, the stage stays dark."
    *   "The spotlight only loves the unmatched."
    *   "The curtain vanishes and the two wings collapse into one stage." -> This implies the output grid is likely half the width of the input grid, or represents the comparison result.
    *   "What remains is a smaller floor plan lit only by red spotlights where solitary dancers stood, surrounded by the darkness of matched pairs and empty silence." -> Output contains Red (R) and Black (.).

**2. Analyze the Training Example:**
*   **Input:**
    ```
    . A . . Y . X X .
    A A . A Y X . . X
    A A . . Y X . . X
    . A . A Y . . X .
    . . A . Y . X . X
    ```
    *   Dimensions: 5 rows, 9 columns.
    *   Center column seems to be 'Y' (Yellow). Let's check indices.
    *   Row 0: `. A . . Y . X X .` -> Index 4 is 'Y'. Left side: `. A . .`, Right side: `. X X .`.
    *   Row 1: `A A . A Y X . . X` -> Index 4 is 'Y'. Left side: `A A . A`, Right side: `X . . X`.
    *   Row 2: `A A . . Y X . . X` -> Index 4 is 'Y'. Left side: `A A . .`, Right side: `X . . X`.
    *   Row 3: `. A . A Y . . X .` -> Index 4 is 'Y'. Left side: `. A . A`, Right side: `. . X .`.
    *   Row 4: `. . A . Y . X . X` -> Index 4 is 'Y'. Left side: `. . A .`, Right side: `. X . X`.
    *   The 'Y' column acts as the "curtain" or divider.
    *   Left Wing: Columns 0-3 (4 columns).
    *   Right Wing: Columns 5-8 (4 columns).
    *   The Right Wing seems to be a mirror image or just a separate set of data. The description says "grey performers mirror the same stage layout". This might mean spatial mirroring or just that they occupy the corresponding positions. Let's look at the mapping.
    *   Usually, in these puzzles, "mirror" implies reflection. If the curtain is in the middle, the right side is the reflection of the left side.
    *   Let's check the comparison logic.
    *   Output Dimensions: 5 rows, 4 columns. This matches the width of one wing.
    *   Output Content:
        ```
        . . R .
        . R . .
        . R . R
        . R R R
        . R R R
        ```
    *   Let's compare Left Win

... [8521 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.35)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 214: "A jeweler counts the perfect emeralds among rough stones and ... [38 chars truncated]" k=1 alts: 0/0 3b4c2228

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Example 4

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Output

Example 5

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Output

Literal Description

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

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

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

Figurative Descriptions (1 variants)

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

qwen3.5-122b: k=1

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

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

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

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (11246 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Input:** "Scattered across a dark workbench are green and red stones of various sizes. Some stones are perfectly cut — flawless 2×2 emeralds that catch the light. Others are rough chunks of red garnet in similar shapes, and lone gem chips of both colors lie strewn about like shavings from the cutting wheel."
    *   "Dark workbench" implies a black background (`.`).
    *   "Green and red stones" implies `G` and `R` pixels.
    *   "Perfectly cut — flawless 2×2 emeralds" implies 2x2 blocks of `G`.
    *   "Rough chunks of red garnet" implies `R` shapes (maybe 2x2 or other).
    *   "Lone gem chips" implies single pixels or small clusters.
*   **Task:** "The jeweler inspects the workbench and counts only the perfect emeralds — the ones with that unmistakable 2×2 cut. For each true emerald found, the jeweler descends one step into the cellar, lighting a blue candle on each landing as they go. The staircase runs diagonally from the top landing to the bottom, and only as many candles are lit as emeralds were counted above."
    *   Count the number of 2x2 `G` blocks in the input.
    *   Output is a "cellar staircase" which is a "small 3×3 chamber of darkness".
    *   "Blue candle flames mark each step taken along the diagonal descent from the upper-left landing to the lower-right."
    *   This implies the output grid is 3x3.
    *   The background is black (`.`).
    *   Blue candles (`B`) are placed on the diagonal.
    *   The number of `B`s on the diagonal equals the count of 2x2 `G` blocks found in the input.
    *   The diagonal starts at top-left (0,0) and goes to bottom-right (2,2).
    *   So, if count = 1, `B` at (0,0). If count = 2, `B` at (0,0) and (1,1). If count = 3, `B` at (0,0), (1,1), (2,2).

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input:
        ```
        . G G . .
        . G G . .
        . . . . .
        R R . . R
        R R . . .
        . . . R R
        . . . R R
        ```
    *   Let's look for 2x2 `G` blocks.
        *   Rows 0-1, Cols 1-2:
            ```
            G G
            G G
            ```
            This is one 2x2 `G` block.
        *   Are there others? No other `G`s.
    *   Count of 2x2 `G` blocks = 1.
    *   Output:
        ```
        B . .
        . . .
        . . .
        ```
    *   Output size is 3x3.
    *   Diagonal `B`s: (0,0) is `B`. (1,1) is `.`. (2,2) is `.`.
    *   This matches the rule: Count = 1 -> 1 `B` on diagonal starting top-left.

*   **Wait, let me double check the output size.**
    *   The description says "cellar staircase below is always a small 3×3 chamber".
    *   Example 1 Output is 3x3.
    *   So the output size is fixed at 3x3 regardless of input size.

**3. Conceptual Digestion:**

1.  **CAST:**
    *   **Input Grid:** A canva

... [8338 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.08)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 223: "Scattered seeds fall and pile into pyramids on the ground." k=2 alts: 0/15 3d6c6e23

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

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

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

Figurative Descriptions (16 variants)

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

qwen3.5-122b: k=2

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

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

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

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (11435 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** "Colored seeds float in vertical columns... hovering in the upper air... ground below sits empty".
*   **Action:** "Gravity finally switches on. Every floating seed in a column falls... accumulate into a neat triangular mound resting on the ground floor".
*   **Shape:** "Triangular mound", "perfect pile", "pyramid".
*   **Ordering:** "Colors preserve their original layering: whatever was highest in the sky settles at the peak of the mound, and the deepest colors spread across its wide base."
*   **Result:** "The sky clears completely — all black — and only the triangular mounds remain, each sitting flush against the bottom edge of the grid, centered beneath where its seeds once floated."
*   **Multiple Columns:** "If multiple columns had seeds, multiple independent pyramids form side by side".

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input: 17 rows, 13 columns.
    *   Seeds: Orange (O) in column 6 (0-indexed, let's check).
        *   Row 1: O at col 6.
        *   Row 2: O at col 6.
        *   Row 4: O at col 6.
        *   Row 5: O at col 6.
        *   Row 6: O at col 6.
        *   Row 8: O at col 6.
        *   Row 10: O at col 6.
        *   Row 11: O at col 6.
        *   Row 12: O at col 6.
        *   Total O seeds = 9.
    *   Output:
        *   The seeds form a pyramid at the bottom.
        *   Row 13 (index 13): O at col 6. (1 seed)
        *   Row 14 (index 14): O at col 5, 6, 7. (3 seeds)
        *   Row 15 (index 15): O at col 4, 5, 6, 7, 8. (5 seeds)
        *   Total seeds in output = 1 + 3 + 5 = 9.
        *   The pyramid is centered on the original column index (col 6).
        *   The pyramid grows upwards from the bottom row.
        *   Wait, the description says "resting on the ground floor". In the output, the pyramid is at the bottom rows (13, 14, 15). The grid height is 17. So rows 13, 14, 15 are the bottom 3 rows.
        *   Shape: 1 on top, 3 in middle, 5 on bottom. This is a triangle/pyramid shape.
        *   Wait, usually a pyramid of height $h$ has $1 + 3 + 5 + ... + (2h-1)$ items. Here $1+3+5 = 9$. So height is 3.
        *   The seeds fall to the bottom. The "highest in the sky" (top-most seed in input) becomes the "peak of the mound" (top-most seed in output pyramid).
        *   In Example 1, all seeds are the same color (O), so layering doesn't matter visually, but the count matters.
        *   Input column 6 has 9 seeds. Output has a pyramid of 9 seeds centered at col 6, sitting on the bottom row.

*   **Example 2:**
    *   Input: 16 rows, 11 columns.
    *   Seeds: Orange (O) in column 5.
        *   Row 0: O
        *   Row 3: O
        *   Row 6: O
        *   Row 9: O
        *   Total O seeds = 4.
    *   Output:
        *   Pyramid at bottom.
        *   Row 14: O at col 5. (1 seed)
   

... [8495 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

No grid

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 227: "Russian nesting dolls carved from colored sticks" k=1 alts: 4/15 3ee1011a

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 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"

qwen3.5-122b: 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.

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (12117 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Input:** "Scattered across a vast dark field lie colored sticks of different lengths — each a single pure color, each lying perfectly straight, no two alike."
    *   This implies the input grid contains lines (sticks) of specific colors.
    *   "No two alike" likely means no two sticks have the same length, or perhaps the same color. Let's check the examples.
    *   "Vast dark field" implies the background is black (`.`).
*   **Transformation:** "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... The tiniest stick... finds itself cradled at the very heart."
    *   This describes a concentric square pattern.
    *   The sticks are transformed into square rings (frames).
    *   The order of nesting is determined by the length of the sticks: Longest -> Outermost, Shortest -> Innermost.
    *   "No darkness remains — every inch is claimed by a shell." This implies the output is a filled square where every cell belongs to one of the nested shells.
*   **Output:** "A perfect square portrait of nested shells, each exactly one layer thick".
    *   The output is a square grid.
    *   The layers are concentric squares.
    *   The thickness of each layer is 1 cell.

**2. Analyze the Training Example:**
*   **Input:**
    *   Grid size: 22 rows x 22 columns (counting dots). Let's verify.
    *   Rows 0-1: Empty.
    *   Row 2: `B` at col 11.
    *   Row 3: `G` at col 4, `B` at col 11.
    *   Row 4: `G` at col 4, `B` at col 11.
    *   Row 5: `G` at col 4, `B` at col 11.
    *   Row 6: `G` at col 4, `B` at col 11.
    *   Row 7: `B` at col 11.
    *   Row 8: `M` at col 8.
    *   Row 9: `M` at col 8.
    *   Rest empty.
    *   Let's identify the "sticks".
        *   Stick 1: Color `B`. Vertical line. Rows 2 to 7. Length = 6 cells.
        *   Stick 2: Color `G`. Vertical line. Rows 3 to 6. Length = 4 cells.
        *   Stick 3: Color `M`. Vertical line. Rows 8 to 9. Length = 2 cells.
    *   Wait, let's look closer at the input grid provided in the prompt text.
    *   Row 2: `... B ...` (index 11)
    *   Row 3: `... G ... B ...` (index 4, 11)
    *   Row 4: `... G ... B ...`
    *   Row 5: `... G ... B ...`
    *   Row 6: `... G ... B ...`
    *   Row 7: `... B ...`
    *   Row 8: `... M ...` (index 8)
    *   Row 9: `... M ...`
    *   So we have:
        *   Blue (`B`): Vertical segment from row 2 to 7. Length = 6.
        *   Green (`G`): Vertical segment from row 3 to 6. Length = 4.
        *   Magenta (`M`): Vertical segment from row 8 to 9. Length = 2.
    *   Are there horizontal sticks? No, they look vert

... [9153 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 246: "A volcano fills its crater and erupts a plume of its unique ... [30 chars truncated]" k=1 alts: 0/0 444801d8

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Literal Description

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

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

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

Figurative Descriptions (1 variants)

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

qwen3.5-122b: k=1

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

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

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

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (11448 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** Blue volcanic craters on a black landscape.
*   **Structure:**
    *   "Blue-walled basin five columns across".
    *   "Sturdy walls on three sides, but the top edge is fractured, with only the corner stones remaining."
    *   "Ember sits somewhere in the three-column-wide hollow within."
*   **Action:**
    *   "Magma surges upward, flooding every dark hollow inside the crater with its molten color." -> The inside of the crater fills with the color of the ember.
    *   "Lava seals the broken rim shut, fusing the gap closed." -> The top edge of the crater (which was open/broken) gets filled with the magma color.
    *   "Plume of that same radiant color bursts above the sealed peak, painting the sky directly over the volcano in a banner as wide as the mountain itself." -> The row immediately above the volcano gets filled with the magma color, spanning the width of the volcano (5 columns).

**2. Analyze the Training Example:**
*   **Input:**
    *   Row 2: `. B B . B B . . . .` (Wait, looking at the input grid provided in the prompt)
    *   Let's look at the actual input grid provided in Example 1.
    *   Input Grid:
        ```
        . . . . . . . . . .
        . . . . . . . . . .
        . B B . B B . . . .
        . B . R . B . . . .
        . B . . . B . . . .
        . B B B B B . . . .
        . . . . . . . . . .
        . . . . B B . B B .
        . . . . B . G . B .
        . . . . B B B B B .
        ```
    *   There are two distinct structures here.
    *   Structure 1 (Top):
        *   Rows 2-5 (0-indexed: 2, 3, 4, 5).
        *   Row 2: `. B B . B B` -> This looks like the top corners. `B B` at col 1,2 and `B B` at col 4,5? No, let's look closer.
        *   Row 2: `. B B . B B . . . .` -> Indices 1,2 are B. Indices 4,5 are B. Gap at 3.
        *   Row 3: `. B . R . B . . . .` -> Indices 1, 5 are B. Index 3 is R (Ember).
        *   Row 4: `. B . . . B . . . .` -> Indices 1, 5 are B.
        *   Row 5: `. B B B B B . . . .` -> Indices 1,2,3,4,5 are B. This is the bottom wall.
        *   So the "crater" is defined by Blue (B) pixels.
        *   Width: From col 1 to col 5 (5 columns).
        *   Height: Rows 2 to 5 (4 rows).
        *   Top edge (Row 2): `B B . B B`. The middle (col 3) is empty (`.`). This matches "top edge is fractured, with only the corner stones remaining".
        *   Sides (Row 3, 4): `B . . . B`.
        *   Bottom (Row 5): `B B B B B`.
        *   Ember: `R` at (3, 3).
    *   Structure 2 (Bottom):
        *   Rows 7-9.
        *   Row 7: `. . . . B B . B B .` -> Indices 4,5 are B. Indices 7,8 are B. Gap at 6.
        *   Row 8: `. . . . B . G . B .` -> Indices 4, 8 are B. Index 6 is G (Ember).
        *   Row 9: `. . . . B B B B B .` -> Indices 4,5,6,7,8 are B.
        *   Width: Cols 4 to 8 (5 c

... [8508 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 277: "Geological strata reveal the age of the earth when read in s ... [7 chars truncated]" k=3 alts: 0/0 4be741c5

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

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

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

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

Figurative Descriptions (1 variants)

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

qwen3.5-122b: k=3

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

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

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

qwen3.5-122b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (14362 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Context:** "Grid is a cross-section of ancient rock", "each color is a geological layer".
*   **Action:** "Read the rock like a geologist: identify each distinct stratum and record the ages in the order they were deposited — from the oldest exposed edge to the youngest."
*   **Output:** "The fossil record is a single core sample — one cell per era, arranged in the order the layers appear across the rock face."
*   **Key Insight:** The output seems to be a list of unique colors found in the input grid, ordered in a specific way. The metaphor suggests "layers" and "order of deposition". In geological terms, usually, older layers are at the bottom and younger on top, or layers are deposited sequentially. However, looking at the examples will clarify the ordering logic. The phrase "from the oldest exposed edge to the youngest" suggests a sequence. The output is a single column or row of colors representing the distinct layers.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input: A 9x7 grid.
        *   Top rows: Mostly R (Red).
        *   Middle rows: Mix of R and A (Azure).
        *   Bottom rows: Mix of A and X (Grey).
        *   Visually, it looks like horizontal bands. Top is R, middle is A, bottom is X.
    *   Output:
        ```
        R
        A
        X
        ```
    *   Observation: The output lists the unique colors present in the grid. The order is R, then A, then X. This corresponds to the vertical arrangement from top to bottom. Top layer = R, Middle layer = A, Bottom layer = X.

*   **Example 2:**
    *   Input: A 14x17 grid.
        *   Left side: Y (Yellow).
        *   Middle: R (Red).
        *   Right side: A (Azure).
        *   Visually, it looks like vertical bands. Left is Y, Middle is R, Right is A.
    *   Output:
        ```
        Y R A
        ```
    *   Observation: The output lists the unique colors present in the grid. The order is Y, R, A. This corresponds to the horizontal arrangement from left to right. Left layer = Y, Middle layer = R, Right layer = A.
    *   Note: In Example 1, the output was a column (vertical). In Example 2, the output was a row (horizontal). Why?
        *   Example 1 layers were horizontal bands (stacked vertically). The "core sample" extracted the sequence top-to-bottom.
        *   Example 2 layers were vertical bands (stacked horizontally). The "core sample" extracted the sequence left-to-right.
        *   Wait, let's look closer at Example 1 output format.
            Output:
            R
            A
            X
            This is a 3x1 grid.
        *   Example 2 output format:
            Y R A
            This is a 1x3 grid.
        *   Hypothesis: The output shape matches the orientation of the layers. If layers are stacked vertically (horizontal boundaries), output is ve

... [11438 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 363: "A herald's banner unfurls across a great hall, its emblem re ... [38 chars truncated]" k=3 alts: 4/15 62b74c02

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 a rectangular pattern of colored cells on the left side, followed by a region of black (.) cells extending to the right. The pattern has a key property: in each row, the first and last cells of the pattern share the same color, forming a 'border' color for that row. The interior cells between these matching border cells may be different colors.

Do: 1. Identify the pattern block on the left side of the grid (all columns before the black/dot region). Note its width W and the total grid width T. 2. For each row, identify the border color, which is the color of the first (and last) cell of the pattern block. 3. Construct the output row as follows: place the original pattern block at the left edge, place a mirrored copy of the pattern block at the right edge (so columns T-W through T-1 are the same as columns 0 through W-1), and fill all cells in between with that row's border color. 4. Repeat for every row.

Grid: The output grid has the same dimensions as the input grid (same number of rows and columns). The height equals the height of the input pattern. The width equals the full grid width including the dot region. No black cells remain in the output; they are all replaced by either the repeated border color or the mirrored pattern.

Figurative Descriptions (16 variants)

"A herald's banner unfurls across a great hall, its emblem reflected in the mirror at the far wall."

qwen3.5-122b: k=3

See: On the left edge of the hall hangs a narrow heraldic banner — each horizontal stripe bears a distinct coat of arms, framed on both sides by that stripe's own house color. The rest of the hall stretches away into darkness, an empty corridor of black stone.

Do: The banner is carried in procession across the hall. As it moves, each stripe leaves a ribbon of its house color trailing behind it, like a carpet unrolling. When the procession reaches the far wall, a great mirror reflects the banner's image back — an identical copy appears flush against the opposite wall. Between the real banner and its reflection, the hall is flooded with each row's house color, as though the family's standard has claimed every stone in its path.

Grid: The hall is exactly as wide and tall as before — no stones are added or removed. The darkness is banished entirely; every black stone is now draped in color. The original banner holds its place at the left wall, its twin gazes back from the right, and between them stretches an unbroken field of each row's own heraldic hue.

qwen3.5-122b — MARC valid, solved with 3 examples

Input

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Prediction

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Expected

Reasoning (11547 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A "hall" (grid).
*   **Left Edge:** A "narrow heraldic banner" hangs on the left edge.
    *   "Each horizontal stripe bears a distinct coat of arms, framed on both sides by that stripe's own house color."
    *   Looking at the examples, the input grids have non-black pixels on the left side (columns 0, 1, 2 usually) and black pixels (.) on the right.
    *   The "banner" seems to be the non-black part on the left.
    *   "Framed on both sides by that stripe's own house color": This suggests the pattern on the left is symmetric or has a specific structure. Let's look at the examples.
*   **Action:** "The banner is carried in procession across the hall."
    *   "Each stripe leaves a ribbon of its house color trailing behind it".
    *   "When the procession reaches the far wall, a great mirror reflects the banner's image back — an identical copy appears flush against the opposite wall."
    *   "Between the real banner and its reflection, the hall is flooded with each row's house color".
*   **Result:**
    *   "The original banner holds its place at the left wall".
    *   "Its twin gazes back from the right".
    *   "Between them stretches an unbroken field of each row's own heraldic hue".
    *   "Every black stone is now draped in color".

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input: 4 rows, 12 columns.
        Row 0: `G R G . . . . . . . . .`
        Row 1: `B R B . . . . . . . . .`
        Row 2: `G R G . . . . . . . . .`
        Row 3: `B G B . . . . . . . . .`
    *   Output: 4 rows, 12 columns.
        Row 0: `G R G G G G G G G G R G`
        Row 1: `B R B B B B B B B B R B`
        Row 2: `G R G G G G G G G G R G`
        Row 3: `B G B B B B B B B B G B`
    *   Observation:
        *   The input has 3 non-black columns on the left.
        *   The output has the original 3 columns on the left.
        *   The output has 3 columns on the right that look like a mirror image of the left 3 columns.
            *   Row 0 Left: `G R G`. Right: `R G`. Wait, let's look closer.
            *   Row 0 Output: `G R G` (cols 0-2) ... `G G G G G G` (cols 3-8) ... `R G` (cols 9-10)? No.
            *   Let's check the indices. Width = 12.
            *   Left part: Cols 0, 1, 2. Pattern `G R G`.
            *   Right part: Cols 9, 10, 11. Pattern `G R G`?
                *   Row 0 Output ends with `R G`. Wait, `G R G G G G G G G G R G`.
                *   Indices: 0:G, 1:R, 2:G, 3:G, 4:G, 5:G, 6:G, 7:G, 8:G, 9:G, 10:R, 11:G.
                *   Left block: `G R G`.
                *   Right block: `G R G` (indices 9, 10, 11).
                *   Middle block: `G G G G G G` (indices 3 to 8).
                *   The middle block is filled with the "house color". What is the house color?
                *   In Row 0, the pattern is `G R G`. Th

... [8559 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 386: "A stained-glass window unfolds its hidden reflections when t ... [30 chars truncated]" k=2 alts: 6/15 67e8384a

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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Literal Description

See: The input is a 3×3 grid of colored cells. Each cell contains one of several colors, with no special structural constraints — any arrangement of colors is valid.

Do: 1. Start with the original 3×3 grid. 2. Create a horizontal mirror (flip left-to-right) of the original and place it to the right, forming a 3×6 grid. 3. Create a vertical mirror (flip top-to-bottom) of that entire 3×6 grid and place it below, forming the final 6×6 output.

Grid: The input is always a 3×3 grid. The output is always a 6×6 grid — the input tiled with its reflections to produce four-fold symmetry (left-right and top-bottom).

Figurative Descriptions (16 variants)

"A stained-glass window unfolds its hidden reflections when the cathedral doors swing open."

qwen3.5-122b: k=2

See: A small square of stained glass, three panes across and three down, each shard holding its own color — a fragment of a larger window that has been folded in on itself, concealing its full design.

Do: The window remembers its complete form. First, the glass unfolds to the right, as though a hinged panel swings open to reveal the twin that was always pressed against it face-to-face. Then the entire doubled panel drops its reflection downward, like a window over still water, so that every shard finds its counterpart above and below. The cathedral reveals what symmetry had kept hidden.

Grid: The original fragment is a modest 3×3 piece of stained glass. When the cathedral fully opens its doors and the reflection pool settles beneath, the complete rose window stands 6×6 — four copies of the fragment facing inward like hands pressed together in prayer, symmetric in every direction.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (10606 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Input:** A 3x3 grid ("small square of stained glass, three panes across and three down").
*   **Transformation:**
    *   "Unfolds to the right": This suggests a horizontal reflection or mirroring. The 3x3 becomes a 3x6.
    *   "Drops its reflection downward": This suggests a vertical reflection or mirroring of the result from the previous step. The 3x6 becomes a 6x6.
    *   "Four copies of the fragment facing inward like hands pressed together in prayer, symmetric in every direction": This confirms the 2D mirroring process.
*   **Output:** A 6x6 grid.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input (3x3):
        ```
        R X R
        R M Y
        R R R
        ```
    *   Output (6x6):
        ```
        R X R R X R
        R M Y Y M R
        R R R R R R
        R R R R R R
        R M Y Y M R
        R X R R X R
        ```
    *   Let's check the mirroring logic.
    *   Top-left 3x3 is the input.
    *   Top-right 3x3:
        Row 1: `R X R` -> `R X R` (Wait, looking at output row 1: `R X R R X R`. The right half is `R X R`. This is a mirror of `R X R`? No, `R X R` reversed is `R X R`. Let's look at row 2.)
        Row 2: `R M Y` -> `Y M R`. Output row 2 is `R M Y Y M R`. So the right half is the reverse of the left half.
        Row 3: `R R R` -> `R R R`. Output row 3 is `R R R R R R`.
    *   So, the top half (rows 1-3) is constructed by taking the input row and appending its reverse.
        *   Row 1: `R X R` + `R X R` (Reverse of `R X R` is `R X R`) -> `R X R R X R`.
        *   Row 2: `R M Y` + `Y M R` (Reverse of `R M Y` is `Y M R`) -> `R M Y Y M R`.
        *   Row 3: `R R R` + `R R R` -> `R R R R R R`.
    *   Bottom half (rows 4-6):
        *   Row 4: `R R R R R R`. Matches Row 3.
        *   Row 5: `R M Y Y M R`. Matches Row 2.
        *   Row 6: `R X R R X R`. Matches Row 1.
    *   So the bottom half is the vertical mirror of the top half.
    *   Overall transformation:
        1.  Horizontal Mirror: For each row, append the reverse of that row.
        2.  Vertical Mirror: Append the reverse of the resulting rows (from bottom to top).
    *   Essentially, create a 6x6 grid where `Output[i][j]` depends on `Input`.
    *   Let $H=3, W=3$. Output is $2H \times 2W$.
    *   Top-Left quadrant ($0 \le i < 3, 0 \le j < 3$) = Input.
    *   Top-Right quadrant ($0 \le i < 3, 3 \le j < 6$) = Horizontal Flip of Input.
    *   Bottom-Left quadrant ($3 \le i < 6, 0 \le j < 3$) = Vertical Flip of Input.
    *   Bottom-Right quadrant ($3 \le i < 6, 3 \le j < 6$) = Vertical Flip of Horizontal Flip (or Horizontal Flip of Vertical Flip) of Input.
    *   Basically, it's a point reflection across the center of the 6x6 grid, or simply mirroring across the right edge and then the bottom edge.

*   **Example 2

... [7687 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 416: "A conductor reads the harmony of an orchestra to choose the ... [23 chars truncated]" k=3 alts: 15/15 6e02f1e3

Training Examples

Example 1

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Output

Example 2

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Example 3

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Example 4

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Example 5

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Literal Description

See: The input is a 3x3 grid filled with colored cells. The cells may all be the same color, or they may contain two or three distinct colors arranged in any pattern.

Do: Count the number of distinct colors present in the input grid. Create a 3x3 output grid filled with black (.). Then place exactly three grey (X) cells according to the count: If there is 1 distinct color, place X across the entire top row (positions (0,0), (0,1), (0,2)) forming a horizontal line. If there are 2 distinct colors, place X along the main diagonal (positions (0,0), (1,1), (2,2)) running from top-left to bottom-right. If there are 3 distinct colors, place X along the anti-diagonal (positions (0,2), (1,1), (2,0)) running from top-right to bottom-left.

Grid: Both input and output are 3x3 grids. The output grid has a black (.) background with exactly three grey (X) cells arranged in one of three fixed patterns depending on the color count in the input.

Figurative Descriptions (16 variants)

"A conductor reads the harmony of an orchestra to choose the curtain call formation."

qwen3.5-122b: k=3

See: A small stage is filled with performers dressed in colored costumes. Sometimes the entire ensemble wears matching outfits; other times, factions in different colors share the stage.

Do: After the performance, the curtain falls and the stage goes dark. A spotlight operator counts how many distinct factions performed. The fewer the factions, the more unified the bow — a single troupe lines up shoulder to shoulder across the front of the stage. A duo takes a bow along the grand staircase from balcony to pit. A trio crosses paths, saluting from opposite wings through center stage.

Grid: The dark stage is the same size as the original. Exactly three spotlights (grey) illuminate the bowing positions against the blackout, their arrangement a silent review of the evening's diversity.

qwen3.5-122b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (10147 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Context:** A stage with performers in colored costumes.
*   **Action:** Curtain falls, stage goes dark.
*   **Spotlight Operator:** Counts distinct factions (colors).
*   **Rule:**
    *   "The fewer the factions, the more unified the bow — a single troupe lines up shoulder to shoulder across the front of the stage." -> 1 faction = 1 row of spotlights?
    *   "A duo takes a bow along the grand staircase from balcony to pit." -> 2 factions = diagonal line?
    *   "A trio crosses paths, saluting from opposite wings through center stage." -> 3 factions = ?
*   **Output:** "Exactly three spotlights (grey) illuminate the bowing positions against the blackout".
*   **Grid details:** Output grid size is same as input. Background is black (.). Spotlights are grey (X).
*   **Key Insight:** The number of distinct colors in the input grid determines the pattern of grey 'X's in the output grid. The rest of the grid is black '.'.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input:
        G G G
        G G G
        G G G
    *   Colors present: Green (G). Count = 1.
    *   Output:
        X X X
        . . .
        . . .
    *   Pattern: Top row filled with X.
    *   Interpretation: 1 distinct color -> Top row of Xs.

*   **Example 2:**
    *   Input:
        G G G
        Y R R
        Y Y R
    *   Colors present: Green (G), Yellow (Y), Red (R). Count = 3.
    *   Output:
        . . X
        . X .
        X . .
    *   Pattern: Anti-diagonal (top-right to bottom-left).
    *   Interpretation: 3 distinct colors -> Anti-diagonal of Xs.

*   **Example 3:**
    *   Input:
        Y Y Y
        Y Y Y
        Y Y Y
    *   Colors present: Yellow (Y). Count = 1.
    *   Output:
        X X X
        . . .
        . . .
    *   Pattern: Top row filled with X.
    *   Interpretation: 1 distinct color -> Top row of Xs. (Consistent with Example 1).

*   **Missing Case:** What about 2 distinct colors?
    *   The metaphor says: "A duo takes a bow along the grand staircase from balcony to pit."
    *   "Grand staircase from balcony to pit" usually implies a diagonal.
    *   In a 3x3 grid, there are two diagonals: Main diagonal (top-left to bottom-right) and Anti-diagonal (top-right to bottom-left).
    *   Example 2 (3 colors) used the Anti-diagonal.
    *   Example 1 & 3 (1 color) used the Top Row.
    *   Hypothesis for 2 colors: Main diagonal (top-left to bottom-right).
    *   Let's check the metaphor again: "A trio crosses paths, saluting from opposite wings through center stage." This sounds like an X shape or crossing lines, but the output for 3 colors is a single anti-diagonal line. Wait, "opposite wings through center stage" could imply the anti-diagonal (top-right wing to bottom-left pit/wing).
    *   "A duo takes a bow along the grand s

... [7245 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 421: "A vampire stands before a mirror that reveals not its reflec ... [48 chars truncated]" k=1 alts: 0/0 6f473927

Training Examples

Example 1

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Output

Example 2

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Example 3

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Output

Example 4

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Output

Literal Description

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

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

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

Figurative Descriptions (1 variants)

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

qwen3.5-122b: k=1

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

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

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

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (11661 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A figure made of red embers (R) stands in a dark room (.).
*   **Action:** Facing a wall-sized mirror.
*   **Vampire Logic:** The vampire (Red) cannot see itself in the mirror. So, where the vampire is, the mirror shows darkness (black, .).
*   **Mirror Logic:** Where empty space surrounds the vampire, the mirror glows azure (A).
*   **Layout:** The mirror doubles the world horizontally.
    *   Left side: The original room (unchanged).
    *   Right side: The mirror's vision (reversed? or just transformed?).
    *   "The vampire and its anti-reflection stand side by side, the original on the left, the haunted mirror on the right."
    *   "The mirror doubles the world horizontally." -> Output width = Input width * 2.
    *   "The left side is the room as it is — embers and darkness unchanged." -> Left half of output = Input grid.
    *   "The right side is the mirror's vision: a reversed world where the vampire's red form casts no reflection (black) and the surrounding darkness lights up in azure."
    *   Wait, does "reversed world" mean horizontally flipped? Or just the transformation logic applied?
    *   Let's check the training example to clarify "reversed".

**2. Analyze Training Example 1:**
*   **Input:**
    ```
    . R .
    . R R
    . . R
    ```
    Dimensions: 3 rows, 3 columns.
*   **Output:**
    ```
    . R . A . A
    . R R . . A
    . . R . A A
    ```
    Dimensions: 3 rows, 6 columns.
    This confirms the "doubles the world horizontally" rule. Output width = 2 * Input width.
    Left half (cols 0-2):
    ```
    . R .
    . R R
    . . R
    ```
    This matches the Input exactly. So Left Side = Input.

    Right half (cols 3-5):
    ```
    A . A
    . . A
    . A A
    ```
    Let's compare Input vs Right Half.
    Input Row 0: `. R .` -> Right Row 0: `A . A`
    Input Row 1: `. R R` -> Right Row 1: `. . A`
    Input Row 2: `. . R` -> Right Row 2: `. A A`

    Transformation Logic Hypothesis:
    For each cell in the input grid at (r, c):
    If Input(r, c) is Red (R):
        Output(r, c + width) is Black (.)
    If Input(r, c) is Black (.):
        Output(r, c + width) is Azure (A)

    Let's check this hypothesis against the Right Half.
    Row 0:
    Input: . R .
    Map:   A . A
    Matches hypothesis.

    Row 1:
    Input: . R R
    Map:   . . A
    Matches hypothesis.

    Row 2:
    Input: . . R
    Map:   . A A
    Matches hypothesis.

    Does "reversed world" mean horizontal flip?
    If it were flipped, Row 0 Input `. R .` flipped is `. R .`.
    Row 1 Input `. R R` flipped is `R R .`.
    Row 2 Input `. . R` flipped is `R . .`.
    If we apply the color swap logic to the flipped version:
    Row 0 Flipped: `. R .` -> `A . A`. (Matches)
    Row 1 Flipped: `R R .` -> `. . A`. (Matches)
    Row 2 Flipped: `R . 

... [8865 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.42)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 430: "Rockets on a launchpad ignite according to their fuel type." k=3 alts: 8/15 72a961c9

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Literal Description

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

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

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

Figurative Descriptions (16 variants)

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

qwen3.5-122b: k=3

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

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

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

qwen3.5-122b — MARC valid, solved with 3 examples

Input

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Prediction

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Expected

Reasoning (10142 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A launchpad (solid blue runway) with special rocket engines embedded in it.
*   **Engine Colors:** Azure (A) or Red (R).
*   **Action:** When triggered, engines fire a plume straight up.
*   **Plume Composition:** A column of blue exhaust (B) capped by a bright flare matching the engine's color (A or R).
*   **Height:** Red rockets burn hotter and reach higher than Azure ones.
*   **Constraints:** Engines stay bolted to the launchpad. Plumes only fire upward. Nothing falls below. No rocket escapes the edge.
*   **Background:** Night sky stays dark (black '.') except for exhaust trails.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input: 9x6 grid. Row 4 (0-indexed) is `B A B B B B`.
    *   Output: Row 4 is `B A B B B B`. Above it, at column 1 (where 'A' is), there is a column going up.
    *   Let's check the column above 'A' at (3, 1).
    *   Output grid at (2, 1) is 'B'. Output grid at (1, 1) is 'B'. Output grid at (0, 1) is 'A'.
    *   Wait, let's look closer.
    *   Input Row 3 (0-indexed): `B A B B B B`.
    *   Output Row 3: `B A B B B B`.
    *   Output Row 2: `. B . . . .` (Col 1 is B)
    *   Output Row 1: `. B . . . .` (Col 1 is B)
    *   Output Row 0: `. A . . . .` (Col 1 is A)
    *   So, for an 'A' engine at row $r$, column $c$:
        *   The engine stays at $(r, c)$.
        *   A column of 'B's goes up from $(r-1, c)$ to some height.
        *   The top of the column is 'A'.
        *   In this example, the 'A' is at row 3. The plume goes up to row 0.
        *   Height calculation: Row 3 to Row 0 is 3 steps up.
        *   Is there a specific height rule? "Red rockets burn hotter and their plumes reach higher than azure ones."
        *   Here we only have 'A'. The plume reaches the top edge (row 0).
        *   Let's check the other cells in the row. They are 'B'. They don't seem to trigger plumes. Only 'A' and 'R' are engines. 'B' is the runway.

*   **Example 2:**
    *   Input: 10x7 grid. Row 5 is `B B B R B B B`.
    *   Output: Row 5 is `B B B R B B B`.
    *   Above the 'R' at (5, 3):
        *   Row 4: `B`
        *   Row 3: `B`
        *   Row 2: `B`
        *   Row 1: `R`
        *   Row 0: `.`
    *   So the plume for 'R' goes from row 4 up to row 1.
    *   Height: 4 cells high (rows 1, 2, 3, 4).
    *   Top cell is 'R'. Rest are 'B'.
    *   Compare with Example 1 ('A' engine):
        *   'A' at row 3. Plume went to row 0. Height = 3 cells (rows 0, 1, 2).
        *   Wait, in Ex 1, 'A' was at row 3. Plume occupied rows 0, 1, 2. That's 3 cells.
        *   In Ex 2, 'R' was at row 5. Plume occupied rows 1, 2, 3, 4. That's 4 cells.
        *   Wait, let's re-read the height rule. "Red rockets burn hotter and their plumes reach higher than azure ones."
        *   In Ex 1, 'A' reached the top (row 0).
        *   In Ex 2

... [7151 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.26)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 436: "A painting hung on a dark gallery wall faces a mirror." k=2 alts: 0/0 7468f01a

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Literal Description

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

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

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

Figurative Descriptions (1 variants)

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

qwen3.5-122b: k=2

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

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

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

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (10183 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Context:** A dark gallery wall (black `.` background).
*   **Object:** A single small painting (a colored rectangle) hanging on the wall.
*   **Action:** Lift the painting off the wall and hold it before a mirror.
*   **Result:** The reflection (left becomes right, right becomes left).
*   **Output:** Only the mirror's image (the reflected painting), discarding the empty wall (background).

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   **Input:** A 12x16 grid. Most cells are `.` (black). There is a rectangular region containing `Y` (yellow) and `B` (blue).
    *   **Region:** Rows 1-5 (0-indexed: 1, 2, 3, 4, 5), Columns 3-7 (0-indexed: 3, 4, 5, 6, 7).
        *   Row 1: `Y Y Y Y Y`
        *   Row 2: `Y Y Y Y Y`
        *   Row 3: `Y B B Y Y`
        *   Row 4: `Y Y B B Y`
        *   Row 5: `Y Y B Y Y`
    *   **Output:** A 5x5 grid.
        *   Row 1: `Y Y Y Y Y`
        *   Row 2: `Y Y Y Y Y`
        *   Row 3: `Y Y B B Y`
        *   Row 4: `Y B B Y Y`
        *   Row 5: `Y Y B Y Y`
    *   **Comparison:**
        *   Input subgrid:
            ```
            Y Y Y Y Y
            Y Y Y Y Y
            Y B B Y Y
            Y Y B B Y
            Y Y B Y Y
            ```
        *   Output subgrid:
            ```
            Y Y Y Y Y
            Y Y Y Y Y
            Y Y B B Y
            Y B B Y Y
            Y Y B Y Y
            ```
        *   Wait, let's look closer.
        *   Input Row 3: `Y B B Y Y` -> Output Row 3: `Y Y B B Y`. This is a horizontal flip (mirror).
        *   Input Row 4: `Y Y B B Y` -> Output Row 4: `Y B B Y Y`. This is a horizontal flip.
        *   Input Row 5: `Y Y B Y Y` -> Output Row 5: `Y Y B Y Y`. This is symmetric, so flip looks the same.
        *   Rows 1 and 2 are all `Y`, so flip looks the same.
    *   **Conclusion:** The task is to extract the non-background rectangular region and horizontally flip (mirror) it.

*   **Example 2:**
    *   **Input:** A 10x15 grid. Background `.`.
    *   **Region:** Rows 5-8, Columns 2-9.
        *   Row 5: `A A A A A A R A`
        *   Row 6: `A R R A A A A A`
        *   Row 7: `A A R R A A A A`
        *   Row 8: `A A A A A A A A`
    *   **Output:** A 4x8 grid.
        *   Row 1: `A R A A A A A A`
        *   Row 2: `A A A A A R R A`
        *   Row 3: `A A A A R R A A`
        *   Row 4: `A A A A A A A A`
    *   **Comparison:**
        *   Input Row 5: `A A A A A A R A` -> Output Row 1: `A R A A A A A A`. (Reversed: `A R A A A A A A`). Correct.
        *   Input Row 6: `A R R A A A A A` -> Output Row 2: `A A A A A R R A`. (Reversed: `A A A A A R R A`). Correct.
        *   Input Row 7: `A A R R A A A A` -> Output Row 3: `A A A A R R A A`. (Reversed: `A A A A R R A A`). Correct.
        *   Input Row 8: `A A A A A A A A` -> Output Row 4: `A A A A A A A A`. (

... [7250 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.09)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 454: "A compass rose unfurls from a single petal, each cardinal di ... [47 chars truncated]" k=1 alts: 7/15 7953d61e

Training Examples

Example 1

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Output

Example 2

Input

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Output

Example 3

Input

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Output

Example 4

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Output

Example 5

Input

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Output

Literal Description

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

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

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

Figurative Descriptions (16 variants)

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

qwen3.5-122b: k=1

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

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

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

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (10986 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Input:** "A small mosaic tile — a 4×4 swatch of stained glass". Wait, the description says "4x4 swatch". Let's check the training example input.
    *   Example 1 Input:
        Y W B A
        A Y B A
        Y A A B
        B B B A
        This is a 4x4 grid.
    *   Test Input:
        Y M Y Y
        Y M Y Y
        O M O W
        W Y W O
        This is also a 4x4 grid.
*   **Output:** "The cathedral floor is exactly four tiles wide and four tiles tall — a 2×2 arrangement of the original swatch and its three rotated echoes."
    *   Wait, the text says "cathedral floor is exactly four tiles wide and four tiles tall". This implies the output is 4x4?
    *   Let's check the Example 1 Output.
        Y W B A A A B A
        A Y B A B B A B
        Y A A B W Y A B
        B B B A Y A Y B
        A B B B B Y A Y
        B A A Y B A Y W
        A B Y A B A B B
        A B W Y A B A A
        This is an 8x8 grid.
    *   There is a contradiction in the metaphorical description text provided in the prompt versus the actual data.
    *   Text says: "cathedral floor is exactly four tiles wide and four tiles tall".
    *   Data says: Input is 4x4, Output is 8x8.
    *   Text says: "2x2 arrangement of the original swatch and its three rotated echoes".
    *   If the original swatch is 4x4, a 2x2 arrangement of them would be 8x8.
    *   So the text "four tiles wide and four tiles tall" likely refers to the *tiles* in the arrangement (meaning 2x2 tiles, where each tile is 4x4 pixels), or it's a slight error in the metaphor description provided in the prompt context. Given the training example clearly shows an 8x8 output from a 4x4 input, I must follow the pattern in the data.
    *   The pattern is: Input 4x4 -> Output 8x8.
    *   The output is composed of 4 quadrants (2x2 arrangement).
    *   The quadrants are transformations of the input grid.
    *   "The tile dreams of itself from every direction. It gazes north and sees its own face." -> Top-Left quadrant is likely the original.
    *   "It turns its head east, west, and south, and at each glance the reflection has spun — as if the tile were placed on a lazy Susan and photographed at each quarter-turn." -> The other three quadrants are rotations of the original.
    *   "These four portraits are pressed together... the original anchoring one corner while its dizzied twins fill the remaining three."
    *   Let's determine the specific rotations for each quadrant.
    *   Standard layout for 2x2 arrangement of rotations usually follows a specific order.
    *   Let's analyze Example 1 to deduce the rotation mapping.

**2. Analyze Example 1:**
Input (4x4):
Row 0: Y W B A
Row 1: A Y B A
Row 2: Y A A B
Row 3: B B B A

Output (8x8):
Row 0: Y W B A | A A B A
Row 1: A Y B A | B B A B
Row 2: Y A A B | W

... [8240 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.06)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 467: "A comet streaks away from its home planet, leaving a glowing ... [28 chars truncated]" k=1 alts: 5/15 7ddcd7ec

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Literal Description

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

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

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

Figurative Descriptions (16 variants)

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

qwen3.5-122b: k=1

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

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

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

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (10614 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A 10x10 grid of black void (`.`).
*   **Objects:**
    *   "Planet": A solid 2x2 world.
    *   "Comets": One or two comets launched from its corners. Each is a single bright spark sitting diagonally adjacent to the planet's surface.
    *   "Color": The planet and its comets share one color.
*   **Action:**
    *   Comets hurtle away from the planet.
    *   They blaze a trail across the void.
    *   They drop one spark of light in every row they cross.
    *   They fly diagonally outward until they crash into the edge of the universe.
    *   The planet stays fixed.
*   **Constraints:**
    *   Planet is far enough from edges for comets to streak.
    *   Grid is 10x10.

**2. Analyze the Training Example:**
*   **Input:**
    *   Grid size: 10x10.
    *   Background: `.` (black).
    *   Object: A cluster of `Y` (yellow) pixels.
    *   Let's locate the `Y` pixels in the input:
        *   Row 1 (index 1): Col 6 (index 6) -> `(1, 6)`
        *   Row 2 (index 2): Col 4, 5 -> `(2, 4), (2, 5)`
        *   Row 3 (index 3): Col 4, 5 -> `(3, 4), (3, 5)`
        *   Row 4 (index 4): Col 6 -> `(4, 6)`
    *   Wait, let's look closer at the shape.
        *   Row 1: `......Y...` (index 1, col 6)
        *   Row 2: `....YY....` (index 2, col 4, 5)
        *   Row 3: `....YY....` (index 3, col 4, 5)
        *   Row 4: `......Y...` (index 4, col 6)
    *   This looks like a 2x2 square in the middle `(2,4), (2,5), (3,4), (3,5)` plus two "comets" at `(1,6)` and `(4,6)`.
    *   Wait, the description says "comets... sitting diagonally adjacent to the planet's surface".
    *   Planet: 2x2 block. Let's assume the 2x2 block is the core.
        *   Core: `(2,4), (2,5), (3,4), (3,5)`.
    *   Comets:
        *   One at `(1,6)`. Relative to the top-right corner of the 2x2 block `(2,5)`, `(1,6)` is `(-1, +1)`. This is diagonally adjacent (top-right).
        *   One at `(4,6)`. Relative to the bottom-right corner of the 2x2 block `(3,5)`, `(4,6)` is `(+1, +1)`. This is diagonally adjacent (bottom-right).
    *   So the input contains the "Planet" (2x2) and the initial "Comets" (1 pixel each).
    *   Total color: Yellow (`Y`).

*   **Output:**
    *   The 2x2 planet remains at `(2,4), (2,5), (3,4), (3,5)`.
    *   The comets have left trails.
    *   Let's trace the trails.
    *   Top-right comet started at `(1,6)`. It moves diagonally outward.
        *   Direction: Top-Right (Up-Right). Row decreases, Col increases.
        *   Path: `(1,6) -> (0,7)`.
        *   Output shows `Y` at `(0,7)`.
        *   Wait, looking at the output grid provided in the prompt:
            *   Row 0: `.......Y..` -> `(0, 7)` is `Y`.
            *   Row 1: `......Y...` -> `(1, 6)` is `Y`.
            *   Row 2: `....YY....` -> `(2, 4), (2, 5)` are `Y`.
            *   Row 3: `....YY.

... [7724 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.47)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 475: "A mirror hangs on the wall, and everything reflected in it a ... [25 chars truncated]" k=3 alts: 0/0 7ee1c6ea

Training Examples

Example 1

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Output

Example 2

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Output

Example 3

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Output

Literal Description

See: The input grid contains a rectangular border made of X (grey) cells embedded within the larger grid. This X border forms a closed rectangle. Inside the X-bordered rectangle, there are exactly two non-black colors (e.g., blue and orange, or azure and magenta) intermixed with black (.) cells. Outside the X border, the same two colors and black cells appear but are not part of the transformation.

Do: 1. Locate the rectangular border of X cells within the grid. 2. Identify the interior region enclosed by the X border (excluding the X cells themselves). 3. Determine the two non-black colors present inside this interior region. 4. Swap every occurrence of these two colors within the interior: replace each cell of color A with color B, and each cell of color B with color A. 5. Leave all black (.) cells inside the rectangle unchanged. 6. Leave all cells outside the X border (and the X border itself) unchanged.

Grid: The grid is 10x10. Black (.) serves as a neutral background/filler. A rectangular frame of X (grey) cells is embedded in the grid, typically spanning most of the grid but offset from the edges. The frame is exactly one cell thick. The interior of the frame contains a mix of two non-black colors and black cells. The exterior also contains those same two colors and black cells but is not modified.

Figurative Descriptions (1 variants)

"A mirror hangs on the wall, and everything reflected in it appears in swapped colors."

qwen3.5-122b: k=3

See: A grey picture frame sits within a larger scene. Inside the frame, two rival pigments dance together against patches of empty canvas. The same pigments wander freely outside the frame, untouched by its magic.

Do: The frame is an enchanted mirror — it shows the world inside in reversed costume. Each pigment gazes into the glass and sees itself wearing the other's color. They swap disguises, trading identities completely, while the empty canvas spaces remain bare. Nothing beyond the frame's edge feels its spell.

Grid: A 10×10world. Black (.) is bare canvas — neutral, invisible, unmoved. A grey (X) picture frame, one cell thick, hangs somewhere within the scene, enclosing a smaller chamber. Two colorful pigments inhabit both sides of the frame, but only those caught inside the mirror's reach exchange their masks. The frame itself stands unchanged, stoic as ever.

qwen3.5-122b — MARC valid, solved with 3 examples

Input

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Prediction

vs

Expected

Reasoning (10185 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A 10x10 world.
*   **Elements:**
    *   `.` (black): Bare canvas, neutral, invisible, unmoved.
    *   `X` (grey): Picture frame, one cell thick.
    *   Two colorful pigments (let's call them Color 1 and Color 2).
*   **Action:**
    *   The frame (`X`) encloses a smaller chamber.
    *   Inside the frame, the two pigments swap colors.
    *   Outside the frame, the pigments remain unchanged.
    *   The frame itself (`X`) remains unchanged.
    *   The bare canvas (`.`) remains unchanged.
*   **Key Insight:** Identify the two specific colors involved in the swap. Look at the examples to see which colors are swapping.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input Colors: `A` (azure), `M` (magenta), `X` (grey), `.` (black).
    *   Frame: `X` forms a rectangular border.
    *   Inside the frame: There are `A`s and `M`s.
    *   Outside the frame: There are `A`s and `M`s.
    *   Transformation:
        *   Inside the frame: `A` becomes `M`, `M` becomes `A`.
        *   Outside the frame: `A` stays `A`, `M` stays `M`.
        *   Frame `X` stays `X`.
        *   Background `.` stays `.`.
    *   Let's verify specific cells.
        *   Row 2 (index 1): `A X X X X X X X X .` -> `A X X X X X X X X .` (Frame boundary, no change).
        *   Row 3 (index 2): `. X . A A M M . X A` -> `. X . M M A A . X A`. Inside the X-border (cols 1 to 8), `A` became `M` and `M` became `A`. The `A` at col 9 is outside, stays `A`.
        *   Row 4 (index 3): `M X M M M A . M X A` -> `M X A A A M . A X A`. Inside: `M`->`A`, `A`->`M`. Outside `A` stays `A`.
    *   Conclusion: The two colors swapping are `A` and `M`.

*   **Example 2:**
    *   Input Colors: `W` (maroon), `Y` (yellow), `X` (grey), `.` (black).
    *   Frame: `X` forms a rectangular border.
    *   Inside the frame: `W` and `Y`.
    *   Outside the frame: `W` and `Y`.
    *   Transformation:
        *   Inside the frame: `W` becomes `Y`, `Y` becomes `W`.
        *   Outside the frame: `W` stays `W`, `Y` stays `Y`.
    *   Let's verify.
        *   Row 3 (index 2): `. . X X X X X X . W` -> `. . X X X X X X . W`.
        *   Row 4 (index 3): `W Y X W . W W X . Y` -> `W Y X Y . Y Y X . Y`. Inside (cols 2 to 7): `W`->`Y`, `Y`->`W`. Outside `W` at col 0, `Y` at col 9 stay same.
    *   Conclusion: The two colors swapping are `W` and `Y`.

*   **Example 3:**
    *   Input Colors: `G` (green), `R` (red), `X` (grey), `.` (black).
    *   Frame: `X` forms a rectangular border.
    *   Inside the frame: `G` and `R`.
    *   Outside the frame: `G` and `R`.
    *   Transformation:
        *   Inside the frame: `G` becomes `R`, `R` becomes `G`.
        *   Outside the frame: `G` stays `G`, `R` stays `R`.
    *   Let's verify.
        *   Row 3 (index 2): `G X G R R R R . X R` -> `G X R 

... [7359 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.33)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 488: "A beacon sinks one step into the earth, and its light rains ... [69 chars truncated]" k=1 alts: 6/15 834ec97d

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 has a black background with exactly one non-black colored cell located somewhere in the grid.

Do: 1. Locate the single colored cell at row R, column C. Note its color. 2. Determine the parity (even or odd) of column C. 3. Move the colored cell down by one row to position (R+1, C). 4. Fill every cell from row 0 through row R (inclusive) with yellow, but ONLY at columns that share the same parity as C. All other cells in those rows remain black. 5. All rows below the colored cell's new position remain unchanged (black).

Grid: The grid dimensions match the input. The background is black (.). The coordinate system is zero-indexed with row 0 at the top and column 0 at the left. The grid contains exactly one non-black cell in the input.

Figurative Descriptions (16 variants)

"A beacon sinks one step into the earth, and its light rains upward in alternating columns like prison bars against the night sky."

qwen3.5-122b: k=1

See: A single beacon glows alone in a dark field — a solitary flame in an ocean of night.

Do: The beacon is heavy; it sinks one step deeper into the ground. As it falls, it casts its light upward like rain falling in reverse, illuminating every other column above where it once stood — golden bars of light striping the darkness. The columns that catch the light share a kinship with the beacon's own column, stepping in rhythm with it (every other one). The sky above fills with these golden stripes, but the darkness below the beacon remains untouched, as light cannot fall downward from a thing that has already fallen.

Grid: The dark field keeps its original shape. Night is black (.), and the beacon's golden rain is yellow (Y). The beacon itself keeps its original color and identity. Only the sky above the beacon's resting place is painted — the ground beneath stays dark and silent.

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (11207 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** "A single beacon glows alone in a dark field". This implies there is one distinct object (the beacon) in a background of black (.) cells.
*   **Action:** "The beacon is heavy; it sinks one step deeper into the ground." This suggests the beacon moves down by one row.
*   **Effect:** "As it falls, it casts its light upward like rain falling in reverse, illuminating every other column above where it once stood".
    *   "Casts its light upward": The effect happens in the rows *above* the beacon's position.
    *   "Every other column": This implies a pattern of columns. If the beacon is at column $c$, the light affects columns $c, c-2, c+2, c-4, c+4, \dots$ (columns with the same parity as $c$).
    *   "Golden bars of light": The color of the light is Yellow (Y).
    *   "The columns that catch the light share a kinship with the beacon's own column, stepping in rhythm with it (every other one)": Confirms the parity rule.
    *   "The sky above fills with these golden stripes, but the darkness below the beacon remains untouched": The transformation only affects rows *above* the beacon's final position. The rows below or at the beacon's position (except the beacon itself) remain black.
*   **Beacon Identity:** "The beacon itself keeps its original color and identity."
*   **Grid Details:** Dark field = black (.). Beacon's rain = yellow (Y).

**2. Analyze the Training Example:**
*   **Input:**
    ```
    . . . . .
    . . . . .
    . . M . .
    . . . . .
    . . . . .
    ```
    *   Grid size: 5x5.
    *   Beacon: 'M' (Magenta) at row 2, column 2 (0-indexed). Let's check indices.
        *   Row 0: . . . . .
        *   Row 1: . . . . .
        *   Row 2: . . M . .  -> Row index 2, Col index 2.
        *   Row 3: . . . . .
        *   Row 4: . . . . .
*   **Output:**
    ```
    Y . Y . Y
    Y . Y . Y
    Y . Y . Y
    . . M . .
    . . . . .
    ```
    *   Beacon 'M' is now at Row 3, Column 2.
    *   Wait, the description says "sinks one step deeper". In the input, M was at Row 2. In the output, M is at Row 3. So it moved down by 1.
    *   The "light" (Y) appears in rows *above* the beacon's *new* position? Or *old* position?
    *   Let's look at the output rows.
        *   Row 0: Y . Y . Y
        *   Row 1: Y . Y . Y
        *   Row 2: Y . Y . Y
        *   Row 3: . . M . .  (Beacon is here)
        *   Row 4: . . . . .
    *   The beacon moved from (2, 2) to (3, 2).
    *   The yellow stripes are in rows 0, 1, 2. These are the rows *above* the beacon's new position (Row 3).
    *   The columns with Y are 0, 2, 4. The beacon is at column 2. So columns with the same parity as the beacon's column (even columns) are filled with Y.
    *   The rows affected are all rows strictly above the beacon's final row.
    *   The beacon's original position (2, 2) is now part of

... [8267 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.12)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

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

Training Examples

Example 1

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Output

Example 2

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Output

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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Output

Literal Description

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

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

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

Figurative Descriptions (16 variants)

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

qwen3.5-122b: k=2

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

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

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

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (10999 chars)

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

**1. Analyze the Metaphorical Description:**
*   **"Crowded square buzzes with chatter... seven paces on each side."**: The input grid is 7x7.
*   **"Most voices are faint... one color is practically shouting over everyone else"**: There is a dominant color in the input grid. I need to count the occurrences of each color to find the most frequent one.
*   **"That dominant voice... chooses a signature gesture, a pose struck in azure light on a small dark stage."**: The output grid is 3x3 ("tiny three-by-three platform"). The background of the output grid seems to be black (represented by `.`). The "pose" is drawn in Azure (`A`).
*   **"Each color-voice has rehearsed its own distinctive pose... The loudest voice steps onto the stage and strikes the only pose it knows."**: This implies that the dominant color in the input determines the shape/pattern drawn in Azure (`A`) on the 3x3 output grid. Different dominant colors map to different 3x3 patterns.
*   **"No matter how chaotic the crowd, only one pose appears — chosen not by where anyone stood, but simply by who was loudest."**: The position of the dominant color in the input doesn't matter, only the count. The output is always 3x3.

**2. Analyze the Training Examples:**

**Example 1:**
Input:
```
B . B . O . .
B B W B . B .
. . B B . R .
. . . . G . B
. Y . B . . B
. . B . R . A
. . B . O G B
```
Grid size: 7x7.
Let's count the colors:
B (Blue):
Row 1: 2
Row 2: 4
Row 3: 2
Row 4: 1
Row 5: 2
Row 6: 1
Row 7: 2
Total B: 2+4+2+1+2+1+2 = 14.

O (Orange): 2
W (Maroon): 1
R (Red): 2
G (Green): 2
Y (Yellow): 1
A (Azure): 1

Dominant color: **B (Blue)** with 14 occurrences.

Output:
```
. . A
A A .
. A .
```
This is a 3x3 grid.
Pattern:
(0,2) is A
(1,0) is A, (1,1) is A
(2,1) is A
Rest are `.`.
Shape looks like a 'Z' or a specific symbol. Let's visualize:
. . #
# # .
. # .

**Example 2:**
Input:
```
. G . G X G .
. . G G . . .
A . . . . . G
G Y G W G . G
. . W G B G G
. G G G . G .
. . . . . . G
```
Grid size: 7x7.
Let's count the colors:
G (Green):
Row 1: 3
Row 2: 2
Row 3: 1
Row 4: 4
Row 5: 3
Row 6: 4
Row 7: 1
Total G: 3+2+1+4+3+4+1 = 18.

X (Grey): 1
A (Azure): 1
Y (Yellow): 1
W (Maroon): 2
B (Blue): 1

Dominant color: **G (Green)** with 18 occurrences.

Output:
```
. A A
. A .
. A .
```
This is a 3x3 grid.
Pattern:
(0,1) is A, (0,2) is A
(1,1) is A
(2,1) is A
Rest are `.`.
Shape looks like a '7' or a specific symbol.
. # #
. # .
. # .

**3. Synthesize the Transformation Rule:**
1.  **Count Frequencies**: Count the number of cells for each color in the 7x7 input grid.
2.  **Identify Dominant Color**: Find the color with the highest count.
3.  **Map Color to Pattern**: There is a mapping from the dominant color to a specific 3x3 pattern drawn in Azure (`A`) on a black (`.`) background.
    *   Blue (B) -> Pattern 1:
        . . A
        A A .
        . A .
    *   Green (G) -> P

... [8056 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.33)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 596: "A reflection pool mirrors what stands at its edge, rippling ... [20 chars truncated]" k=2 alts: 0/15 9b30e358

Training Examples

Example 1

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Output

Example 2

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Output

Literal Description

See: The input grid is divided into two regions: an upper region filled entirely with a single background color, and a lower region containing a multi-colored pattern anchored to the bottom of the grid. The pattern region consists of the bottommost rows that contain at least one non-background color. The background color is the color that fills the upper region completely.

Do: 1. Identify the background color: the color that fills the top rows uniformly. 2. Identify the pattern: the contiguous block of rows at the bottom of the grid that contain non-background pixels. Call this block P, with P[0] being the topmost pattern row and P[n-1] being the bottommost. 3. Count the number of blank rows above the pattern (rows filled entirely with the background color). 4. Fill the blank rows by tiling the pattern upward, cycling through the pattern rows in reverse. Starting from the blank row immediately above the pattern, assign it the last row of P, the next blank row up gets the second-to-last row of P, and so on. When you exhaust the pattern rows, wrap around and continue from the last row of P again. 5. Keep the original pattern rows in place at the bottom.

Grid: The grid dimensions vary across instances. The width and height are not fixed. The output grid has the same dimensions as the input grid. The pattern occupies the bottom portion and the remaining rows above are filled by tiling the pattern upward with wraparound.

Figurative Descriptions (16 variants)

"A reflection pool mirrors what stands at its edge, rippling upward into the sky."

qwen3.5-122b: k=2

See: A quiet, empty expanse of still water stretches across the upper portion of the world. At the shore along the bottom edge, a colorful monument stands — a small sculptural arrangement of vivid tiles rising from the earth. The water above is perfectly calm, showing nothing yet, waiting to be disturbed.

Do: The monument at the water's edge gazes down into the pool and sees its own reflection climbing upward through the stillness. The reflection doesn't simply mirror once — it keeps echoing, like a stone's ripple that never fades. The monument's image scrolls upward through the water, its bottom reaching up first, then its middle, then its top, and when the whole shape has appeared, it begins again from the bottom, endlessly tiling its echo toward the horizon. The original monument never moves — it remains planted at the shore while its ghost fills every empty inch of sky-water above.

Grid: The world varies in size but the shore is always at the bottom. The still water is one uniform color. The monument is the cluster of living colors rooted to the bottom edge. After the reflection, every row of water has been claimed by the monument's upward echo, and the world is the same size as before.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (11171 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** "Quiet, empty expanse of still water stretches across the upper portion... At the shore along the bottom edge, a colorful monument stands".
*   **Action:** "The monument at the water's edge gazes down into the pool and sees its own reflection climbing upward... The monument's image scrolls upward through the water... endlessly tiling its echo toward the horizon."
*   **Constraint:** "The original monument never moves — it remains planted at the shore while its ghost fills every empty inch of sky-water above."
*   **Grid details:** "The world varies in size but the shore is always at the bottom. The still water is one uniform color. The monument is the cluster of living colors rooted to the bottom edge. After the reflection, every row of water has been claimed by the monument's upward echo, and the world is the same size as before."

**Interpretation:**
*   **Input Grid:** Contains a background color (water) in the upper rows and a pattern (monument) in the lower rows.
*   **Transformation:** The pattern at the bottom is repeated upwards to fill the entire grid.
*   **Direction:** The pattern starts from the bottom and repeats upwards.
*   **Mechanism:** It looks like a vertical tiling or repetition of the bottom section.
*   **Key phrase:** "The monument's image scrolls upward... endlessly tiling its echo". This suggests the bottom pattern is the source, and it repeats to fill the space above.
*   **Key phrase:** "The original monument never moves". This implies the bottom rows of the output should match the bottom rows of the input.
*   **Key phrase:** "The world is the same size as before". Input and Output dimensions are identical.

**2. Analyze the Training Examples:**

**Example 1:**
*   **Input:** 10 rows, 5 columns.
    *   Rows 0-4: All 'X' (grey).
    *   Rows 5-9: A pattern involving 'R' (red) and 'A' (azure).
    *   Row 5: `X R R R X`
    *   Row 6: `X X R X X`
    *   Row 7: `X A A X X`
    *   Row 8: `X X A A X`
    *   Row 9: `X X A X X`
*   **Output:** 10 rows, 5 columns.
    *   Row 0: `X R R R X` (Matches Input Row 5)
    *   Row 1: `X X R X X` (Matches Input Row 6)
    *   Row 2: `X A A X X` (Matches Input Row 7)
    *   Row 3: `X X A A X` (Matches Input Row 8)
    *   Row 4: `X X A X X` (Matches Input Row 9)
    *   Row 5: `X R R R X` (Matches Input Row 5)
    *   Row 6: `X X R X X` (Matches Input Row 6)
    *   Row 7: `X A A X X` (Matches Input Row 7)
    *   Row 8: `X X A A X` (Matches Input Row 8)
    *   Row 9: `X X A X X` (Matches Input Row 9)
*   **Observation:** The bottom 5 rows (the "monument") are repeated to fill the top 5 rows. The pattern height seems to be 5 rows. The input had 5 rows of background 'X' and 5 rows of pattern. The output replaces the background rows with the pattern rows, repeating the pattern from the bottom up.
*   **

... [8177 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 645: "A shadow falls beneath everything that floats." k=3 alts: 0/0 a79310a0

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 a black (.) background with a single connected shape made of azure (A) cells. The shape can be any configuration (single cell, square block, line, L-shape, etc.) and is positioned somewhere within the grid.

Do: 1. Identify all azure (A) cells in the input grid. 2. Move every azure cell down by exactly one row. 3. Change the color of each moved cell from azure (A) to red (R). 4. Set all original azure positions to black (.) background. The output grid has the same dimensions as the input, with the shape shifted one row downward and recolored red.

Grid: The grid dimensions match the input exactly. The background is black (.). The grid is large enough that the azure shape, when shifted down by one row, remains within bounds.

Figurative Descriptions (1 variants)

"A shadow falls beneath everything that floats."

qwen3.5-122b: k=3

See: Against a night sky, an azure cloud drifts somewhere above the ground — it may be a wisp, a broad bank, or a towering column.

Do: As the sun passes overhead, the cloud casts its shadow directly below itself. The cloud dissolves into clear sky, and where its shadow lands, the ground glows red with the warmth it absorbed.

Grid: The sky is uniformly dark. The red warmth appears just beneath where the azure cloud once hung — same shape, same size, one step closer to the earth.

qwen3.5-122b — MARC valid, solved with 3 examples

Input

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Prediction

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Expected

Reasoning (10729 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** Night sky (dark background), Azure cloud (A), Ground.
*   **Action:** Sun passes overhead, cloud casts shadow directly below.
*   **Result:** Cloud dissolves (disappears), shadow lands on ground, ground glows red (R).
*   **Grid details:** Sky is uniformly dark (black `.`). Red warmth appears just beneath where the azure cloud once hung. Same shape, same size, one step closer to the earth.
*   **Key implication:** The Azure pixels (`A`) move down by one row and change color to Red (`R`). The original `A` pixels become black (`.`).

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input:
        ```
        . A .
        . . .
        . . .
        ```
    *   Output:
        ```
        . . .
        . R .
        . . .
        ```
    *   Observation: The `A` at (0, 1) moved to (1, 1) and became `R`. The original position became `.`.

*   **Example 2:**
    *   Input:
        ```
        A A . . .
        A A . . .
        . . . . .
        . . . . .
        . . . . .
        ```
    *   Output:
        ```
        . . . . .
        R R . . .
        R R . . .
        . . . . .
        . . . . .
        ```
    *   Observation: The block of `A`s at rows 0 and 1 moved down to rows 1 and 2. They changed color to `R`. The original `A` positions became `.`.
    *   Wait, let's look closer.
    *   Input `A`s: (0,0), (0,1), (1,0), (1,1).
    *   Output `R`s: (1,0), (1,1), (2,0), (2,1).
    *   Transformation: Every `A` at $(r, c)$ becomes `R` at $(r+1, c)$. The original `A` at $(r, c)$ becomes `.`.
    *   This matches the "one step closer to the earth" description (assuming row 0 is top/sky and row N is bottom/ground).

*   **Example 3:**
    *   Input:
        ```
        . . . . .
        . A A A .
        . . . . .
        . . . . .
        . . . . .
        ```
    *   Output:
        ```
        . . . . .
        . . . . .
        . R R R .
        . . . . .
        . . . . .
        ```
    *   Observation: `A`s at row 1 moved to row 2. Color changed to `R`.
    *   Transformation: $A(r, c) \rightarrow R(r+1, c)$.

**3. Conceptual Digestion:**

1.  **CAST:**
    *   **Background:** Black (`.`) represents the sky/ground void.
    *   **Agent:** Azure (`A`) represents the cloud.
    *   **Effect:** Red (`R`) represents the shadow/warmth on the ground.
2.  **AFFORDANCES:**
    *   `A` can move down one cell.
    *   `A` can change color to `R` upon moving.
    *   The space vacated by `A` becomes `.`.
3.  **TRANSFORMATION RULE:**
    *   Iterate through the grid.
    *   If a cell contains `A`, place an `R` in the cell directly below it (row + 1, same column).
    *   Set the original cell containing `A` to `.`.
    *   All other cells remain `.` (or whatever they were, but in these examples, the background is always `.`).
    *   *Constraint Check:* What i

... [7774 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.04)

Prediction

Expected

Figurative + 3 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 663: "Seeds planted in a garden plot grow into bushes whose size d ... [41 chars truncated]" k=2 alts: 0/0 ac0a08a4

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 3×3 grid with a black background. Some cells contain colored pixels (non-black) and the rest are black. The colored pixels are scattered at various positions within the grid.

Do: 1. Count the number of non-black cells in the input grid. Call this count N. 2. Create an output grid of size (3×N) rows by (3×N) columns, filled entirely with black. 3. For each cell (r, c) in the input grid, if it contains a non-black color, fill an N×N block in the output grid starting at row r×N, column c×N with that color.

Grid: The input is always a 3×3 grid. The output grid dimensions are (3×N) by (3×N), where N is the number of non-black cells in the input. The background is black. Each non-black cell from the input maps to an N×N solid block of its color, positioned by scaling the original row and column coordinates by N.

Figurative Descriptions (1 variants)

"Seeds planted in a garden plot grow into bushes whose size depends on how many were planted together."

qwen3.5-122b: k=2

See: A small 3×3 garden plot sits in darkness. A few colored seeds have been scattered across its soil, each claiming a cell, while the remaining cells lie fallow and black.

Do: The seeds sense one another — the more companions planted, the more ambitious each one grows. Every seed swells into a square bush, and the entire garden expands to accommodate their collective ambition. Each bush takes root exactly where its seed was sown, just scaled up to the new garden's proportions.

Grid: The garden grows in lockstep with the seeds' count: more seeds mean a bigger garden and bigger bushes alike. Empty patches of soil scale up too, preserving the original spacing. The harvest mirrors the planting — same layout, grander scale.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (11530 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Input:** A small 3x3 grid ("garden plot"). Some cells have colored seeds (non-black), others are black (fallow).
*   **Transformation:**
    *   "Seeds sense one another — the more companions planted, the more ambitious each one grows." -> This suggests the scaling factor depends on the number of seeds.
    *   "Every seed swells into a square bush" -> Each colored cell becomes a square block of that color.
    *   "The entire garden expands to accommodate their collective ambition." -> The output grid size is larger than the input grid size.
    *   "Each bush takes root exactly where its seed was sown, just scaled up to the new garden's proportions." -> The relative positions are preserved, but the cells are expanded.
    *   "The garden grows in lockstep with the seeds' count: more seeds mean a bigger garden and bigger bushes alike." -> This is the key rule. The scaling factor $k$ seems to be related to the number of colored seeds $N$.
    *   "Empty patches of soil scale up too, preserving the original spacing." -> Black cells also expand into $k \times k$ blocks of black.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input: 3x3 grid.
        ```
        . Y .
        . . A
        M . .
        ```
    *   Colored cells: Y (0,1), A (1,2), M (2,0). Total seeds $N = 3$.
    *   Output: 9x9 grid.
        ```
        . . . Y Y Y . . .
        . . . Y Y Y . . .
        . . . Y Y Y . . .
        . . . . . . A A A
        . . . . . . A A A
        . . . . . . A A A
        M M M . . . . . .
        M M M . . . . . .
        M M M . . . . . .
        ```
    *   Observation: The input is 3x3. The output is 9x9.
    *   Each cell in the input becomes a $3 \times 3$ block in the output.
    *   Scaling factor $k = 3$.
    *   Number of seeds $N = 3$.
    *   Hypothesis: Scaling factor $k = N$.

*   **Example 2:**
    *   Input: 3x3 grid.
        ```
        R . .
        . . O
        . . .
        ```
    *   Colored cells: R (0,0), O (1,2). Total seeds $N = 2$.
    *   Output: 6x6 grid.
        ```
        R R . . . .
        R R . . . .
        . . . . O O
        . . . . O O
        . . . . . .
        . . . . . .
        ```
    *   Observation: The input is 3x3. The output is 6x6.
    *   Each cell in the input becomes a $2 \times 2$ block in the output.
    *   Scaling factor $k = 2$.
    *   Number of seeds $N = 2$.
    *   Hypothesis confirmed: Scaling factor $k = N$ (number of non-black cells in the input grid).

**3. Conceptual Digestion:**

1.  **CAST:**
    *   **Seeds:** Colored cells (non-black) in the input grid.
    *   **Soil:** Black cells (.) in the input grid.
    *   **Garden:** The grid itself.
    *   **Bushes:** The expanded colored blocks in the output grid.

2.  **AFFORDANCES:**
    *   Seeds determine the scale of t

... [8602 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.01)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 674: "Loyal pets hear their owner's whistle and come running home." k=1 alts: 4/15 ae3edfdc

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 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."

qwen3.5-122b: 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.

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (10919 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A 15x15 dark field (black dots `.`).
*   **Homes:** Two homes, one Blue (`B`), one Red (`R`).
*   **Pets:**
    *   Blue owner keeps Orange (`O`) cats.
    *   Red owner keeps Green (`G`) dogs.
*   **Movement:** Pets wander off along roads (rows and columns) from their homes.
*   **Strays:** Some animals roam the field but belong to nobody (wrong color for the home, or maybe just extra pets).
*   **Action:** Owners call pets home.
*   **Pet Behavior:** Pets bolt straight back along the road (row/column) they came from. They stop at the "yard" — the very first patch of grass next to the front door.
*   **Stray Behavior:** Strays vanish (disappear).
*   **Result:** Only homes and their returned pets remain. Pets huddle as close as possible, one on each side they returned from.

**2. Analyze the Training Example:**
*   **Input:**
    *   Grid size: 15x15.
    *   Blue Home (`B`) at (2, 3) (0-indexed: row 2, col 3).
    *   Red Home (`R`) at (10, 11).
    *   Orange (`O`) pets:
        *   (0, 3) - Same column as B, above.
        *   (2, 0) - Same row as B, left.
        *   (2, 9) - Same row as B, right.
        *   (8, 3) - Same column as B, below.
    *   Green (`G`) pets:
        *   (10, 5) - Same row as R, left.
        *   (14, 11) - Same column as R, below.
    *   Other `O` or `G`? No other colors mentioned in the text, but let's check the grid.
    *   Wait, let's look at the input grid provided in Example 1.
        *   Row 0: `O` at col 3.
        *   Row 2: `O` at col 0, `B` at col 3, `O` at col 9.
        *   Row 8: `O` at col 3.
        *   Row 10: `G` at col 5, `R` at col 11.
        *   Row 14: `G` at col 11.
    *   So, `B` is at (2,3). `R` is at (10,11).
    *   `O`s are at (0,3), (2,0), (2,9), (8,3). All are in the same row or column as `B`.
    *   `G`s are at (10,5), (14,11). All are in the same row or column as `R`.
    *   Are there any strays? The description says "A few stray animals roam the field too". In Example 1, all `O`s are associated with `B` and all `G`s with `R`. There are no `O`s near `R` or `G`s near `B`. Wait, let's check the output.
*   **Output:**
    *   `B` remains at (2,3).
    *   `R` remains at (10,11).
    *   `O`s are now at:
        *   (1, 3) - Above `B`.
        *   (2, 2) - Left of `B`.
        *   (2, 4) - Right of `B`.
        *   (3, 3) - Below `B`.
    *   `G`s are now at:
        *   (10, 10) - Left of `R`.
        *   (11, 11) - Below `R`.
    *   All other cells are `.`.
    *   Wait, looking closely at the output grid for Example 1:
        *   Row 1: `O` at col 3. (Was at 0,3). Moved to adjacent cell (1,3).
        *   Row 2: `O` at col 2, `B` at col 3, `O` at col 4. (Was at 2,0 and 2,9). Moved to adjacent cells (2,2) and (2,4).
        *   Row 3: `O` at col 3. (Was at 8,3). Moved to adjacent cell (3,3).
      

... [7982 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 679: "Each neighborhood votes, and the winning party's flag flies ... [15 chars truncated]" k=2 alts: 0/0 af24b4cc

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 contains six 3x2 rectangular blocks of colored cells, arranged in a 2-row by 3-column layout. The blocks are separated and surrounded by black (.) cells, forming a grid with black borders and black dividers between blocks. Each block is exactly 2 cells wide and 3 cells tall. Within each block, one color dominates (appears in the majority of the 6 cells), while one or two cells contain a different 'impurity' color.

Do: For each of the six blocks, count the occurrences of each color within that block's 6 cells. Identify the majority (most frequent) color. Replace the entire block with a single cell of that majority color. Arrange these six reduced cells in the same 2-row by 3-column layout as the original blocks, surrounded by a single-cell-wide black (.) border. The result is a 4x5 output grid.

Grid: The input grid is 10 columns by 9 rows. It consists of a 2x3 arrangement of 2-wide by 3-tall blocks, with 1-cell-wide black separators and borders throughout. The output grid is 5 columns by 4 rows: a single-cell black border surrounding a 3-wide by 2-tall interior, where each cell corresponds to the majority color of the respective block from the input.

Figurative Descriptions (1 variants)

"Each neighborhood votes, and the winning party's flag flies over city hall."

qwen3.5-122b: k=2

See: A city is divided into six neighborhoods by dark rivers. Each neighborhood is home to citizens of various colors, but in every district one color clearly outnumbers the rest — a few dissidents or immigrants live among the majority, but the dominant tribe holds sway.

Do: Hold an election in each neighborhood. The color with the most citizens wins the seat. Shrink each bustling district down to a single flag flying its winning color. Arrange the six victory flags in the same district layout on a small memorial plaque, framed by the dark rivers that once divided them.

Grid: The sprawling city map spans ten streets wide and nine avenues tall, its six neighborhoods nestled in a two-row, three-column arrangement with dark river channels flowing between them. The memorial plaque is a modest five-by-four tile — dark border enclosing six winning flags, each one the voice of a whole neighborhood distilled to a single proud color.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (9941 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Input:** A "city" map, 10 streets wide (columns) and 9 avenues tall (rows).
*   **Structure:** Six neighborhoods arranged in a 2-row, 3-column layout.
*   **Separators:** "Dark rivers" divide the neighborhoods. In the grid, these are represented by black dots (`.`).
*   **Content:** Each neighborhood has citizens of various colors. One color is dominant (majority).
*   **Task:** "Hold an election" -> Find the most frequent color in each neighborhood.
*   **Output:** A "memorial plaque" (5x4 grid).
*   **Output Structure:** Dark border enclosing six winning flags. The flags are arranged in the same district layout (2 rows, 3 columns).
*   **Dimensions:**
    *   Input: 10x9.
    *   Output: 5x4.
    *   Wait, let's look at the training examples to verify dimensions.

**2. Analyze Training Examples:**

**Example 1:**
Input:
```
. . . . . . . . . .
. B B . X X . Y Y .
. B B . G G . Y Y .
. G G . X X . Y A .
. . . . . . . . . .
. R R . O B . W W .
. R R . O O . B W .
. R R . O B . W W .
. . . . . . . . . .
```
Input Dimensions: 9 rows, 10 columns.
The description says "ten streets wide and nine avenues tall". This matches.
The "dark rivers" seem to be the rows and columns of `.` that separate the blocks.
Let's identify the blocks.
Row 0: All `.`
Row 1: `. B B . X X . Y Y .` -> Blocks seem to be columns 1-2, 4-5, 7-8.
Row 2: `. B B . G G . Y Y .`
Row 3: `. G G . X X . Y A .`
Row 4: All `.`
Row 5: `. R R . O B . W W .`
Row 6: `. R R . O O . B W .`
Row 7: `. R R . O B . W W .`
Row 8: All `.`

So the grid is divided into 6 rectangular regions by the `.` lines.
Top-Left (TL): Rows 1-3, Cols 1-2.
Top-Middle (TM): Rows 1-3, Cols 4-5.
Top-Right (TR): Rows 1-3, Cols 7-8.
Bottom-Left (BL): Rows 5-7, Cols 1-2.
Bottom-Middle (BM): Rows 5-7, Cols 4-5.
Bottom-Right (BR): Rows 5-7, Cols 7-8.

Let's check the Output for Example 1:
```
. . . . .
. B X Y .
. R O W .
. . . . .
```
Output Dimensions: 4 rows, 5 columns.
Row 0: `. . . . .` (Border)
Row 1: `. B X Y .` (Top row of flags)
Row 2: `. R O W .` (Bottom row of flags)
Row 3: `. . . . .` (Border)

The output is a 4x5 grid.
The inner content is 2x3.
The border is `.`.
The inner cells correspond to the dominant color of the 6 neighborhoods.

Let's verify the dominant colors for Example 1.
**TL (Rows 1-3, Cols 1-2):**
(1,1)=B, (1,2)=B
(2,1)=B, (2,2)=B
(3,1)=G, (3,2)=G
Counts: B=4, G=2. Winner: **B**.
Output (1,1) is B. Matches.

**TM (Rows 1-3, Cols 4-5):**
(1,4)=X, (1,5)=X
(2,4)=G, (2,5)=G
(3,4)=X, (3,5)=X
Counts: X=4, G=2. Winner: **X**.
Output (1,2) is X. Matches.

**TR (Rows 1-3, Cols 7-8):**
(1,7)=Y, (1,8)=Y
(2,7)=Y, (2,8)=Y
(3,7)=Y, (3,8)=A
Counts: Y=5, A=1. Winner: **Y**.
Output (1,3) is Y. Matches.

**BL (Rows 5-7, Cols 1-2):**
(5,1)=R, (5,2)=R
(6,1)=R, (6,2)=R
(7,1)=R, (7,2)=R
Counts: R=6. Winner: **R**.
Output (2,1) is R. Matches.

**BM (

... [6959 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 684: "A rain gauge measures the empty sky above the waterline." k=2 alts: 0/0 b0c4d837

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Example 5

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Example 6

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Literal Description

See: The input grid contains a bucket or container made of grey (X) cells. The container is open at the top and closed at the bottom and sides. Inside the container, the lower portion is filled with azure (A) cells and the upper portion is empty (black/dot cells). The rest of the grid outside the container is also black.

Do: 1. Locate the grey (X) container in the input grid. 2. Identify the interior of the container (the rectangular region enclosed by the grey walls, excluding the walls themselves). 3. Count the number of completely empty rows inside the container (rows that contain only black/dot cells, above the azure fill). Call this count N. 4. Create a 3×3 output grid filled entirely with black (dot) cells. 5. Place N azure (A) cells into the output grid in reading order (left to right, top to bottom), starting at the top-left corner. All remaining cells stay black.

Grid: The output grid is always 3×3. The background color is black (dot). Azure (A) cells appear starting from the top-left corner and fill in reading order (left to right, top to bottom). The number of azure cells ranges from 0 to 9, determined by the number of empty interior rows in the input container.

Figurative Descriptions (1 variants)

"A rain gauge measures the empty sky above the waterline."

qwen3.5-122b: k=2

See: A grey stone well sits in a dark field. Azure water has partially filled the well from the bottom up, but the upper part of the well is dry — open air between the water's surface and the rim.

Do: Read the well like a rain gauge in reverse: count the layers of empty air trapped above the waterline inside the stone walls. Each breath of empty air becomes a single azure droplet that falls onto a small 3×3 tray, pooling from the top-left corner and flowing in reading order — left to right, row by row — like water filling an ice-cube tray one cell at a time.

Grid: The tray is always a 3×3 darkness. Azure droplets land one by one starting at the top-left, spilling across each row before dripping to the next. The emptier the well, the more droplets condense on the tray.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (11080 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A grey stone well in a dark field. Azure water partially filled from the bottom up. Upper part is dry (empty air).
*   **Task:** Read the well like a rain gauge in reverse. Count the layers of empty air trapped above the waterline inside the stone walls.
*   **Output Mechanism:** Each breath of empty air becomes a single azure droplet.
*   **Output Grid:** A 3x3 tray (darkness/black background).
*   **Filling Order:** Azure droplets land one by one starting at the top-left, spilling across each row before dripping to the next (reading order: left-to-right, top-to-bottom).
*   **Relationship:** "The emptier the well, the more droplets condense on the tray." This implies the number of droplets corresponds to the amount of empty space (air) inside the well structure.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   **Input:** 9x9 grid.
        *   Background: `.` (black)
        *   Walls: `X` (grey) forming a U-shape or container.
        *   Water: `A` (azure) filling the bottom part of the container.
        *   Structure:
            *   Row 0-1: Empty
            *   Row 2: `X` at col 2 and 6.
            *   Row 3: `X` at col 2 and 6.
            *   Row 4: `X` at col 2, `A` at 3,4,5, `X` at 6.
            *   Row 5: `X` at col 2, `A` at 3,4,5, `X` at 6.
            *   Row 6: `X` at col 2, `A` at 3,4,5, `X` at 6.
            *   Row 7: `X` at col 2, `A` at 3,4,5, `X` at 6.
            *   Row 8: `X` at col 2,3,4,5,6.
        *   The "well" is defined by the `X` walls. The interior is columns 3, 4, 5. Rows 4 to 8 contain the well structure.
        *   Water (`A`) occupies rows 4, 5, 6, 7 in columns 3, 4, 5.
        *   Wait, let's look closer at the "empty air" part.
        *   The well walls are `X`. The water is `A`.
        *   The "well" seems to be the rectangular region enclosed by `X`.
        *   In Example 1:
            *   Top of walls: Row 2.
            *   Bottom of walls: Row 8.
            *   Left wall: Col 2.
            *   Right wall: Col 6.
            *   Interior width: Cols 3, 4, 5 (3 cells wide).
            *   Interior height: Rows 2 to 8 (7 rows high).
            *   Water level: Rows 4, 5, 6, 7 are filled with `A`. Row 8 is the floor (`X`).
            *   So water occupies 4 rows of the interior.
            *   Empty air occupies Rows 2 and 3 inside the walls. That is 2 rows of empty space.
            *   Total interior cells = 3 columns * 7 rows = 21 cells.
            *   Water cells = 3 columns * 4 rows = 12 cells.
            *   Air cells = 3 columns * 2 rows = 6 cells.
        *   **Output:** 3x3 grid.
            *   `A A .`
            *   `. . .`
            *   `. . .`
            *   Total `A`s = 2.
        *   **Hypothesis:** The number of `A`s in the output corresponds to the number of *rows* of empty air 

... [8086 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.89)

Prediction

Expected

Figurative + 2 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

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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."

qwen3.5-122b: 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.

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (9166 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Background:** "Orange lake" -> Orange cells (O) are the background/water.
*   **Objects:** "Sculptures made of magenta clay" -> Magenta cells (M) form connected shapes.
*   **Agents:** "Droplets of vivid color" -> Single cells of colors other than Orange (O) and Magenta (M). Examples given: Green (G), Yellow (Y), Blue (B).
*   **Action:**
    *   Droplets reach out to what they touch.
    *   If a droplet touches a clay sculpture (M), the sculpture absorbs the color.
    *   "Every cell of connected clay transforms to match the dye." -> This implies connected components of M change color if adjacent to a specific droplet color.
    *   "The droplet, spent, dissolves back into the orange water and vanishes." -> Droplet cells become Orange (O).
    *   "Droplets that float alone, touching no sculpture, simply sink and disappear without a trace." -> Droplets not touching M become Orange (O).
    *   "Any sculpture that no droplet touched remains its original magenta clay." -> M cells not adjacent to any droplet stay M.
*   **Summary of Transformation:**
    1.  Identify connected components of Magenta (M).
    2.  Identify single cells of other colors (let's call them "Dyes").
    3.  Check adjacency between Dyes and M components.
    4.  If a Dye cell is adjacent (orthogonally, presumably) to an M component:
        *   All M cells in that connected component change to the Dye's color.
        *   The Dye cell itself changes to Orange (O).
    5.  If a Dye cell is not adjacent to any M component:
        *   The Dye cell changes to Orange (O).
    6.  M components not adjacent to any Dye remain M.
    7.  Orange (O) cells remain Orange (O).

**2. Analyze Training Example 1:**
Input:
O M M G O
O O O Y O
O O O M O
O O M M M
O O O M O

Grid:
(0,0)O (0,1)M (0,2)M (0,3)G (0,4)O
(1,0)O (1,1)O (1,2)O (1,3)Y (1,4)O
(2,0)O (2,1)O (2,2)O (2,3)M (2,4)O
(3,0)O (3,1)O (3,2)M (3,3)M (3,4)M
(4,0)O (4,1)O (4,2)O (4,3)M (4,4)O

Magenta Components:
1.  Top-left cluster: (0,1), (0,2).
    *   Adjacent to G at (0,3).
    *   Adjacent to Y at (1,3)? No, (0,2) is adjacent to (0,3)G. (0,2) is adjacent to (1,2)O. (0,1) is adjacent to (1,1)O.
    *   Wait, let's look at connectivity.
    *   M at (0,1) connects to M at (0,2).
    *   M at (0,2) is adjacent to G at (0,3).
    *   So this component should turn Green.
2.  Bottom cluster: (2,3), (3,2), (3,3), (3,4), (4,3).
    *   (2,3) connects to (3,3).
    *   (3,2) connects to (3,3).
    *   (3,3) connects to (3,4).
    *   (3,3) connects to (4,3).
    *   This is one large connected component.
    *   Is it adjacent to any dye?
    *   (2,3) is adjacent to Y at (1,3).
    *   So this component should turn Yellow.

Dyes:
*   G at (0,3). Adjacent to M component 1. Becomes O.
*   Y at (1,3). Adjacent to M component 2. Becomes O.

Output:
O 

... [6346 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.67)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 723: "An elevator descending floor by floor — predict which ... [25 chars truncated]" k=2 alts: 0/0 ba1aa698

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 is divided into a row of equally-sized rectangular panels separated by single-width border lines of a uniform border color. Each panel has the same dimensions and is filled with a background color. Exactly one panel contains a small accent pattern (a distinct shape made of a third color) placed at a specific vertical position within the panel. The accent pattern appears once per panel, and its vertical position shifts downward by a constant step from one panel to the next (left to right). The horizontal position of the pattern within each panel remains the same.

Do: 1. Identify the border color (the color forming the grid lines separating panels) and the panel dimensions. 2. Segment the input into its constituent panels (excluding the shared border lines). 3. In each panel, locate the accent pattern (the cluster of cells that are neither the border color nor the background fill color) and record its vertical (row) position within the panel. 4. Determine the arithmetic progression: compute the constant vertical step between successive panels' pattern positions. 5. Extrapolate to find the next position in the sequence — i.e., add one more step beyond the last panel's pattern position. 6. Produce a single output panel (with its surrounding border) of the same dimensions as one input panel, containing the accent pattern placed at the extrapolated vertical position, with the same horizontal placement. All other cells in the output panel are filled with the background color, and the panel is framed by the border color.

Grid: The output grid has the dimensions of a single panel from the input, including its surrounding single-cell-wide border. Specifically, if each panel's interior is H rows by W columns, the output is (H+2) rows by (W+2) columns. The outermost ring of cells is the border color. The interior is filled with the background color except where the accent pattern is placed at the extrapolated position.

Figurative Descriptions (1 variants)

"An elevator descending floor by floor — predict which floor it arrives at next."

qwen3.5-122b: k=2

See: A building's facade is split into adjacent shafts, each one a tall column of identical rooms framed by structural beams. A single glowing elevator cab rides somewhere inside each shaft. Glancing left to right, the cab sits a little lower in each successive shaft — it's descending at a steady pace, one stop at a time, like a metronome ticking downward.

Do: Watch the elevator drop from shaft to shaft and feel its rhythm. It falls the same number of floors between each stop. Now the building extends by one more shaft to the right — where does the elevator land? Let it keep falling at the same tempo and place it on the next floor down. Build that final shaft with the cab resting at its predicted stop.

Grid: The output is a single shaft — one column of rooms wrapped in its structural beams. Every room is empty except the one where the elevator comes to rest after continuing its steady descent one stop beyond the last shaft you observed.

qwen3.5-122b — MARC valid, solved with 2 examples

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Prediction

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Reasoning (11220 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A building facade split into adjacent shafts (columns).
*   **Structure:** Each shaft is a tall column of identical rooms framed by structural beams.
*   **Object:** A single glowing elevator cab rides inside each shaft.
*   **Pattern:** The cab sits a little lower in each successive shaft (left to right). It descends at a steady pace (one stop at a time).
*   **Task:** The building extends by one more shaft to the right. I need to predict where the elevator lands in this new shaft.
*   **Output:** A single shaft (one column of rooms) with the elevator at the predicted stop.
*   **Key Insight:** The input grid contains multiple shafts side-by-side. The output grid should be a single shaft representing the *next* step in the sequence. The "elevator" is a specific pattern of pixels inside the shaft. The "structural beams" are the borders.

**2. Analyze the Training Examples:**

**Example 1:**
*   **Input:**
    *   Grid size: 16 rows x 21 columns.
    *   Structure: There are vertical columns of 'B' (blue) acting as separators/borders.
    *   Let's count the shafts.
    *   Row 0: All 'B'.
    *   Row 15: All 'B'.
    *   Columns 0, 5, 10, 15, 20 seem to be 'B'.
    *   So, shafts are between these 'B' columns.
    *   Shaft 1: Cols 1-4 (width 4).
    *   Shaft 2: Cols 6-9 (width 4).
    *   Shaft 3: Cols 11-14 (width 4).
    *   Shaft 4: Cols 16-19 (width 4).
    *   Total 4 shafts visible in the input.
    *   Content inside shafts: Mostly 'R' (red).
    *   Special pattern (Elevator): 'G' (green) pixels.
    *   Let's locate the 'G' pixels in each shaft.
        *   Shaft 1 (Cols 1-4): Row 2 has 'G G' at cols 2-3. (0-indexed rows: Row 2). Wait, let's look closer.
        *   Row 0: B...
        *   Row 1: B R R R R B ...
        *   Row 2: B R G G R B ... -> 'G' at (2, 2) and (2, 3).
        *   Row 3: B R R R R B ...
        *   ...
        *   Shaft 2 (Cols 6-9):
        *   Row 3: B R G G R B ... -> 'G' at (3, 7) and (3, 8).
        *   Shaft 3 (Cols 11-14):
        *   Row 4: B R G G R B ... -> 'G' at (4, 12) and (4, 13).
        *   Shaft 4 (Cols 16-19):
        *   Row 5: B R G G R B ... -> 'G' at (5, 17) and (5, 18).
    *   Pattern of 'G' (Elevator):
        *   Shaft 1: Row 2.
        *   Shaft 2: Row 3.
        *   Shaft 3: Row 4.
        *   Shaft 4: Row 5.
    *   The elevator descends by 1 row for each shaft to the right.
    *   The elevator shape is a 1x2 horizontal block of 'G's.
    *   The background is 'R'. The frame is 'B'.
*   **Output:**
    *   Grid size: 16 rows x 6 columns.
    *   Structure: One shaft. Width 4 + 2 borders = 6 columns.
    *   Content: Background 'R', Frame 'B'.
    *   Elevator position:
        *   Input had 4 shafts. Elevator rows were 2, 3, 4, 5.
        *   Next shaft (5th) should have elevator at Row 6.
        *

... [8274 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 2 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: 7/15 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."

qwen3.5-122b: 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.

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

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Reasoning (12323 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A grey wall divides two rooms.
*   **Left Room:** A blue vault door with gaps (empty keyholes).
*   **Right Room:** A colored key floating in darkness.
*   **Action:** Slide the key into the lock.
*   **Condition:** If every tooth fits perfectly into every keyhole (no extra teeth, no empty holes), the key merges with the vault door.
*   **Result:**
    *   Match: The door is transformed (blue + key color).
    *   Mismatch: The vault stays sealed (unchanged).
*   **Grid Details:**
    *   Grey wall (`X`) is in the center.
    *   Vault door is blue (`B`) with dark gaps (`.`).
    *   Key is a single color (e.g., `M`, `R`, etc.).

**2. Analyze the Training Example:**
*   **Input:**
    ```
    B B B B X . . . .
    B . . B X . M M .
    B . . B X . M M .
    B B B B X . . . .
    ```
    *   Left side (Lock): 4x4 grid.
        *   Row 0: `B B B B`
        *   Row 1: `B . . B`
        *   Row 2: `B . . B`
        *   Row 3: `B B B B`
        *   This looks like a frame of `B` with a 2x2 hole of `.` in the middle.
    *   Separator: Column 4 is `X` (grey wall).
    *   Right side (Key): 4x4 grid.
        *   Row 0: `. . . .`
        *   Row 1: `. M M .`
        *   Row 2: `. M M .`
        *   Row 3: `. . . .`
        *   This looks like a 2x2 block of `M` (magenta) surrounded by `.`.
*   **Output:**
    ```
    B B B B
    B M M B
    B M M B
    B B B B
    ```
    *   The output is just the left side (the lock), but the `.` gaps are filled with the key color `M`.
    *   The separator `X` and the right side are gone.
    *   The transformation happened because the shape of the key (`M` block) matched the shape of the gaps (`.` block) in the lock.
    *   Lock gaps: Rows 1-2, Cols 1-2 (relative to left grid).
    *   Key shape: Rows 1-2, Cols 1-2 (relative to right grid).
    *   They match perfectly.

**3. Analyze the Test Input:**
*   **Input:**
    ```
    B B B B X R . . .
    . B B . X R R R R
    . B B . X R . . .
    . . . . X . . . .
    ```
*   **Dimensions:** 4 rows, 9 columns.
*   **Separator:** Column 4 is `X`.
*   **Left Side (Lock):** Columns 0-3 (4x4).
    *   Row 0: `B B B B`
    *   Row 1: `. B B .`
    *   Row 2: `. B B .`
    *   Row 3: `. . . .`
    *   Let's identify the "gaps" (`.`) inside the blue structure.
    *   Row 0: All `B`.
    *   Row 1: `.` at col 0, `B` at 1, `B` at 2, `.` at 3.
    *   Row 2: `.` at col 0, `B` at 1, `B` at 2, `.` at 3.
    *   Row 3: All `.`.
    *   Wait, the metaphor says "blue vault door has gaps cut into it". Usually, the `B` forms the structure and `.` forms the holes.
    *   In Example 1:
        *   Lock: `B B B B`, `B . . B`, `B . . B`, `B B B B`.
        *   Holes were the 2x2 `.` in the center.
        *   Key was 2x2 `M` in the center.
        *   Match -> Fill holes with `M`.
    *   In Test Input:
        *

... [9347 chars truncated]

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 742: "Two rivers flow toward each other and mark their confluence ... [10 chars truncated]" k=2 alts: 0/0 bdad9b1f

Training Examples

Example 1

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Example 2

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Literal Description

See: The input grid contains two short line segments on a black background: a vertical segment of azure (A) cells occupying part of one column, and a horizontal segment of red (R) cells occupying part of one row. These two segments do not overlap and are located in different rows and columns.

Do: 1. Identify the column containing the azure (A) segment and the row containing the red (R) segment. 2. Extend the azure segment to fill its entire column from top to bottom with azure (A). 3. Extend the red segment to fill its entire row from left to right with red (R). 4. At the cell where the azure column and red row intersect, place a yellow (Y) cell instead.

Grid: The grid is rectangular (6 rows by 6 columns in the examples) with a black (.) background. The output grid has the same dimensions as the input grid.

Figurative Descriptions (1 variants)

"Two rivers flow toward each other and mark their confluence with gold."

qwen3.5-122b: k=2

See: Two rivers have begun to carve their paths through a dark landscape — one azure stream trickling downward through a narrow channel, one red stream flowing sideways along a shallow bed. They have not yet met; each is still just a trickle, a promise of the full river to come.

Do: Each river yearns to complete its course. The azure river swells to fill its entire channel from source to mouth, running the full length of the land. The red river does the same, flooding its banks until it spans the entire breadth of the terrain. Where the two rivers finally converge — where vertical meets horizontal — a yellow sun rises at the confluence, marking the sacred crossing point.

Grid: The landscape is a rectangular dark plain. After the rivers have run their full courses, every cell along each river's path carries its color, except at the single crossing where yellow shines through.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (12326 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Context:** A dark landscape (black background, represented by `.`).
*   **Elements:**
    *   "Azure stream trickling downward": This implies a vertical line of Azure (`A`) pixels.
    *   "Red stream flowing sideways": This implies a horizontal line of Red (`R`) pixels.
    *   "They have not yet met": In the input, the lines are partial or disjoint.
    *   "Azure river swells to fill its entire channel": The vertical line of `A` should extend to cover the full height of the grid (or at least the column it is in).
    *   "Red river... flooding its banks until it spans the entire breadth": The horizontal line of `R` should extend to cover the full width of the grid (or at least the row it is in).
    *   "Where the two rivers finally converge... a yellow sun rises": The intersection point of the vertical `A` line and the horizontal `R` line becomes Yellow (`Y`).
*   **Goal:** Extend the partial lines to full lines across the grid dimensions, and mark the intersection with `Y`.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input:
        ```
        . A . . . .
        . A . . . .
        . . . . . .
        . . . . R R
        . . . . . .
        . . . . . .
        ```
        Grid size: 6 rows x 6 columns.
        Azure (`A`) is in column 1 (0-indexed) at rows 0 and 1.
        Red (`R`) is in row 3 at columns 4 and 5.
    *   Output:
        ```
        . A . . . .
        . A . . . .
        . A . . . .
        R Y R R R R
        . A . . . .
        . A . . . .
        ```
        Observation:
        *   The `A`s in column 1 have been extended to fill the entire column 1.
        *   The `R`s in row 3 have been extended to fill the entire row 3.
        *   The intersection is at (row 3, col 1). In the output, this cell is `Y`.
        *   Wait, looking closely at the output for Example 1:
            Row 0: `. A . . . .`
            Row 1: `. A . . . .`
            Row 2: `. A . . . .`
            Row 3: `R Y R R R R` -> The intersection is at (3, 1). It is `Y`. The rest of row 3 is `R`.
            Row 4: `. A . . . .`
            Row 5: `. A . . . .`
        *   So, Column 1 becomes all `A` except at the intersection. Row 3 becomes all `R` except at the intersection. The intersection is `Y`.

*   **Example 2:**
    *   Input:
        ```
        . . . . A .
        . . . . A .
        R R . . . .
        . . . . . .
        . . . . . .
        . . . . . .
        ```
        Grid size: 6 rows x 6 columns.
        Azure (`A`) is in column 4 at rows 0 and 1.
        Red (`R`) is in row 2 at columns 0 and 1.
    *   Output:
        ```
        . . . . A .
        . . . . A .
        R R R R Y R
        . . . . A .
        . . . . A .
        . . . . A .
        ```
        Observation:
        *   Column 4 is filled with `A`.
        *   Row 2 is fille

... [9329 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.44)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 786: "A fabric swatch dreams of becoming the whole bolt of cloth." k=2 alts: 3/15 ccd554ac

Training Examples

Example 1

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Example 2

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Example 3

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Example 4

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Example 5

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Example 6

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Literal Description

See: The input is a small grid of N rows by M columns containing a pattern made of one color and black (background) cells. The grid functions as a single tile or motif.

Do: Tile the input grid to fill a larger output grid by repeating it M times horizontally and N times vertically. That is, place copies of the input side by side to form a row of M tiles, then stack N such rows on top of each other. The result is an (N×N) by (M×M) output grid where the input pattern repeats seamlessly in both directions.

Grid: The input grid has dimensions N rows by M columns. The output grid has dimensions (N×N) rows by (M×M) columns. The number of horizontal repetitions equals M (the column count of the input) and the number of vertical repetitions equals N (the row count of the input). Colors are preserved exactly; no cells change color.

Figurative Descriptions (16 variants)

"A fabric swatch dreams of becoming the whole bolt of cloth."

qwen3.5-122b: k=2

See: A small swatch of fabric displays a motif woven from a single dye color against an undyed background. This fragment remembers the dimensions of the loom it was cut from.

Do: The swatch is placed on the loom and allowed to replicate itself — it knows how many times to repeat across the warp by counting its own columns, and how many times to stack along the weft by counting its own rows. The pattern propagates like a crystal growing from a seed, each copy seamlessly kissing its neighbor at the edges until the bolt is complete.

Grid: The seed swatch carries its own multiplication instructions in its shape. A wider swatch stretches further across; a taller swatch grows further down. The dye never bleeds or shifts — every copy is a perfect echo of the original.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

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Expected

Reasoning (11872 chars)

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

**1. Analyze the Metaphorical Description:**
*   "A small swatch of fabric displays a motif woven from a single dye color against an undyed background." -> There is a pattern (motif) and a background.
*   "This fragment remembers the dimensions of the loom it was cut from." -> The input grid size might be relevant, or the pattern size.
*   "The swatch is placed on the loom and allowed to replicate itself" -> Tiling / Repetition.
*   "it knows how many times to repeat across the warp by counting its own columns, and how many times to stack along the weft by counting its own rows." -> This is the crucial instruction.
    *   Number of horizontal repetitions = Number of columns in the input grid? Or number of columns in the pattern?
    *   Number of vertical repetitions = Number of rows in the input grid? Or number of rows in the pattern?
*   "The pattern propagates like a crystal growing from a seed, each copy seamlessly kissing its neighbor at the edges until the bolt is complete." -> Tiling the input grid to fill a larger area.
*   "A wider swatch stretches further across; a taller swatch grows further down." -> Confirms the dimensions determine the repetition count.
*   "The dye never bleeds or shifts — every copy is a perfect echo of the original." -> No modification of the pattern itself, just repetition.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input:
        ```
        . . A
        A A A
        A . .
        ```
        Dimensions: 3 rows, 3 columns.
    *   Output:
        ```
        . . A . . A . . A
        A A A A A A A A A
        A . . A . . A . .
        . . A . . A . . A
        A A A A A A A A A
        A . . A . . A . .
        . . A . . A . . A
        A A A A A A A A A
        A . . A . . A . .
        ```
        Dimensions: 9 rows, 9 columns.
    *   Observation:
        *   Input width = 3. Output width = 9. Repetition factor = 3.
        *   Input height = 3. Output height = 9. Repetition factor = 3.
        *   The output is the input grid tiled 3x3 times.
        *   Does the repetition count match the input dimensions? Yes, 3x3 input -> 3x3 tiling.

*   **Example 2:**
    *   Input:
        ```
        B .
        B B
        ```
        Dimensions: 2 rows, 2 columns.
    *   Output:
        ```
        B . B .
        B B B B
        B . B .
        B B B B
        ```
        Dimensions: 4 rows, 4 columns.
    *   Observation:
        *   Input width = 2. Output width = 4. Repetition factor = 2.
        *   Input height = 2. Output height = 4. Repetition factor = 2.
        *   The output is the input grid tiled 2x2 times.
        *   Does the repetition count match the input dimensions? Yes, 2x2 input -> 2x2 tiling.

**3. Conceptual Digestion:**

1.  **CAST:**
    *   **Input Grid:** The "seed swatch". It contains the pattern to be replicated.

... [8944 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 798: "Three stained glass windows shine through each other, and th ... [23 chars truncated]" k=1 alts: 6/15 cf98881b

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 4×14 grid containing three 4×4 panels separated by two vertical columns of red (R) cells. The left panel contains yellow (Y) cells and black (.) cells. The middle panel contains maroon (W) cells and black (.) cells. The right panel contains blue (B) cells and black (.) cells. Each panel represents a layer of colored positions against a black background.

Do: Extract the three 4×4 panels by removing the two red divider columns. Overlay the three panels into a single 4×4 output grid using the following priority: yellow (Y) takes highest priority, then maroon (W), then blue (B), then black (.). For each cell position, check the left panel first — if it contains Y, the output is Y. If the left panel is black at that position, check the middle panel — if it contains W, the output is W. If both the left and middle panels are black, check the right panel — if it contains B, the output is B. If all three panels are black at that position, the output is black (.).

Grid: The input grid is 4 rows by 14 columns. It consists of three 4×4 content panels separated by two 4×1 columns of red (R) cells at columns 4 and 9. The output grid is 4×4. Colors used are yellow (Y), maroon (W), blue (B), red (R) as dividers, and black (.) as background.

Figurative Descriptions (16 variants)

"Three stained glass windows shine through each other, and the brightest light wins."

qwen3.5-122b: k=1

See: A triptych of stained glass windows is mounted in a cathedral wall, separated by pillars of red stone. The left window glows with golden sunlight (Y), the center with a deep wine-colored warmth (W), and the right with a cool blue moonlight (B). Where the glass is clear (.), no light passes through at all.

Do: Remove the red stone pillars and stack the three windows one behind the other, letting light shine through. Golden sunlight is the most powerful — wherever it streams through the left window, it dominates. Where the golden pane is clear, the wine-colored warmth from the middle window seeps through instead. Only where both the gold and wine panes are clear can the blue moonlight from the farthest window reach the viewer. Where all three windows are clear glass, only darkness remains.

Grid: The cathedral wall holds three square panes of equal size, braced apart by two narrow columns of red stone. Each pane is a mosaic of colored and clear tiles. When the pillars are removed and the panes are layered, the congregation sees a single window where the nearest light always outshines the farther ones.

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (10559 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A triptych of stained glass windows separated by pillars of red stone.
*   **Components:**
    *   Left window: Golden sunlight (Y).
    *   Center window: Wine-colored warmth (W).
    *   Right window: Cool blue moonlight (B).
    *   Separators: Red stone pillars (R).
    *   Clear glass: Black/Darkness (.).
*   **Action:** Remove the red stone pillars and stack the three windows one behind the other.
*   **Layering Logic (Priority):**
    *   Nearest (Left/Yellow) dominates.
    *   If Left is clear (.), then Middle (Wine/White) shows through.
    *   If Left and Middle are clear (.), then Right (Blue) shows through.
    *   If all three are clear (.), darkness remains (.).
*   **Grid Structure:** The input grid contains three square panes separated by columns of red stone.
    *   Left Pane: Yellow (Y) and Clear (.).
    *   Separator: Red (R).
    *   Middle Pane: Wine (W) and Clear (.).
    *   Separator: Red (R).
    *   Right Pane: Blue (B) and Clear (.).
*   **Output:** A single window (grid) representing the stacked result.

**2. Analyze the Training Example:**
*   **Input:**
    ```
    . . . Y R . . . W R . . . .
    Y Y . Y R W . W . R . . . .
    Y . Y Y R . W W . R B B . B
    . Y Y Y R . W . . R B B B B
    ```
    *   Dimensions: 4 rows, 14 columns.
    *   Structure:
        *   Left Pane: Columns 0-3 (4x4).
        *   Separator 1: Column 4 (Red R).
        *   Middle Pane: Columns 5-8 (4x4).
        *   Separator 2: Column 9 (Red R).
        *   Right Pane: Columns 10-13 (4x4).
    *   Let's check the content of the panes.
        *   Left (Cols 0-3): Contains Y and ..
        *   Middle (Cols 5-8): Contains W and ..
        *   Right (Cols 10-13): Contains B and ..
        *   Separators (Cols 4, 9): Contain R.
*   **Output:**
    ```
    . . . Y
    Y Y W Y
    Y W Y Y
    B Y Y Y
    ```
    *   Dimensions: 4 rows, 4 columns.
    *   This confirms the output is the size of one pane (4x4).
    *   Let's verify the layering logic row by row.
    *   **Row 0:**
        *   Left: `. . . Y`
        *   Middle: `. . . W`
        *   Right: `. . . .`
        *   Logic:
            *   Col 0: L=., M=., R=. -> Output .
            *   Col 1: L=., M=., R=. -> Output .
            *   Col 2: L=., M=., R=. -> Output .
            *   Col 3: L=Y, M=W, R=. -> Output Y (Y dominates).
        *   Result: `. . . Y`. Matches.
    *   **Row 1:**
        *   Left: `Y Y . Y`
        *   Middle: `W . W .`
        *   Right: `. . . .`
        *   Logic:
            *   Col 0: L=Y -> Y
            *   Col 1: L=Y -> Y
            *   Col 2: L=., M=W -> W
            *   Col 3: L=Y -> Y
        *   Result: `Y Y W Y`. Matches.
    *   **Row 2:**
        *   Left: `Y . Y Y`
        *   Middle: `. W W .`
        *   Right: `B B . B`
        *   Logic:
    

... [7745 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 815: "Each blue star is a compass rose, casting its colored light ... [32 chars truncated]" k=1 alts: 7/15 d364b489

Training Examples

Example 1

Input

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Output

Example 2

Input

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Output

Literal Description

See: The input is a grid with a black (.) background containing several blue (B) cells scattered at various positions. No other colors are present.

Do: For each blue (B) cell in the grid, add four colored neighbors in the cardinal directions: place red (R) one cell above, orange (O) one cell to the left, magenta (M) one cell to the right, and azure (A) one cell below. If any of these positions fall outside the grid boundaries, skip that marker. The blue cell itself remains unchanged. All other cells stay black.

Grid: The grid is 10x10 with a black (.) background. Row 0 is the top and column 0 is the left. The grid dimensions remain the same between input and output.

Figurative Descriptions (16 variants)

"Each blue star is a compass rose, casting its colored light in the four cardinal directions."

qwen3.5-122b: k=1

See: A dark night sky dotted with bright blue stars, each one alone in the void, quietly waiting to orient lost travelers.

Do: When dawn begins, each blue star awakens as a compass rose, projecting its cardinal beams into the surrounding darkness — a warm glow to the north, a sunset hue to the west, a violet flash to the east, and a cool shimmer to the south. The star itself remains blue at the center of its cross. Stars near the edge of the sky simply lose whichever beam would fly beyond the horizon.

Grid: The night sky is a square canvas of darkness. North is at the top, west is at the left. The sky does not grow or shrink when the stars ignite their beacons.

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (8720 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Input:** "A dark night sky dotted with bright blue stars, each one alone in the void..." -> The input grid contains black dots (.) and blue dots (B).
*   **Action:** "When dawn begins, each blue star awakens as a compass rose, projecting its cardinal beams into the surrounding darkness..." -> Each 'B' in the input triggers a transformation in its neighbors.
*   **Beams:**
    *   "a warm glow to the north" -> North is Up. Color? "Warm glow" usually implies Red or Orange. Let's look at the examples.
    *   "a sunset hue to the west" -> West is Left. Color? "Sunset" often implies Orange or Red.
    *   "a violet flash to the east" -> East is Right. Color? "Violet" implies Magenta or Purple.
    *   "a cool shimmer to the south" -> South is Down. Color? "Cool shimmer" implies Blue, Cyan, or Azure.
    *   "The star itself remains blue at the center of its cross." -> The 'B' stays 'B'.
*   **Edge Cases:** "Stars near the edge of the sky simply lose whichever beam would fly beyond the horizon." -> If a neighbor is out of bounds, no color is placed there.
*   **Grid Details:** "North is at the top, west is at the left." Standard grid orientation.

**2. Analyze the Training Examples:**

**Example 1:**
Input Grid (10x10):
Row 0: . . . . . B . . . . (B at 0,5)
Row 1: . . . . . . . . . .
Row 2: B . . . . . . . . . (B at 2,0)
Row 3: . . . . . . . . . B (B at 3,9)
Row 4: . . . . . . . . . .
Row 5: . . . . . B . . . . (B at 5,5)
Row 6: . . . . . . . . . .
Row 7: . . . . . . . . . .
Row 8: . . B . . . . . . . (B at 8,2)
Row 9: . . . . . . . . . B (B at 9,9)

Output Grid (10x10):
Row 0: . . . . O B M . . .
Row 1: R . . . . A . . . .
Row 2: B M . . . . . . . R
Row 3: A . . . . . . . O B
Row 4: . . . . . R . . . A
Row 5: . . . . O B M . . .
Row 6: . . . . . A . . . .
Row 7: . . R . . . . . . .
Row 8: . O B M . . . . . R
Row 9: . . A . . . . . O B

Let's map the colors to directions based on the description and the output.
Center 'B' is at (0,5).
Neighbors in Output:
(0,4) is 'O'. West of (0,5).
(0,6) is 'M'. East of (0,5).
(1,5) is 'A'. South of (0,5).
North of (0,5) is out of bounds.

Center 'B' is at (2,0).
Neighbors in Output:
(2,1) is 'M'. East of (2,0).
(1,0) is 'R'. North of (2,0).
(3,0) is 'A'. South of (2,0).
West of (2,0) is out of bounds.

Center 'B' is at (3,9).
Neighbors in Output:
(3,8) is 'O'. West of (3,9).
(2,9) is 'R'. North of (3,9).
(4,9) is 'A'. South of (3,9).
East of (3,9) is out of bounds.

Center 'B' is at (5,5).
Neighbors in Output:
(5,4) is 'O'. West.
(5,6) is 'M'. East.
(4,5) is 'R'. North.
(6,5) is 'A'. South.

Center 'B' is at (8,2).
Neighbors in Output:
(8,1) is 'O'. West.
(8,3) is 'M'. East.
(7,2) is 'R'. North.
(9,2) is 'A'. South.

Center 'B' is at (9,9).
Neighbors in Output:
(9,8) is 'O'. West.
(8,9) is 'R'. North.
South and East are out of 

... [5876 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

No grid

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 819: "Every tribe has a sacred sigil, and scattering the warriors ... [66 chars truncated]" k=1 alts: 15/15 d4469b4b

Training Examples

Example 1

Input

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Output

Example 2

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Output

Example 3

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Output

Example 4

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Output

Example 5

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Output

Example 6

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Output

Example 7

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Output

Literal Description

See: A 5x5 grid containing scattered cells of a single non-black color (blue, red, or green) against a black (.) background. The specific spatial arrangement of the colored cells varies but is irrelevant to the transformation. The only thing that matters is which color is present.

Do: Identify which color appears in the input grid. Produce a 3x3 output grid based solely on the color identity: (1) If the color is blue (B), output a plus/cross shape: row 1 = . X ., row 2 = X X X, row 3 = . X . (2) If the color is red (R), output an inverted-T shape: row 1 = X X X, row 2 = . X ., row 3 = . X . (3) If the color is green (G), output a bottom-right L shape: row 1 = . . X, row 2 = . . X, row 3 = X X X. Each output shape contains exactly 5 grey (X) cells and 4 black (.) cells.

Grid: Input: a 5x5 grid with cells that are either black (.) or one of three possible colors (blue B, red R, or green G). Only one non-black color appears per grid. Output: a 3x3 grid using grey (X) for the pattern and black (.) for background.

Figurative Descriptions (16 variants)

"Every tribe has a sacred sigil, and scattering the warriors across the battlefield doesn't change the banner they march under."

qwen3.5-122b: k=1

See: A battlefield (5×5) is strewn with warriors of a single tribe — blue, red, or green — scattered among empty darkness. Their positions are chaotic, as if flung by a storm, but every warrior wears the same color, and that color is the name of their tribe.

Do: Ignore where the warriors fell — their arrangement is a feint. Instead, read the color of their armor to learn which tribe has taken the field. Each tribe carries an ancestral sigil, a compact grey emblem stamped onto a 3×3 seal. The blue tribe's sigil radiates outward from the center in four directions. The red tribe's sigil stands tall, crowned with a broad brim. The green tribe's sigil hunkers into one corner, bracing two walls that meet at the foundation. Summon the correct sigil and the battle resolves.

Grid: The battlefield is a 5×5 expanse of darkness dotted with a single tribe's colored warriors. The ancestral seal is a 3×3 tablet where the sigil is rendered in grey (X) against black emptiness — always five stones placed, four spaces left bare.

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (13498 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Input:** A 5x5 grid ("battlefield").
*   **Content:** "Warriors of a single tribe" (Blue, Red, or Green) scattered among "empty darkness" (black `.`).
*   **Task:** Identify the tribe color from the input grid.
*   **Output:** A 3x3 grid ("ancestral seal").
*   **Sigils:**
    *   **Blue Tribe:** "radiates outward from the center in four directions". This sounds like a plus sign `+` shape. Center + Up + Down + Left + Right.
    *   **Red Tribe:** "stands tall, crowned with a broad brim". This sounds like a T shape or an inverted T. "Stands tall" implies vertical. "Crowned with a broad brim" implies a horizontal top. So, a T shape.
    *   **Green Tribe:** "hunkers into one corner, bracing two walls that meet at the foundation". This sounds like an L shape. "One corner", "two walls".
*   **Sigil Color:** Grey (`X`).
*   **Sigil Background:** Black (`.`).
*   **Sigil Size:** 3x3.
*   **Sigil Stones:** "always five stones placed". Wait, let's check the shapes.
    *   Blue (Plus): Center (1) + 4 directions (4) = 5 stones. Matches.
    *   Red (T): Top row (3) + Middle column (2 below top) = 5 stones. Matches.
    *   Green (L): Corner (1) + 2 walls (2 vertical, 2 horizontal? No, usually L is 3x3 corner). Let's visualize an L in 3x3.
        *   Option 1: Left col (3) + Bottom row (3). Overlap at corner. Total 5 stones.
        *   Option 2: Top row (3) + Right col (3). Overlap. Total 5 stones.
        *   Description: "hunkers into one corner, bracing two walls that meet at the foundation". "Foundation" usually implies bottom. "Corner" implies a specific corner. "Two walls" implies vertical and horizontal lines meeting.
        *   Let's check the training example to confirm the Green shape.

**2. Analyze the Training Example:**
*   **Input:**
    ```
    B . B . .
    B . . B B
    B B . B .
    . B . B .
    B . . . B
    ```
    *   Color: Blue (`B`).
    *   Pattern: Scattered `B`s.
*   **Output:**
    ```
    . X .
    X X X
    . X .
    ```
    *   Shape: A plus sign `+`.
    *   Center is `X`. Top, Bottom, Left, Right are `X`. Corners are `.`.
    *   This matches the "Blue tribe's sigil radiates outward from the center in four directions" description.
    *   It confirms the output is 3x3.
    *   It confirms the sigil color is Grey (`X`).
    *   It confirms the background is Black (`.`).

**3. Analyze the Test Input:**
*   **Input:**
    ```
    . G . G G
    . . G . .
    G . . . .
    . . G . G
    . . . . G
    ```
*   **Color:** Green (`G`).
*   **Task:** Determine the Green tribe's sigil based on the description and apply it to a 3x3 grid.

**4. Determine the Green Sigil Shape:**
*   Description: "The green tribe's sigil hunkers into one corner, bracing two walls that meet at the foundation."
*   "Hunkers into one corner": Suggests an L-shape occupying a corner of the 3

... [10510 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.22)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 893: "The hottest ember escapes the dying campfires" k=2 alts: 4/15 e50d258f

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 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"

qwen3.5-122b: k=2

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.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (9469 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Context:** "Scattered across the darkness like campfires in a valley".
*   **Elements:**
    *   "Darkness" = Black (`.`).
    *   "Campfires" = Rectangular patches of Azure (`A`) coals.
    *   "Sparks of red flame" = Red (`R`) embers.
    *   "Blue smoke" = Blue (`B`) cinders.
    *   "Valley floor" = Black background.
*   **Action:** "Count the red-hot embers in each hearth — they are the true measure of its heat."
*   **Selection:** "The fire burning hottest, the one with the most living flame, refuses to die. Rescue it from the night and carry it forward whole."
*   **Output:** "Lift the hottest fire out intact — every coal, ember, and cinder in its exact arrangement — leaving the cold night behind."

**Interpretation:**
1.  Identify distinct rectangular regions (campfires) composed primarily of Azure (`A`), containing Red (`R`) and Blue (`B`) pixels, surrounded by Black (`.`).
2.  Count the number of Red (`R`) pixels in each region.
3.  Select the region with the highest count of Red (`R`) pixels.
4.  Extract that specific rectangular region as the output grid.

**2. Analyze the Training Examples:**

**Example 1:**
Input Grid (10x10):
```
B B B A . . . . . .
B A B B . B A A B A
A R A B . A B A R A
B B B A . A A A A B
A B A A . A B R A R
. . . . . A A A B A
. . . . . B B A B A
. A R R . A B B A R
. R R B . . . . . .
. R B A . . . . . .
```
Let's identify the "campfires". They seem to be connected components of non-black pixels, or specifically rectangular blocks.
Looking at the input, there are two distinct clusters separated by columns of dots.
Cluster 1 (Left): Columns 0-3.
Cluster 2 (Right): Columns 5-9.

Let's look at Cluster 1 (Left):
Rows 0-9, Cols 0-3.
It looks like a 10x4 block, but let's check the content.
Row 0: B B B A
Row 1: B A B B
Row 2: A R A B
Row 3: B B B A
Row 4: A B A A
Row 5: . . . . (Wait, row 5 starts with dots)
Row 6: . . . .
Row 7: . A R R
Row 8: . R R B
Row 9: . R B A

Actually, looking closely at the structure:
There is a block on the left (cols 0-3) and a block on the right (cols 5-9).
Left Block:
Rows 0-4 seem to form a shape. Rows 7-9 form another shape?
Let's check the connectivity.
Row 0: B B B A
Row 1: B A B B
Row 2: A R A B
Row 3: B B B A
Row 4: A B A A
Row 5: . . . .
Row 6: . . . .
Row 7: . A R R
Row 8: . R R B
Row 9: . R B A

Wait, the description says "compact rectangular bed".
Let's look at the Right Block (Cols 5-9):
Row 0: . . . . .
Row 1: . B A A B A
Row 2: . A B A R A
Row 3: . A A A A B
Row 4: . A B R A R
Row 5: . A A A B A
Row 6: . B B A B A
Row 7: . A B B A R
Row 8: . . . . .
Row 9: . . . . .

This looks like a rectangular block from Row 1 to Row 7, Cols 5 to 9.
Let's count Red (`R`) in the Right Block:
Row 1: 0
Row 2: 1 (at col 8)
Row 3: 0
Row 4: 2 (at col 7, 9)
Row 5: 0
Row 6: 0
Row 7: 1 (at col 9)
Total R in Right 

... [6502 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 898: "A photograph printed with extra-thick borders, like a Polaro ... [28 chars truncated]" k=2 alts: 7/15 e633a9e5

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: A 3x3 grid of colored cells. Each cell contains one of several possible colors. The grid has three rows and three columns, with no special background color or distinguished elements — every cell is equally significant.

Do: Expand the 3x3 input grid into a 5x5 output grid by duplicating the border rows and columns while keeping the center row and column single. Specifically: (1) Duplicate each column: the first column appears twice, the middle column appears once, and the last column appears twice, producing 5 columns per row. (2) Duplicate each row: the first row appears twice, the middle row appears once, and the last row appears twice, producing 5 rows total. In index terms, output row i maps to input row [0,0,1,2,2][i], and output column j maps to input column [0,0,1,2,2][j].

Grid: Input is always a 3x3 grid. Output is always a 5x5 grid. There is no background color; all cells carry meaningful color values. The transformation preserves all original colors and spatial relationships, only scaling the grid by stretching the border rows and columns.

Figurative Descriptions (16 variants)

"A photograph printed with extra-thick borders, like a Polaroid that bleeds at the edges."

qwen3.5-122b: k=2

See: A tiny mosaic tile, three paces by three paces — a miniature world where every colored stone carries equal weight, none more important than another.

Do: The edges of the mosaic are sticky — they cling to the frame and leave an echo of themselves as the tile is stretched onto a larger wall. The outermost stones on every side press themselves into the plaster twice, as if they're bracing against the border, while the center stones, confident in their position, sit calmly without doubling. Think of bread dough rolled outward: the crust thickens at the rim while the middle stays thin.

Grid: The miniature mosaic is always three-by-three. The wall it's mounted on is always five-by-five. No stone changes color during the stretching — they simply leave shadows of themselves along the edges, like footprints pressed deeper at the margins of a path.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (11036 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Input:** A 3x3 grid ("tiny mosaic tile, three paces by three paces").
*   **Output:** A 5x5 grid ("wall it's mounted on is always five-by-five").
*   **Transformation Logic:**
    *   "Edges of the mosaic are sticky — they cling to the frame and leave an echo of themselves".
    *   "Outermost stones on every side press themselves into the plaster twice".
    *   "Center stones... sit calmly without doubling".
    *   "Crust thickens at the rim while the middle stays thin".
    *   "No stone changes color".
    *   Essentially, this sounds like an upscaling or padding operation where the border pixels are duplicated.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input (3x3):
        ```
        B G X
        B R A
        A G A
        ```
    *   Output (5x5):
        ```
        B B G X X
        B B G X X
        B B R A A
        A A G A A
        A A G A A
        ```
    *   Let's check the mapping.
    *   Input Row 0: `B G X` -> Output Rows 0 & 1: `B B G X X`
    *   Input Row 1: `B R A` -> Output Row 2: `B B R A A`
    *   Input Row 2: `A G A` -> Output Rows 3 & 4: `A A G A A`
    *   Wait, let's look closer at the columns.
    *   Input Col 0: `B B A` -> Output Cols 0 & 1: `B B`, `B B`, `B B`, `A A`, `A A`
    *   Input Col 1: `G R G` -> Output Col 2: `G`, `G`, `R`, `G`, `G`
    *   Input Col 2: `X A A` -> Output Cols 3 & 4: `X X`, `X X`, `A A`, `A A`, `A A`

    *   It looks like the 3x3 grid is expanded to 5x5.
    *   The corners are duplicated.
    *   The edges (non-corner) are duplicated.
    *   The center is not duplicated.
    *   Let's visualize the indices.
    *   Input indices: (0,0) to (2,2).
    *   Output indices: (0,0) to (4,4).
    *   Mapping hypothesis:
        *   Input (0,0) -> Output (0,0), (0,1), (1,0), (1,1) ? No, looking at Ex 1:
            *   Input (0,0) is B. Output (0,0), (0,1), (1,0), (1,1) are all B.
            *   Input (0,1) is G. Output (0,2), (1,2) are G.
            *   Input (0,2) is X. Output (0,3), (0,4), (1,3), (1,4) are X.
            *   Input (1,0) is B. Output (2,0), (2,1) are B.
            *   Input (1,1) is R. Output (2,2) is R.
            *   Input (1,2) is A. Output (2,3), (2,4) are A.
            *   Input (2,0) is A. Output (3,0), (3,1), (4,0), (4,1) are A.
            *   Input (2,1) is G. Output (3,2), (4,2) are G.
            *   Input (2,2) is A. Output (3,3), (3,4), (4,3), (4,4) are A.

    *   This looks like a specific scaling rule.
    *   Let's define the output grid $O$ of size $5 \times 5$ based on input grid $I$ of size $3 \times 3$.
    *   $O_{i,j}$ depends on $I_{r,c}$.
    *   Let's look at the "doubling" description again. "Outermost stones on every side press themselves into the plaster twice".
    *   This implies the border rows and col

... [8244 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.32)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 906: "Each colored layer is a reflection pool — the surface ... [38 chars truncated]" k=2 alts: 0/0 e74e1818

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 colored shapes arranged as vertically stacked blocks against a black background. Each distinct non-black color occupies a contiguous band of consecutive rows, forming a group. These color groups are stacked on top of each other with no vertical gaps between them (though they may not span the full width of the grid). Within each color group, the rows may differ in width and pixel pattern, giving each group an asymmetric top-to-bottom profile.

Do: For each color group (a set of consecutive rows sharing the same non-black color), reverse the vertical order of its rows in place. That is, the first row of the group swaps with the last, the second with the second-to-last, and so on. Each group stays in the same vertical position within the grid — only the internal ordering of its rows is flipped. The horizontal positions of all pixels remain unchanged. Repeat this for every color group independently.

Grid: The grid has a black (.) background. Its dimensions vary but include a border of black cells around the colored content. The colored regions collectively tile a vertical band of rows in the interior of the grid without overlap or gaps between adjacent color groups. Each color appears in exactly one contiguous vertical band of rows.

Figurative Descriptions (1 variants)

"Each colored layer is a reflection pool — the surface wants to trade places with the depths."

qwen3.5-122b: k=2

See: The grid is a tower of colored strata, like geological layers pressed into a cliff face. Each colored band is a still pool of water, and within each pool the top ripple and the bottom sediment tell different stories — one ornate, one simple, or vice versa. The pools are stacked flush against each other in a dark cavern, each one a different hue.

Do: A tremor runs through the cavern and each pool flips like a shaken snow globe — what floated at the surface sinks to the bottom, and what lay at the bottom rises to the top. Each pool churns independently within its own basin; no water spills into a neighbor's territory. The pools stay exactly where they were in the stack, but their internal reflections are now upside down.

Grid: The cavern walls are black darkness. Each colored pool occupies its own horizontal shelf of rows, and together they fill a continuous vertical column of the cavern with no empty shelves between them. No two pools share a color.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (11208 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Visual:** "Tower of colored strata", "geological layers", "colored band is a still pool of water".
*   **Action:** "Tremor runs through the cavern", "each pool flips like a shaken snow globe".
*   **Specifics:** "what floated at the surface sinks to the bottom, and what lay at the bottom rises to the top."
*   **Constraint:** "Each pool churns independently within its own basin; no water spills into a neighbor's territory." "The pools stay exactly where they were in the stack".
*   **Interpretation:** The grid consists of horizontal bands of different colors. Each band (or "pool") is a contiguous set of rows containing a specific color pattern. The transformation is a vertical flip (reflection) of the pattern *within* each colored band. The background (black/dots) remains unchanged or acts as the container. The bands themselves do not move relative to each other, only the content inside them flips vertically.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input Grid Size: 11x11
    *   Structure:
        *   Row 0: All dots (background)
        *   Rows 1-2: Blue (B) pattern.
            *   Row 1: `. . B B B B B B B . .`
            *   Row 2: `. . . B B . B B . . .`
        *   Row 3: Azure (A) pattern.
            *   Row 3: `. . . A A A A A . . .`
        *   Rows 4-6: Grey (X) pattern.
            *   Row 4: `. . . X . X . X . . .`
            *   Row 5: `. . . X . . . X . . .`
            *   Row 6: `. . . X X X X X . . .`
        *   Rows 7-8: Red (R) pattern.
            *   Row 7: `. . . . R R R . . . .`
            *   Row 8: `. . . . . R . . . . .`
        *   Row 9: Green (G) pattern.
            *   Row 9: `. . . G G G G G . . .`
        *   Row 10: All dots.
    *   Output Grid:
        *   Row 0: All dots.
        *   Rows 1-2: Blue pattern flipped vertically.
            *   Old Row 1 becomes New Row 2.
            *   Old Row 2 becomes New Row 1.
            *   Check: New Row 1 is `. . . B B . B B . . .` (matches old Row 2). New Row 2 is `. . B B B B B B B . .` (matches old Row 1).
        *   Row 3: Azure pattern.
            *   Only 1 row, so it stays the same.
        *   Rows 4-6: Grey pattern flipped vertically.
            *   Old Row 4 -> New Row 6.
            *   Old Row 5 -> New Row 5.
            *   Old Row 6 -> New Row 4.
            *   Check: New Row 4 is `. . . X X X X X . . .` (matches old Row 6). New Row 6 is `. . . X . X . X . . .` (matches old Row 4).
        *   Rows 7-8: Red pattern flipped vertically.
            *   Old Row 7 -> New Row 8.
            *   Old Row 8 -> New Row 7.
            *   Check: New Row 7 is `. . . . . R . . . . .` (matches old Row 8). New Row 8 is `. . . . R R R . . . .` (matches old Row 7).
        *   Row 9: Green pattern.
            *   Only 1 row, stays same.
        *   Row 10

... [8223 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.10)

Prediction

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 971: "A popularity contest among rare wildflowers in a vast meadow" k=2 alts: 9/15 f8b3ba0a

Training Examples

Example 1

Input

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Output

Example 2

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Output

Example 3

Input

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Output

Example 4

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Output

Literal Description

See: The input grid is composed of 2×2 colored blocks arranged in a regular grid pattern, separated by single-cell-wide black (.) borders. One color serves as the dominant background, appearing far more frequently than the others. The remaining minority colors each appear in one or more 2×2 block positions scattered among the background blocks.

Do: 1. Identify all distinct 2×2 colored blocks by scanning the grid at every position where blocks occur (they are spaced 3 cells apart both horizontally and vertically, starting at row 1, column 1). 2. Count the occurrences of each color across all block positions. 3. The color with the highest count is the background color — set it aside. 4. For each remaining minority color, record its count. 5. Sort the minority colors in descending order by count (most frequent first). 6. Output each minority color as a single row, one per line, from most frequent to least frequent.

Grid: The output grid is a single column with one row per minority color (typically 3 rows, 1 column). Each cell contains the color code of a minority color, ordered from most to least frequent. The input grid dimensions vary but always follow the pattern (2k+1) rows by (2m+1) columns, where k and m reflect the number of block rows and columns, with single-cell black borders separating all 2×2 blocks.

Figurative Descriptions (16 variants)

"A popularity contest among rare wildflowers in a vast meadow"

qwen3.5-122b: k=2

See: A meadow stretches before you, tiled with patches of flowers. One species dominates the landscape so thoroughly it has become the grass itself — the wallpaper of the world. But scattered among this sea of sameness, a few rare wildflowers have taken root, their colors defiant against the monotony. Each flower bed is a small square plot, and the black soil paths between them form a quiet grid.

Do: The meadow keeper conducts an annual census of the rare species. She walks every plot, ignoring the common ground-cover entirely — it is invisible to her practiced eye. For each rare bloom she encounters, she places a tally mark in her notebook. When the walk is done, she ranks the rare species from most abundant to least, crowning the one closest to overtaking the meadow as the first name on her list. The rarest flower, barely clinging to existence, goes last.

Grid: The keeper's final report is a single column in her ledger — one flower color per line, written top to bottom from the most commonly spotted rarity down to the loneliest bloom in the field.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (10437 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Context:** A meadow with patches of flowers.
*   **Dominant Element:** "One species dominates the landscape so thoroughly it has become the grass itself — the wallpaper of the world." This implies there is a background color that is ignored.
*   **Rare Elements:** "Scattered among this sea of sameness, a few rare wildflowers have taken root." These are the non-background colors.
*   **Structure:** "Each flower bed is a small square plot, and the black soil paths between them form a quiet grid." This suggests the input grid consists of blocks of colors separated by black lines (dots `.`).
*   **Task:** "The keeper's final report is a single column in her ledger — one flower color per line, written top to bottom from the most commonly spotted rarity down to the loneliest bloom in the field."
*   **Transformation Rule:**
    1.  Identify the background color (the "grass").
    2.  Identify the "flower beds" (blocks of non-background colors).
    3.  Count the occurrences of each distinct non-background color.
    4.  Sort these colors by frequency (count) in descending order (most common to least common).
    5.  Output a single column grid containing these colors in that sorted order.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input Grid: 13 rows, 10 columns.
    *   Background: `.` (black).
    *   Structure: Rows 1, 3, 5, 7, 9, 11, 13 are all `.`. Rows 2, 4, 6, 8, 10, 12 contain colored blocks.
    *   Let's look at the colored blocks. They seem to be 2x2 blocks or similar.
    *   Row 2: `. G G . G G . G G .` -> Three `G` blocks.
    *   Row 4: `. B B . G G . G G .` -> One `B` block, Two `G` blocks.
    *   Row 6: `. G G . A A . G G .` -> Two `G` blocks, One `A` block.
    *   Row 8: `. G G . A A . G G .` -> Two `G` blocks, One `A` block.
    *   Row 10: `. G G . R R . R R .` -> One `G` block, Two `R` blocks.
    *   Row 12: `. R R . G G . G G .` -> Two `R` blocks, Two `G` blocks.
    *   Wait, let's look closer at the structure.
    *   The grid is 13x10.
    *   Rows 0, 2, 4, 6, 8, 10, 12 (0-indexed) are all `.`.
    *   Rows 1, 3, 5, 7, 9, 11 contain the data.
    *   In Row 1: `G G` at cols 1-2, `G G` at cols 4-5, `G G` at cols 7-8.
    *   In Row 3: `B B` at cols 1-2, `G G` at cols 4-5, `G G` at cols 7-8.
    *   In Row 5: `G G` at cols 1-2, `A A` at cols 4-5, `G G` at cols 7-8.
    *   In Row 7: `G G` at cols 1-2, `A A` at cols 4-5, `G G` at cols 7-8.
    *   In Row 9: `G G` at cols 1-2, `R R` at cols 4-5, `R R` at cols 7-8.
    *   In Row 11: `R R` at cols 1-2, `G G` at cols 4-5, `G G` at cols 7-8.
    *   It seems the "flower beds" are 2x2 blocks of color.
    *   Let's count the blocks.
    *   `G`: Row 1 (3), Row 3 (2), Row 5 (2), Row 7 (2), Row 9 (1), Row 11 (2). Total = 3+2+2+2+1+2 = 12 blocks.
    *   `B`: Row 3 (1)

... [7500 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.20)

Prediction

Expected

Figurative + 2 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: 9/15 f9012d9b

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 a pattern of colored cells that tiles periodically in both rows and columns, forming a repeating 2D mosaic. A rectangular region of the grid has been replaced with black (.) cells, creating a 'hole' in the otherwise regular tiling pattern. The non-black portion of the grid is fully consistent with a single repeating tile.

Do: 1. Identify the repeating tile by finding the row period and column period of the non-black cells. Compare rows and columns in the intact (non-black) region to determine the smallest periods P_r (row period) and P_c (column period) such that the pattern repeats every P_r rows and every P_c columns. 2. Extract one copy of the repeating tile: a P_r × P_c subgrid from any fully intact region of the grid. 3. Locate the rectangular region of black (.) cells. 4. For each black cell at position (r, c), compute the tile value as tile[r mod P_r][c mod P_c]. 5. Output only the rectangular block of restored values that replaces the black cells, matching the dimensions of the hole.

Grid: The grid dimensions vary across instances. The grid is composed entirely of colored cells arranged in a periodic tiling pattern, with one contiguous rectangular region of black (.) cells representing the missing portion. The output grid has the same dimensions as the missing rectangular region and contains the tile values that fill the hole.

Figurative Descriptions (16 variants)

"A tapestry weaver mends a moth-eaten hole by reading the rhythm of the surviving threads."

qwen3.5-122b: 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.

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

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Expected

Reasoning (10829 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Context:** A "tapestry" with a repeating motif (pattern).
*   **Problem:** A "moth-eaten hole" (rectangle of black canvas, represented by `.`) exists in the grid.
*   **Task:** Identify the repeating pattern (the "refrain") from the intact parts of the grid.
*   **Goal:** Fill in the missing part (the hole) with the correct colors based on the repeating pattern.
*   **Output:** The prompt asks for the "patch that makes the tapestry whole again". However, looking at the training example, the output is just a single character `A`. Let's look closer at the training example.

**2. Analyze Training Example 1:**
*   **Input:**
    ```
    A M . M
    M A M A
    A M A M
    M A M A
    ```
    *   Grid size: 4x4.
    *   Missing part: `.` at (0, 2) (0-indexed).
    *   Pattern analysis:
        *   Row 0: A M . M
        *   Row 1: M A M A
        *   Row 2: A M A M
        *   Row 3: M A M A
    *   It looks like a checkerboard pattern of A and M.
    *   Row 1: M A M A (Alternating M, A)
    *   Row 2: A M A M (Alternating A, M)
    *   Row 3: M A M A (Alternating M, A)
    *   Row 0 should follow the pattern. If Row 1 starts with M, Row 0 likely starts with A (checkerboard).
    *   Row 0: A M ? M. If it's a checkerboard, (0,0)=A, (0,1)=M, (0,2)=A, (0,3)=M.
    *   So the missing value is `A`.
*   **Output:** `A`.
*   **Interpretation:** The output is *only* the missing patch, not the whole grid. The prompt says "Sing only the missing notes — the patch that makes the tapestry whole again." This confirms I need to output the subgrid corresponding to the black `.` area.

**3. Analyze Test Input:**
*   **Input Grid:**
    ```
    A B A A . . .
    B A A B . . .
    A A B A . . .
    A B A A B A A
    B A A B A A B
    A A B A A B A
    A B A A B A A
    ```
*   **Dimensions:** 7 rows, 7 columns.
*   **Missing Area (Black `.`):**
    *   Row 0: cols 4, 5, 6 are `.`
    *   Row 1: cols 4, 5, 6 are `.`
    *   Row 2: cols 4, 5, 6 are `.`
    *   Rows 3-6: No `.`
    *   So the hole is a 3x3 rectangle at the top right corner.
    *   Coordinates: (0,4), (0,5), (0,6), (1,4), (1,5), (1,6), (2,4), (2,5), (2,6).
*   **Task:** Determine the 3x3 patch that fits into this hole based on the repeating pattern found in the rest of the grid.

**4. Pattern Discovery:**
Let's look at the non-black parts of the grid to find the repeating unit (motif).

Rows 3-6 seem fully intact.
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`

Let's look for periodicity.
Row 3: `A B A A B A A`
Row 6: `A B A A B A A`
Row 3 and Row 6 are identical. This suggests a vertical period of 3?
Let's check Row 4 vs Row 7 (doesn't exist).
Let's check Row 0, 1, 2 against Row 3, 4, 5.
If vertical period is 3:
Row 0 should match Row 3.
Row 1 should match Row 4.
Row 2 should match Row 5.


... [7841 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 983: "A pair of scissors snips along the dotted line, and the scra ... [19 chars truncated]" k=2 alts: 4/15 fbf15a0b

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 has an azure (A) background containing one or more rectangular regions of colored pattern (repeating motifs of a non-azure color on every other cell). Exactly two grey (X) marker cells appear on one edge of the grid, positioned two cells apart from each other along that edge. The X markers always sit on the outermost row or column.

Do: 1. Locate the two X marker cells. They will be on the same edge (top row, bottom row, left column, or right column), spaced 2 cells apart. 2. Determine the axis the X markers define: if they are on the top or bottom row, the axis is vertical (columns); if on the left or right column, the axis is horizontal (rows). 3. Halve the grid along that axis, splitting it into two equal parts. If the axis is vertical, split into a left half and right half; if horizontal, split into a top half and bottom half. 4. Keep the half that contains the X markers; discard the other half. 5. In the kept half, replace every X cell with azure (A). The result is the output grid.

Grid: The input grid has even dimensions along the axis being halved (so it splits cleanly in two). The output grid is exactly half the size of the input along the halved axis and the same size along the other axis. The background color is azure (A). The colored pattern regions and their internal spacing are preserved unchanged in the output, except that X markers become A.

Figurative Descriptions (16 variants)

"A pair of scissors snips along the dotted line, and the scrap paper falls away."

qwen3.5-122b: k=2

See: An azure canvas stretches out, decorated with repeating tapestry patterns woven in various colors. Somewhere along one edge, two grey pins have been pressed into the frame — a perforation mark, like the tear-here dots on a coupon.

Do: The two pins mark where the scissors should cut. They whisper which direction to slice — across or down — like a dotted line on wrapping paper. Cut the canvas in half along that line. The half with the pins is the keeper; the other half flutters to the floor like a trimmed margin. Once you've kept your piece, pull out the pins and patch the tiny holes with azure, leaving no trace they were ever there.

Grid: The canvas is always sized so the scissors cut cleanly in two — no ragged edges. The kept piece is exactly half the original in one direction, unchanged in the other. The woven tapestry patterns survive the cut perfectly intact; only the pin-holes vanish.

qwen3.5-122b — MARC valid, solved with 2 examples

Input

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Prediction

vs

Expected

Reasoning (11876 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Canvas:** The grid itself.
*   **Azure:** The background color (A).
*   **Tapestry patterns:** Other colors forming patterns on the grid.
*   **Grey pins:** Two grey pixels (X) marking a cut line.
*   **Cut:** The grid is cut in half along the line defined by the pins.
*   **Direction:** The pins whisper which direction to slice (across or down).
*   **Keeper:** The half with the pins is kept.
*   **Discard:** The other half is removed.
*   **Patch:** The pin holes (X) are replaced with Azure (A).
*   **Dimensions:** The cut is clean, resulting in exactly half the original size in one direction.

**2. Analyze the Training Examples:**

*   **Example 1:**
    *   Input Size: 20 rows, 21 columns.
    *   Output Size: 10 rows, 21 columns.
    *   Observation: The height is halved (20 -> 10). The width remains the same.
    *   Pin Location: There are two 'X' (grey) pixels in the input.
        *   Row 0, Col 0: X
        *   Row 2, Col 0: X
        *   Wait, let's look closer at the input grid provided in the text.
        *   Input Row 0: `X A A A A A A A A A A A A A A A A A A A A` (21 chars)
        *   Input Row 2: `X B A B A B A B A B A B A B A B A B A B` (21 chars)
        *   The 'X's are in the first column (index 0).
        *   They are in Row 0 and Row 2.
        *   Wait, the description says "two grey pins have been pressed into the frame".
        *   In Example 1, the X's are at (0,0) and (2,0).
        *   The output has 10 rows. The input has 20 rows.
        *   The output rows correspond to the first 10 rows of the input? Or the last 10?
        *   Let's check the content.
        *   Input Row 0: `X A A ...` -> Output Row 0: `A A A ...` (X became A).
        *   Input Row 1: `A A A ...` -> Output Row 1: `A A A ...`
        *   Input Row 2: `X B A ...` -> Output Row 2: `A B A ...` (X became A).
        *   Input Row 3: `A A A ...` -> Output Row 3: `A A A ...`
        *   ...
        *   Input Row 9: `A B A ...` -> Output Row 9: `A B A ...`
        *   Input Row 10: `A B A ...` -> This row is NOT in the output.
        *   So the top half (rows 0-9) is kept. The bottom half (rows 10-19) is discarded.
        *   The pins are in the top half (Row 0 and Row 2).
        *   Rule confirmation: Keep the half containing the pins. Replace pins with Azure (A).
        *   Wait, the description says "The two pins mark where the scissors should cut. They whisper which direction to slice".
        *   In Example 1, the pins are in the first column. They seem to indicate a horizontal cut line? Or do they indicate the side to keep?
        *   The description says "The half with the pins is the keeper".
        *   Since the pins are in the top half (rows 0-9), the top half is kept.
        *   The cut divides the 20 rows into two 10-row sections.
        *   T

... [8968 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.00)

No grid

Expected

Figurative + 2 ex PASS (acc: 1.00)

Prediction

Expected

▶ Task 988: "Each building casts a green shadow whose length reveals how ... [29 chars truncated]" k=1 alts: 0/0 fcc82909

Training Examples

Example 1

Input

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Output

Example 2

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Output

Example 3

Input

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Output

Literal Description

See: The input grid contains several 2x2 blocks of non-black colored cells, each placed at different positions on a black background. Each block occupies exactly a 2-column by 2-row region. The cells within each block may contain repeated or distinct colors.

Do: For each 2x2 colored block in the input: (1) Count the number of unique colors present in that block's four cells. (2) Directly below the block, fill a region that is 2 columns wide (matching the block's columns) and extends downward for a number of rows equal to the unique color count. Fill this region with green (G). (3) Leave the original 2x2 block unchanged.

Grid: The grid is 10x10 with a black (.) background. All non-background content consists of 2x2 blocks of colored cells that do not overlap or touch each other. The output grid has the same dimensions, with the original blocks preserved and green extensions added below each block.

Figurative Descriptions (1 variants)

"Each building casts a green shadow whose length reveals how many departments work inside."

qwen3.5-122b: k=1

See: Scattered across a dark cityscape, small 2×2 buildings stand like colorful office blocks, each floor painted in the livery of the departments housed within.

Do: When the sun rises, every building casts a green shadow straight downward onto the pavement. The more distinct departments (unique colors) sharing a building, the longer its shadow stretches — one story of green for each department. The buildings themselves remain standing, unchanged.

Grid: The city is a 10×10 block of dark pavement. Buildings never crowd each other, and each shadow falls neatly below its building, exactly as wide as the building itself.

qwen3.5-122b — MARC valid, solved with 1 example

Input

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Prediction

vs

Expected

Reasoning (9892 chars)

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

**1. Analyze the Metaphorical Description:**
*   **Scene:** A 10x10 grid representing a dark cityscape (black background `.`).
*   **Objects:** "Small 2x2 buildings" stand on the grid.
*   **Building Composition:** Each building is a 2x2 block of colored cells.
*   **Action:** "When the sun rises, every building casts a green shadow straight downward onto the pavement."
*   **Shadow Length:** "The more distinct departments (unique colors) sharing a building, the longer its shadow stretches — one story of green for each department."
*   **Shadow Width:** "Exactly as wide as the building itself" (so 2 columns wide).
*   **Building State:** "The buildings themselves remain standing, unchanged."
*   **Shadow Color:** Green (`G`).
*   **Shadow Direction:** Straight downward.

**2. Analyze the Training Example:**
*   **Input:**
    *   Row 1: `.`
    *   Row 2: `. . Y A . . . . . .`
    *   Row 3: `. . W Y . . . . . .`
    *   Row 4: `. . . . . . . . . .`
    *   Row 5: `. . . . . . R B . .`
    *   Row 6: `. . . . . . B R . .`
    *   ... rest are empty.
*   **Observation of Buildings:**
    *   Building 1: Top-left at (1, 2) [0-indexed: row 1, col 2].
        *   Cells: (1,2)=Y, (1,3)=A, (2,2)=W, (2,3)=Y.
        *   Colors: Y, A, W, Y.
        *   Unique colors: {Y, A, W}. Count = 3.
    *   Building 2: Top-left at (4, 6).
        *   Cells: (4,6)=R, (4,7)=B, (5,6)=B, (5,7)=R.
        *   Colors: R, B, B, R.
        *   Unique colors: {R, B}. Count = 2.
*   **Observation of Output:**
    *   Building 1 remains at (1,2)-(2,3).
    *   Shadow 1: Starts below the building. Building ends at row 2. Shadow starts at row 3.
    *   Shadow 1 Width: Columns 2 and 3.
    *   Shadow 1 Length: 3 rows (rows 3, 4, 5).
    *   Shadow 1 Color: G.
    *   Building 2 remains at (4,6)-(5,7).
    *   Shadow 2: Starts below the building. Building ends at row 5. Shadow starts at row 6.
    *   Shadow 2 Width: Columns 6 and 7.
    *   Shadow 2 Length: 2 rows (rows 6, 7).
    *   Shadow 2 Color: G.
*   **Verification:**
    *   Building 1 unique colors: Y, A, W. Count = 3. Shadow height = 3.
    *   Building 2 unique colors: R, B. Count = 2. Shadow height = 2.
    *   Shadow position: Directly below the 2x2 block.
    *   Shadow color: Green (G).
    *   Original buildings: Unchanged.

**3. Conceptual Digestion:**
1.  **CAST:**
    *   **Background:** Black (`.`).
    *   **Buildings:** 2x2 blocks of non-black colors.
    *   **Departments:** The individual colored cells within a building.
    *   **Shadow:** Green (`G`) cells generated below buildings.
2.  **AFFORDANCES:**
    *   Buildings can be identified by their 2x2 structure.
    *   Buildings have a set of unique colors.
    *   Shadows can be cast downwards.
    *   Shadow length is determined by the count of unique colors in the building.
3.  **TRANSFORMATION RULE:**
    *   Scan the grid for 

... [6978 chars truncated]

Test

Test Input

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Expected Output

MARC Property (original clue)

Examples Only FAIL (acc: 0.67)

Prediction

Expected

Figurative + 1 ex PASS (acc: 1.00)

Prediction

Expected

MARC2 Puzzle Inspector March 26, 2026

▶ Task 69: "Two teams combine their footprints to map everywhere anyone ... [10 chars truncated]" k=3 alts: 0/0 195ba7dc

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 82: "Two monarchs divide a kingdom, each stamping their seal upon ... [22 chars truncated]" k=2 alts: 0/0 1bfc4729

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 136: "Musical chairs at a costume party — everyone moves one ... [43 chars truncated]" k=1 alts: 1/15 2601afb7

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 174: "The largest kingdom claims the throne." k=3 alts: 0/0 3194b014

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 194: "A curtain divides two dancers, and the spotlight finds whoev ... [16 chars truncated]" k=1 alts: 6/15 34b99a2b

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 214: "A jeweler counts the perfect emeralds among rough stones and ... [38 chars truncated]" k=1 alts: 0/0 3b4c2228

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 223: "Scattered seeds fall and pile into pyramids on the ground." k=2 alts: 0/15 3d6c6e23

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 227: "Russian nesting dolls carved from colored sticks" k=1 alts: 4/15 3ee1011a

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 246: "A volcano fills its crater and erupts a plume of its unique ... [30 chars truncated]" k=1 alts: 0/0 444801d8

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 277: "Geological strata reveal the age of the earth when read in s ... [7 chars truncated]" k=3 alts: 0/0 4be741c5

Training Examples

Literal Description

Figurative Descriptions (1 variants)

Test

MARC Property (original clue)

▶ Task 363: "A herald's banner unfurls across a great hall, its emblem re ... [38 chars truncated]" k=3 alts: 4/15 62b74c02

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 386: "A stained-glass window unfolds its hidden reflections when t ... [30 chars truncated]" k=2 alts: 6/15 67e8384a

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

▶ Task 416: "A conductor reads the harmony of an orchestra to choose the ... [23 chars truncated]" k=3 alts: 15/15 6e02f1e3

Training Examples

Literal Description

Figurative Descriptions (16 variants)

Test

MARC Property (original clue)

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