MARC2 Puzzle Inspector March 26, 2026

We need to solve a puzzle: grid transformation. Input is 3x3 grid with colors and black cells. Output is 9x9 grid. The description: "tiny 3×3 canvas holds a scattered portrait painted in a single color against darkness. Each colored cell is a mirror; each black cell is a curtain drawn shut. The painting gazes into a 3×3 hall of mirrors. Wherever a mirror hangs, the painting sees its own full reflection staring back — a faithful copy of itself. Where a curtain is drawn, only darkness remains. The hall assembles these reflections and shadows into one grand mosaic."

So we have a 3x3 input grid. Each cell is either a color (mirror) or black (curtain). The output is a 9x9 grid. The hall of mirrors is 3x3 of mirrors? Wait: "hall of mirrors expands to 9×9 — three reflections wide, three reflections tall." So each cell of the 3x3 input corresponds to a 3x3 block in the 9x9 output. The rule: For each cell in the input, if it's a mirror (colored), then the 3x3 block in the output is a full reflection of the entire 3x3 input (the painting). If it's a curtain (black), then the 3x3 block is all black.

But we need to confirm with examples.

Example 1:

Input:
M M .
M . .
. M M

Let's label coordinates (row, col) 1-indexed.

Input grid:

Row1: col1 M, col2 M, col3 .
Row2: col1 M, col2 ., col3 .
Row3: col1 ., col2 M, col3 M

So there are 5 M cells, 4 black cells.

Output is 9x9 grid. Provided output:

Row1: M M . M M . . . .
Row2: M . . M . . . . .
Row3: . M M . M M . . .
Row4: M M . . . . . . .
Row5: M . . . . . . . .
Row6: . M M . . . . . .
Row7: . . . M M . M M .
Row8: . . . M . . M . .
Row9: . . . . M M . M M

We need to parse this output into 3x3 blocks of 3x3 each. Let's break into 3x3 blocks:

Block (1,1) top-left 3x3: rows1-3, cols1-3:

Rows1-3, Cols1-3:

Row1: M M .
Row2: M . .
Row3: . M M

Wait row3 col3 is M? Actually row3 col3 is M? Let's check: row3: . M M . M M . . . . Wait row3 is ". M M . M M . . ." So row3 col1 ., col2 M, col3 M. Yes.

So block (1,1) is exactly the input grid. Good.

Block (1,2) top-middle 3x3: rows1-3, cols4-6:

Rows1-3, Cols4-6:

Row1: M M .
Row2: M . .
Row3: . M M

Wait row1 col4 M, col5 M, col6 .; row2 col4 M, col5 ., col6 .; row3 col4 ., col5 M, col6 M. So block (1,2) is also the same as input. So the top row of blocks (1,1),(1,2),(1,3) all are the same? Let's check block (1,3) rows1-3, cols7-9:

Row1: . . .
Row2: . . .
Row3: . . .

Wait row1 col7 ., col8 ., col9 .; row2 col7 ., col8 ., col9 .; row3 col7 ., col8 ., col9 . So block (1,3) is all black. That matches the input cell at (1,3) which is black. So rule: For each input cell, if it's colored, output block is the entire input grid; if it's black, output block is all black.

Let's confirm with other blocks.

Block (2,1) rows4-6, cols1-3:

Rows4-6, Cols1-3:

Row4: M M .
Row5: M . .
Row6: . M M

Yes same as input. Input cell at (2,1) is M, so block is input.

Block (2,2) rows4-6, cols4-6:

Rows4-6, Cols4-6:

Row4: . . .
Row5: . . .
Row6: . . .

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We need to solve a grid transformation puzzle. We have a metaphorical description, training examples, and test input. We need to deduce the transformation rule.

We have a grid of characters: '.' for black, and letters for colors: B=blue, R=red, G=green, Y=yellow, X=grey, M=magenta, O=orange, A=azure, W=maroon.

We have a description: "What you see: A ghostly azure creature drifts through the darkness — shapeless, waiting. Somewhere nearby, a small blue mood ring sits quietly, its facets twisted into one of three emotional poses: pointing down in sorrow, reaching up in joy, or spreading outward in calm. What to do: The chameleon studies the mood ring's posture and feels the emotion wash over it. Sorrow dyes it orange like autumn leaves falling. Joy turns it green like spring growth. Calm flushes it red like a meditative heartbeat. Once the chameleon has absorbed its new hue, the mood ring's purpose is spent — it dissolves into the darkness, no longer needed. Grid details: The dark stage holds two actors that never touch: the large, shapeshifting chameleon and the tiny mood ring in its 3×3 frame. After the transformation, only the newly colored chameleon remains; the ring has faded to black."

So we have a chameleon (azure creature) and a mood ring (blue). The ring is in a 3x3 frame. The ring's posture (pointing down, up, or outward) determines the emotion: sorrow (down), joy (up), calm (outward). The chameleon absorbs the new hue: orange for sorrow, green for joy, red for calm. After transformation, only the newly colored chameleon remains; the ring has faded to black.

So the transformation rule: The chameleon (azure) changes color based on the mood ring's orientation. The ring disappears (becomes black). The chameleon remains in its shape but changes color.

We need to identify the "CAST" and "AFFORDANCES" and "TRANSFORMATION RULE" from the description. But we need to apply to the test input.

We have training example 1. Let's analyze it.

Example 1 Input grid: 14x14? Let's count. The input grid lines:

Line 1: . . . . . . . A A . . . . .
Line 2: . . . . . . . . A A A . . .
Line 3: . . . . . . . . . . A . A .
Line 4: . . . . . A A A A . A A A .
Line 5: . . . . A A . . A A A . A A
Line 6: . . . . . . . A A . . . A .
Line 7: . . . . . . A A . . . A A .
Line 8: . . . . . . . . . A A A . .
Line 9: . . . . . . . . . . . . . .
Line10: . . . . . . . . . . . . . .
Line11: . . . . B B B . . . . . . .
Line12: . . . . B . B . . . . . . .
Line13: . . . . . B . . . . . . . .
Line14: . . . . . . . . . . . . . .

Output grid:

Line 1: . . . . . . . O O . . . . .
Line 2: . . . . . . . . O O O . . .
Line 3: . . . . . . . . . . O . O .
Line 4: . . . . . O O O O . O O O .
Line 5: . . . . O O . . O O O . O O
Line 6: . . . . . . . O O . . . O .
Line 7: . . . . . . O O . . . O O .
Line 8: . . . . . . . . . O O O . .
Line 9: . . . . . . . . . . . . . .
Line10: . . . . . . . . . . . . . .
Line11: . . . . . . . . . . . . . .
Line12: . . . . . . . . . .

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We need to parse the problem. It's a grid transformation puzzle. The description: "What you see: A vast kingdom of uniform terrain is carved up by unbroken fortress walls running horizon to horizon. Some walls run east-west, others north-south, but each wall stretches the entire length of the realm without a single gap. The walls are all the same color—different from the land they partition. Between the walls lie provinces of peaceful, identical countryside. What to do: You are a cartographer flying high above. You don't care about the size of each province or the thickness of the walls—only how many provinces exist. Count the corridors between the east-west walls and the corridors between the north-south walls. On your map, place one tile of countryside for each province, arranged in the same row-and-column pattern the walls create. Grid details: The map has as many rows as there are horizontal corridors and as many columns as there are vertical corridors. Every tile on the map is painted in the color of the countryside—the walls themselves vanish, having served their only purpose: defining borders."

So basically we have a grid with a uniform background color (countryside) and walls of a different color that run across entire rows or columns. The walls are continuous lines that partition the grid into rectangular cells. The walls are of a single color (the "wall color") and the background is another color. The walls are unbroken across the entire grid horizontally or vertically. The walls may be thick? The description says "you don't care about the size of each province or the thickness of the walls—only how many provinces exist." So we need to count the number of horizontal corridors (spaces between horizontal walls) and vertical corridors (spaces between vertical walls). Then produce a grid of size (#horizontal corridors) x (#vertical corridors) where each cell is the background color (countryside). The walls vanish.

Essentially, we need to compress the grid by removing the walls and leaving only one cell per region. The output grid is the number of horizontal segments between horizontal walls times number of vertical segments between vertical walls. Each cell is the background color.

We need to confirm with training examples.

Example 1:

Input grid: 12x11? Let's check. Provided input lines:

"B B B B A B B B B B B" repeated 3 times, then "A A A A A A A A A A A" (row 4), then 3 more rows of B B B B A B B B B B B, then row 10 "A A A A A A A A A A A", then row 11 "B B B B A B B B B B B". So 11 rows, 11 columns? Actually each row has 11 entries. Let's count: "B B B B A B B B B B B" that's 11 tokens. So 11x11 grid.

Walls: The color A appears as a vertical line? Let's examine: In each row, there is a single A at column 5? Actually row 1: B B B B A B B B B B B. So A at column 5. Row 2 same. Row 3 same. Row 4: A A A A A A A A A A A (all A). Row 5: B B B B A B B B B B B. Row 6 same. Row 7 same. Row 8 same. Row 9 same. Row 

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We need to parse the puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid."

We have a color key mapping letters to colors. The puzzle: "What you see: A small 3×3 tapestry hangs in a dark hall. One thread—a single row or column—is woven from a single pure color, forming the flagpole that holds the whole design together. The rest of the weave is a patchwork of different colors. What to do: The flagpole knows which wall it belongs to. A row-pole is horizontal and knows its height; a column-pole is vertical and knows its side. The tapestry longs to be seen, so it unfurls itself three times along the direction of its pole, like a banner repeating in the wind. Wherever the banner doesn't reach, the dark hall remains—empty black stone stretching into shadow. Grid details: The dark hall is a 9×9 chamber of black stone. The flagpole's position decides which strip of the chamber gets decorated: a horizontal pole at the top, middle, or bottom places three copies side by side in the matching horizontal band; a vertical pole on the left, center, or right stacks three copies in the matching vertical band. The rest of the chamber stays dark and bare."

So we have a 3x3 input grid. We need to produce a 9x9 output grid. The input grid has a "flagpole" which is a single row or column that is a single pure color. That row or column is the "pole" that determines orientation and location. The rest of the grid is patchwork of colors. The transformation: replicate the 3x3 tapestry three times along the direction of its pole, like a banner repeating in the wind. The 9x9 output grid is a 3x3 block repeated 3 times along the direction of the pole. The rest of the 9x9 grid remains black (represented by '.' maybe). The 9x9 grid is a "dark hall" of black stone. The flagpole's position decides which strip of the chamber gets decorated: a horizontal pole at the top, middle, or bottom places three copies side by side in the matching horizontal band; a vertical pole on the left, center, or right stacks three copies in the matching vertical band. The rest of the chamber stays dark and bare.

So we need to identify the flagpole: a single row or column that is a single pure color. In the input grid, we need to find a row or column that is all the same color. That row or column is the flagpole. The orientation of the flagpole (horizontal or vertical) determines the direction of replication. The position of the flagpole (top, middle, bottom for horizontal; left, center, right for vertical) determines which band of the 9x9 output grid will be filled with the repeated pattern. The repeated pattern is the entire 3x3 tapestry repeated 3 times along the direction of the pole. So if the pole is horizontal, we replicate the 3x3 block horizontally 3 times, resulting in a 3x9 block. That block will be placed in the corresponding horizontal ba

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We need to solve the puzzle. Let's parse the problem carefully.

We have a grid transformation puzzle. Input is a 3x3 grid. Output is a 9x9 grid. The description: "What you see: A 3×3 organism with one structural spine — a row or column of identical tissue running through it. What to do: The spine determines the axis of mitosis. The organism replicates itself three times along that axis, embedding into a larger 9×9 body of dormant (black) tissue at the position matching the spine's location. Grid details: Input: 3×3. Output: 9×9, mostly black. Three copies of the input arranged in a strip corresponding to the spine's position and orientation."

So we need to identify the "spine" in the 3x3 input: a row or column of identical tissue (i.e., same color). The spine determines the axis of mitosis. The organism replicates itself three times along that axis, embedding into a larger 9x9 body of dormant (black) tissue at the position matching the spine's location.

Thus, we need to find a row or column that has all identical colors. That row/column is the spine. Then we replicate the entire 3x3 input three times along that axis, i.e., we create a 9x9 grid where the 3x3 input is repeated three times along that axis, and the rest of the grid is black (.). The output examples confirm this.

Let's analyze the training examples.

Example 1:

Input:
B B B
M R R
R R M

We need to find a row or column of identical tissue. Let's check rows:

Row 1: B B B -> all B. So row 1 is a spine. Row 2: M R R -> not all same. Row 3: R R M -> not all same.

Columns:

Col 1: B M R -> not all same. Col 2: B R R -> not all same. Col 3: B R M -> not all same.

So the spine is row 1 (top row). The axis of mitosis is horizontal (row). The organism replicates itself three times along that axis, embedding into a larger 9x9 body of dormant (black) tissue at the position matching the spine's location.

So we replicate the 3x3 input three times horizontally? Wait, the axis is horizontal, so we replicate along that axis: we create a 9x9 grid where the 3x3 input is repeated three times along the horizontal axis (i.e., left to right). But the output shows:

Output:
B B B B B B B B B
M R R M R R M R R
R R M R R M R R M
. . . . . . . . .
. . . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .

Let's examine the output: The first row is B B B B B B B B B. That is 9 B's. The second row is M R R M R R M R R. That's 9 cells: M R R repeated 3 times. Third row: R R M repeated 3 times. Then the rest of the grid is black.

So indeed, the 3x3 input is repeated horizontally 3 times, forming a 3x9 block. Then the rest of the 9x9 grid is black. The 3x9 block is placed at the top of the 9x9 grid because the spine is the top row. So the 3x9 block occupies rows 1-3, columns 1-9. The rest rows 4-9 are black.

Thus, the rule: find the spine row or column. If it's a row, replicate the 3x3 input horizontally 3 times, forming a 3x9 block. Plac

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We need to parse the puzzle. The description: "What you see: A 3×3 pastry where one layer is a single pure ingredient — the baking sheet — and the rest is mixed filling. What to do: Place the pastry on a 9×9 oven rack (black background). The baking sheet's position on the rack determines which shelf gets loaded: tile the pastry three times along that shelf, leaving the other shelves empty."

Interpretation: Input is a 3x3 grid. There is a "single pure ingredient" layer: a uniform color? The rest is mixed filling: other colors. The "baking sheet" is the uniform layer. The "position" of that uniform layer in the 3x3 grid determines which shelf (row) in the 9x9 output gets loaded. Then we tile the pastry (the entire 3x3 input) three times along that shelf (i.e., horizontally? or vertically?). The output is a 9x9 grid with a strip of three tiled copies of the input placed at the position indicated by the uniform layer. The rest of the grid is black (represented by .). The output examples confirm this.

Let's analyze the training examples to confirm.

Example 1:

Input:
B B B
M R R
R R M

We need to find the uniform layer: a single pure ingredient. In the input, we see B B B in the first row: all B. So the uniform layer is B. The position of that uniform layer in the 3x3 grid: it's the first row (row index 0). So the shelf to load is row 0? But the output shows the first 3 rows of the 9x9 grid are filled with the tiled copies of the input. Let's examine output:

Output:
B B B B B B B B B
M R R M R R M R R
R R M R R M R R M
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .

So the first 3 rows are filled with the tiled copies of the input. The rest are black. So the uniform layer was in row 0, so the shelf loaded is row 0. The 9x9 grid is 9 rows, each row has 9 columns. The "shelf" is a row of 9 cells. The "tile the pastry three times along that shelf" means we tile the 3x3 pastry horizontally 3 times to fill the 9 cells of that row. But the output shows that the first 3 rows are filled, not just the first row. Wait, the output shows the first 3 rows are filled with the tiled copies of the input. That means the "shelf" might be a vertical column of 3 rows? Let's analyze.

The output shows the first 3 rows are filled with the 3x3 pastry repeated horizontally 3 times. That means the 3x3 pastry is repeated horizontally 3 times to fill a 3x9 block. That block occupies rows 0-2 and columns 0-8. So the "shelf" is a 3-row tall block. The uniform layer's position determines which shelf gets loaded. The uniform layer is in row 0 of the 3x3 pastry. That corresponds to the top shelf (rows 0-2). So the shelf is a 3-row block. The "tile the pastry three times along that shelf" means tile horizontally 3 times across the 9 columns. So the output is 9x9 with a 3x9 block of the tiled pastry at the shelf determined by the uniform layer's row. The rest of the grid is black.

Let's confirm wit

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We need to parse the puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid.

Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

## Metaphorical Description

What you see: A 3×3 formation of players, one row or column wearing matching jerseys.
What to do: On a 9×9 field (empty/black), the uniformed line picks the lane. The whole formation is repeated three times along that lane at the matching position, and the rest of the field stays empty.
Grid details: Input: 3×3. Output: 9×9 empty field with three copies of the formation tiled in a strip matching the uniformed line's position and direction."

So we have a 3x3 input grid. We need to produce a 9x9 output grid. The output grid is empty except for three copies of the formation repeated along a lane (row or column) that matches the uniformed line's position and direction. The uniformed line is a row or column of matching jerseys. So we need to identify a row or column in the 3x3 input that has all same color. That row or column is the "uniformed line". Then we need to replicate the entire 3x3 formation three times along that lane in the 9x9 output. The lane is a row or column in the 9x9 grid. The lane's position and direction correspond to the uniformed line's position and direction. So if the uniformed line is a row (top, middle, bottom) in the 3x3 input, then we replicate the 3x3 formation three times along that row in the 9x9 output. Similarly for a column.

But we need to interpret "the uniformed line picks the lane. The whole formation is repeated three times along that lane at the matching position, and the rest of the field stays empty." So we need to place the 3x3 formation three times along the lane. The lane is a row or column in the 9x9 grid. The lane's position and direction match the uniformed line's position and direction. So if the uniformed line is the top row of the 3x3 input, then the lane is the top row of the 9x9 output. Then we need to tile the 3x3 formation three times along that lane. But how to tile? The 3x3 formation is 3x3. The lane is a row or column of length 9. We need to place the 3x3 formation three times along that lane. That means we need to place the 3x3 formation at positions that align with the lane. For a row lane, we would place the 3x3 formation at columns 0-2, 3-5, 6-8 of that row. But the 3x3 formation is 3x3, so we need to place it in a 3x3 block. For a row lane, we would place the 3x3 formation in the lane row and the two rows below or above? Wait, the lane is a row or column. The formation is 3x3. If the lane is a row, we need to place the formation such that its row aligns with the lane row. But the formation has 3 rows. So we need to decide which rows of the 9x9 output the formation occupies. The lane is a row, but the formation is 3 rows tall. So maybe the lane is a colu

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We need to parse the puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid.

Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

## Metaphorical Description

What you see: A 3×3 blueprint with one structural wall — a row or column built from one uniform material.
What to do: Expand to a 9×9 city block of empty lots (black). The load-bearing wall's orientation and position determine the avenue; tile the blueprint three times along that avenue.
Grid details: Input: 3×3. Output: 9×9 empty block with three copies of the input tiled in a strip matching the wall's position and axis."

So we have a 3x3 input grid. There is a "structural wall" which is a row or column built from one uniform material. That means there is a row or column that is all the same color. That row or column is the "wall". The orientation and position of that wall determine the avenue. Then we tile the blueprint three times along that avenue. The output is a 9x9 grid of empty lots (black) with three copies of the input tiled in a strip matching the wall's position and axis.

We need to analyze the training examples to confirm.

Example 1:

Input:
B B B
M R R
R R M

So the grid is:

Row1: B B B
Row2: M R R
Row3: R R M

We need to find a row or column that is uniform. Let's check rows: Row1 is B B B (uniform). Row2 is M R R (not uniform). Row3 is R R M (not uniform). Columns: Column1: B M R (not uniform). Column2: B R R (not uniform). Column3: B R M (not uniform). So the uniform row is Row1 (top row). So the wall is the top row. Orientation: horizontal. Position: top row. So the avenue is horizontal at the top? The output is 9x9 grid. Let's examine the output:

Output:
B B B B B B B B B
M R R M R R M R R
R R M R R M R R M
. . . . . . . . .
. . . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .
. . . . . . . .

Wait, the output shows 9 rows, each with 9 columns. The first 3 rows are filled with the input repeated horizontally 3 times. The rest 6 rows are all '.' (black). So the output is a 9x9 grid where the first 3 rows contain 3 copies of the input side by side horizontally. The rest rows are empty.

But the description says "tile the blueprint three times along that avenue." The avenue is determined by the wall's orientation and position. In this case, the wall is the top row. So the avenue is horizontal at the top. So we tile the blueprint 3 times along that avenue. That means we replicate the blueprint horizontally 3 times, but only in the rows that correspond to the avenue? Wait, the output shows the blueprint repeated horizontally 3 times across the entire 9x9 grid, but only in the first 3 rows. The rest rows are empty. So the blueprint is repeated horizontally 3 times, but only in the rows that correspond to the wall's position? Actually the blueprint is repeated horizontally 3 

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We need to solve a grid transformation puzzle. We have a metaphorical description, training examples, and a test input grid. We need to produce the output grid.

We have one training example. Let's analyze it.

Input grid 10x10. Provided as 10 lines of 10 tokens each. The input grid has a single colored banner: B at (row 2, col 6?) Wait let's parse.

Input example:

Row 0: . . . . . . . . . .
Row 1: . . . . . . . . . .
Row 2: . . . . . . B . . .
Row 3: . . . . . . . . . .
Row 4: . . . . . . . . . .
Row 5: . . . . . . . . . .
Row 6: . . . . . . . . . .
Row 7: . . . . . Y . . . .
Row 8: . . . . . . . . . .
Row 9: . . . . . . . . . .

So there are two colored cells: B at (2,6) (0-indexed) and Y at (7,5). The output grid:

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
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

So the output shows two rectangular border patterns: one for B, one for Y. The B pattern is a rectangle covering rows 0-4, columns 0-9? Let's examine: B border appears at top row (row 0) all B. Then leftmost column (col 0) all B rows 0-9? Actually row 1 col 0 is B, row 2 col 0 is B, row 3 col 0 is B, row 4 col 0 is B, row 5 col 0 is Y, row 6 col 0 is Y, row 7 col 0 is Y, row 8 col 0 is Y, row 9 col 0 is Y. So leftmost column is B for rows 0-4, Y for rows 5-9. Similarly rightmost column (col 9) is B for rows 0-4, Y for rows 5-9. The B rectangle is top half of grid: rows 0-4. The Y rectangle is bottom half: rows 5-9. The B rectangle has a top border (row 0 all B), left border (col 0 rows 0-4), right border (col 9 rows 0-4), and a middle horizontal border at row 2? Wait row 2 is all B. Actually row 2 is all B. So B rectangle has a horizontal line at row 2 across all columns. So B rectangle is like a shape: top border, middle horizontal line, left and right borders. The Y rectangle has bottom border (row 9 all Y), left border (col 0 rows 5-9), right border (col 9 rows 5-9), and a middle horizontal line at row 7? Actually row 7 is all Y. So Y rectangle has bottom border, middle horizontal line, left and right borders. So each rectangle has a top or bottom border, a middle horizontal line, and left/right borders. The B rectangle has top border at row 0, middle at row 2, left/right at col 0 and 9. The Y rectangle has bottom border at row 9, middle at row 7, left/right at col 0 and 9.

So the pattern: The grid is split into two halves: top half (rows 0-4) and bottom half (rows 5-9). Each half has a colored banner at some location: B at (2,6) in top half, Y at (7,5) in bottom half. The output draws a "fortress" around each half: For the top half, the fortress is a shape that encloses the half: top border at row 0, left/right borders at col 0 and 9, and a horizontal line at row 2 (the row of the banner). For the bottom half, the fortress encloses the half: bottom border at ro

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We need to solve a grid transformation puzzle. The description: "Scattered across a dark sea, azure lighthouses stand on their lonely posts. Some lighthouses happen to gaze directly at another across the water — perfectly aligned along the same shipping lane, either north-south or east-west. Others stand alone, their beams finding no companion on the horizon. What to do: When two lighthouses face each other along the same lane, their beams meet and the water between them glows green with reflected light. The lighthouses themselves remain azure — only the dark water between paired beacons is illuminated. A lighthouse with no partner in its lane keeps its light to itself, illuminating nothing. The beams travel only in straight cardinal lines and never bend or wrap around the edges of the sea."

So we have a grid with '.' for black water, 'A' for azure lighthouses. The output grid will have 'G' for green water between paired lighthouses. The lighthouses themselves remain 'A'. The rule: For each pair of lighthouses that are aligned horizontally or vertically with no other lighthouses between them, fill the cells between them with 'G'. Each lighthouse can participate in up to two connections: one horizontal, one vertical. So we need to find all pairs of A's that are aligned with no other A's between them. For each such pair, fill the cells between them with G. The lighthouses themselves remain A. The rest remains '.'.

We have training example 1: Input grid 9x6? Let's parse. Example 1 Input:

```
. . . . . .
. . A . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. . A . . .
. . . . . .
```

Wait, the grid seems 9 rows, 6 columns? Actually the input shows 9 rows, each row has 6 columns. Let's count: Row1: . . . . . . (6). Row2: . . A . . . (6). Row3: . . . . . . (6). Row4: . . . . . . (6). Row5: . . . . . . (6). Row6: . . . . . . (6). Row7: . . . . . . (6). Row8: . . A . . . (6). Row9: . . . . . . (6). So 9x6 grid.

Output:

```
. . . . . .
. . A . . .
. . G . . .
. . G . . .
. . G . . .
. . G . . .
. . G . . .
. . A . . .
. . . . . .
```

So the two A's are at (row2, col3) and (row8, col3). They are vertically aligned with no other A's between them. So the cells between them (rows3-7, col3) become G. That matches rule.

Now test input: Provided grid is 12 rows? Let's parse. The test input:

```
. . . . . . . . . . . . .
. . A . . . . . . . A . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . A . . . . . A
. . . . . . . . . . . . .
. A . . . . . . . . . . .
. . . . . . . . . . . . .
. . . . . . . . A . . . .
. A . . . . . . . . . . .
. . . . . . . . . . . . .
```

Let's count columns: Row1: . . . . . . . . . . . . . (13). So 13 columns. Rows: 12 rows? Let's count: Row1, Row2, Row3, Row4, Row5, Row6, Row7, Row8, Row9, Row10, Row11, Row12. Yes 12 rows.

We need to find all pairs of A's aligned horizontally or vertically with no other A's between them. Then fill G between them.

We ne

... [9333 chars truncated]

We need to parse the puzzle. The description: 10x10 grid. Row 0: azure heralds (A). Row 6: grey wall (X). Row 8: regiment of soldiers with colors. The courtyard is rows 1-5. The rule: The heralds count off — their number is the royal summons. Each house in the regiment below the wall counts its soldiers. Only houses whose ranks exactly match the herald count are deemed worthy. The chosen houses raise their colored banners in the courtyard: tall columns of color growing upward from the wall's edge, each banner exactly as tall as the number of heralds. Unworthy houses stay silent — their columns in the courtyard remain dark and empty.

So we need to interpret: The number of heralds is the number of A cells in row 0. That number is the "royal summons" or "count". Then we look at row 8: each house's color appears in some columns. The number of soldiers of each house is the number of cells of that color in row 8? But row 8 may have multiple colors. The rule: "Each house in the regiment below the wall counts its soldiers. Only houses whose ranks exactly match the herald count are deemed worthy." So we need to count the number of cells of each color in row 8. If that count equals the number of heralds, then that house is worthy. Then we "raise their colored banners in the courtyard: tall columns of color growing upward from the wall's edge, each banner exactly as tall as the number of heralds." So for each worthy color, we need to fill the courtyard rows 1-5 (i.e., 5 rows) with that color in the columns where that color appears in row 8? Wait: "tall columns of color growing upward from the wall's edge, each banner exactly as tall as the number of heralds." The wall is row 6. The courtyard is rows 1-5. The wall's edge is row 6? Actually the wall is row 6. The courtyard is rows 1-5. The columns of color should be flush against the wall and rising upward. That means the colored columns should be in the same columns as the regiment's colors in row 8, but above the wall (rows 1-5). The height of each column is the number of heralds. But the courtyard only has 5 rows (rows 1-5). So the number of heralds must be <=5? Let's check example 1.

Example 1 Input:
Row 0: A A . . . . . . . .
Row 6: X X X X X X X X X X
Row 8: R G G R G B B G B B

So row 0 has 2 A's. So number of heralds = 2. Row 8 has colors: R appears 3 times? Let's count: R G G R G B B G B B. R appears at positions 0,3 => 2 times. G appears at positions 1,2,4,7 => 4 times. B appears at positions 5,6,8,9 => 4 times. So only R appears 2 times, which matches herald count 2. So R is worthy. Then we need to raise banners of color R in the courtyard rows 1-5, in columns where R appears in row 8. R appears at columns 0 and 3. So we fill rows 1-5, columns 0 and 3 with R. The output shows:

Row 0: A A . . . . . . . .
Row 1: . . . . . . . . . .
Row 2: . . . . . . . . . .
Row 3: . . . . . . . . . .
Row 4: R . . R . . . . . .
Row 5: R . . R . . . . . .
Row 6: X X X X X X X X X X
Row 7: . 

... [10800 chars truncated]

We need to understand the puzzle. We have training examples. Let's parse them.

We have a grid transformation puzzle. The description: "What you see: A small swatch of dark wallpaper with a few colorful creatures resting on it. What to do: As the sun sets from the upper-left, each creature casts a red shadow one diagonal step toward the fading light — if the shadow falls off the edge, it wraps around to the opposite side of the swatch, as if the wallpaper were already a cylinder. Then the completed swatch is stamped out as a 3×3 block of identical copies, like a wallpaper roll unspooling across a wall. Grid details: The finished wall is three swatches tall and three swatches wide. Every tile is the same: the original dark background, the colorful creatures where they stood, and each creature's red sunset shadow sitting one step up and to the left (wrapping at the edges)."

So we have a small swatch (input grid). The creatures are colored cells (non-'.'). They cast a red shadow one diagonal step up-left (i.e., row-1, col-1). If that goes off the edge, wrap around to the opposite side of the swatch (cylinder). Then the completed swatch is repeated 3x3 times to produce the output grid.

We need to confirm with examples.

Example 1:

Input:
. . . .
. . X .
. . . .
. X . .

So 4x4 grid. X at (1,2) (0-indexed? Let's index rows 0-3, columns 0-3). X at (1,2). X at (3,1). The output is a 12x12 grid (3x3 repeats of 4x4). Let's examine output: Provided output is 12x12? Let's count lines: They show 12 lines each with 12 characters? Let's check first line: ". R . . . R . . . R . .". That's 12 tokens: . R . . . R . . . R . . (makes sense). So output is 12x12.

Now we need to see if the output matches the rule: For each X, we add a red cell at (row-1, col-1) with wrap-around. Let's compute for input.

Input grid 4x4:

Row0: . . . .
Row1: . . X .
Row2: . . . .
Row3: . X . .

Coordinates: X at (1,2). X at (3,1).

Compute red shadows:

For X at (1,2): up-left is (0,1). That's inside grid. So we set a red at (0,1).

For X at (3,1): up-left is (2,0). That's inside grid. So red at (2,0).

Now we produce output: The output grid should contain original X cells at same positions, and red cells at those positions. Also the background remains '.'.

Let's produce 4x4 grid with X and R:

Row0: . R . .
Row1: . . X .
Row2: R . . .
Row3: . X . .

Now we need to repeat this 3x3 times. That means we tile the 4x4 block 3 times horizontally and vertically. So output 12x12.

Let's check first row of output: . R . . . R . . . R . . . That matches: first 4 cells: . R . . ; next 4: . R . . ; next 4: . R . . . Wait the pattern: . R . . . R . . . R . . . Actually the first row of output: ". R . . . R . . . R . ." That's 12 tokens: . R . . | . R . . | . R . . . Wait we need to parse: The first 4 tokens: . R . . ; second 4: . R . . ; third 4: . R . . . Wait there are 12 tokens: . R . . . R . . . R . . . Wait that's 13 tokens? Let's count: . (1) R (2) . (3) . (4) . (5) R (6) . (

... [8591 chars truncated]

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

So we have a 3x5 grid. The input grid contains W and Y and . (black). The output grid contains M (magenta) and . (black). The rule: "When the curtain rises, only solo acts earn the magenta spotlight. Where a dancer stands alone on a mark — one troupe claiming it while the other leaves it empty — the spotlight blazes magenta. But where both troupes crowd the same mark, they block each other's light and the spot goes dark. And where neither troupe shows up, the stage stays dark too. The spotlight rewards those who dance where their rival dares not."

So basically we have two sets of positions: W positions (maroon) and Y positions (yellow). For each cell, if exactly one of W or Y is present, output M. If both present, output . (dark). If none present, output . (dark). So basically M if XOR of W and Y. But we need to confirm with training example.

Let's parse Example 1.

Input:
Row1: W . . W W
Row2: . . . . .
Row3: . . W . W
Row4: . . Y Y .
Row5: Y Y Y . .
Row6: Y . Y . Y

Wait, the input grid appears to be 6 rows? But the description says 3 rows by 5 columns. But the example shows 6 rows. Let's examine: The input grid lines:

W . . W W
. . . . .
. . W . W
. . Y Y .
Y Y Y . .
Y . Y . Y

That's 6 rows, each 5 columns. So maybe the grid is 6x5? But the description says 3-row by 5-column. But maybe the example is 6 rows? Let's check the output grid:

Output:
M . M . M
M M M . .
M . . . .

That's 3 rows, 5 columns. So the output grid is 3x5. The input grid is 6x5. So maybe the input grid contains two separate 3x5 grids stacked vertically: the upper balcony (first 3 rows) and lower floor (next 3 rows). The output grid is a single 3x5 grid that merges them according to the rule. That matches the description: "The stage is split into an upper balcony and a lower floor, each holding a troupe of performers. Maroon dancers (W) rehearse above, yellow dancers (Y) rehearse below, both moving across the same five-column, three-row grid of spotlight marks." So the input grid has 6 rows: first 3 rows are the upper balcony (W positions), next 3 rows are the lower floor (Y positions). The output grid is 3x5, representing the combined result.

Thus the rule: For each cell (i,j) where i=1..3, j=1..5, we look at the cell in the upper balcony (row i) and the cell in the lower floor (row i+3). If exactly one of them is W or Y? Wait, the upper balcony has W's, lower floor has Y's. But the input grid may contain '.' in either. So we need to check if the upper cell is W and lower cell is Y? But the rule says: "Where a dancer stands alone on a mark — one troupe claiming it while the other leaves it empty 

... [10856 chars truncated]

We need to understand the puzzle. We have a metaphorical description: "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. What to 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 details: 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."

So we have a grid with colored cells. The input grid has colored cells scattered. The output grid is a square of nested shells, each one layer thick, with colors from outermost to innermost corresponding to the longest to shortest sticks. The longest stick is the longest line of same color? Or the longest contiguous line? The input grid has colored cells forming lines? Let's examine Example 1.

Example 1 Input: 22x? Actually the input grid is 22 columns? Let's count: The first line: ". . . . . . . . . . . . . . . . . . . . . ." That's 22 cells. So grid is 22x22? Actually there are 22 lines. So 22x22 grid. The input has some colored cells: B, G, M. Let's examine the pattern: The B cells form a vertical line at column 12? Let's check: In row 3: ". . . . . . . . . . . . . B . . . . . . . ." So B at column 13? Wait indexing: Let's count: columns 1-22. Row 3: after 12 dots, B at column 13? Actually row 3: ". . . . . . . . . . . . . B . . . . . . . ." So there are 12 dots, then B, then 9 dots? Let's count: 12 dots, B, 9 dots = 22. So B at column 13. Row 4: ". . . . G . . . . . . . . B . . . . . . . ." So G at column 5, B at column 13. Row 5: same. Row 6: same. Row 7: same. Row 8: ". . . . . . . . . . . . . B . . . . . . . ." So B at column 13. Row 9: ". . . . . . . . M . . . . . . . . . . . . ." So M at column 9? Wait row 9: after 8 dots, M at column 9, then 12 dots. Row 10: same. Row 11-22: all dots.

So the input has a vertical line of B at column 13 from rows 3-8. A vertical line of G at column 5 from rows 4-7. A vertical line of M at column 9 from rows 9-10. So we have three vertical lines of different lengths: B line length 6 (rows 3-8 inclusive). G line length 4 (rows 4-7). M line length 2 (rows 9-10). So the longest stick is B, next G, then M. The output grid is a 6x6 square: B outermost, G next, M innermost. Indeed output grid is 6x6: B B B B B B; B G G G G B; B G M M G B; B G M M G B; B G G G G B; B B B B B B. That matches the nested shells: outermost B border

... [10534 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description, training examples, and a test input grid. We need to produce the output grid.

We need to parse the puzzle: The description: "Across a dark field, azure gemstones lie scattered like fallen stars. But among them, two pillars of grey iron stand upright, and azure cornerstone jewels cap their tops and bottoms, forming the frame of a buried chest. Inside the chest, some compartments hold azure gems while others sit empty. The gems strewn outside the chest are fool's gold — glittering distractions left by wanderers. What to do: Find the two iron pillars rising from the darkness — they are the sides of the chest. Look for the azure cornerstones that seal each pillar's top and bottom; these mark where the lid begins and the base ends. Lift the chest out of the ground whole, leaving every scattered gem behind in the dirt. What you hold in your hands is the treasure — nothing more, nothing less."

So we have a grid with black background (.), azure gems (A), grey iron pillars (X), azure cornerstones (A? Wait azure cornerstones are also A? But azure is A. But maybe azure cornerstones are also A but at corners? But we need to differentiate? The description says azure cornerstones are A. But we also have azure gems inside chest. So maybe azure gems inside chest are A as well. So we need to identify the chest boundaries: two vertical pillars of grey iron (X) that are the sides of the chest. The chest is defined by its grey iron walls running vertically and its azure cornerstones and trim running horizontally across the top and bottom. So the chest is a rectangle defined by two vertical X columns and two horizontal A rows at top and bottom. Inside the chest, azure gems (A) may be present or empty (black). Outside the chest, azure gems are scattered (fool's gold). The transformation: "Lift the chest out of the ground whole, leaving every scattered gem behind in the dirt. What you hold in your hands is the treasure — nothing more, nothing less." So we need to extract the chest contents: the rectangle defined by the two X columns and the top and bottom A rows. The output grid should be the chest interior? Or the chest itself? Let's examine training example.

Example 1 Input and Output:

Input:
```
. A . . . . . . . . .
. . A . . . A . . . A
. . . . . . . . . A A
. . A . . . . . A . .
A . X . . . . . X . .
. . X . . A A . X . .
. . X . . . . . X . .
. . A . A . . . A . .
. A . . . . . . A A .
```
Output:
```
A . . . . . A
X . . . . . X
X . . A A . X
X . . . . . X
A . A . . . A
```

Let's analyze. Input grid size: 9 rows, 11 columns? Let's count: first row: ". A . . . . . . . . ." that's 11 columns. So 9x11 grid.

Output grid: 5 rows, 7 columns? Let's count: first row: "A . . . . . A" that's 7 columns. So output is 5x7.

We need to see how output relates to input. Let's map coordinates. We'll index rows 0-8, columns 0-10.

Input grid:

Row0: col0 '.', col1 'A',

... [10064 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "dark ocean with azure bioluminescent plankton drifting randomly. A rectangular porthole: grey iron frame on left and right sides, azure brass fittings along top and bottom edges and at the four corners. Through the glass, azure sea-lights and dark water are visible. Find the porthole — grey iron sides and azure brass fittings — and capture only the sea view framed within. Bioluminescence outside the porthole is hull-side scatter; ignore it."

We have training example 1: Input grid and output grid. We need to deduce transformation rule. Then apply to test input.

We need to parse the training example. Let's rewrite the input and output grids with coordinates.

We have color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon.

In training example 1, input grid is 10x? Let's count columns: Input lines:

1: ". A . . . . . . . . . ." -> 12 columns? Let's count: . (1) space A (2) space . (3) space . (4) space . (5) space . (6) space . (7) space . (8) space . (9) space . (10) space . (11) space . (12). Yes 12 columns.

Row 1: . A . . . . . . . . . .
Row 2: . . A . . . A . . . A
Row 3: . . . . . . . . . A A
Row 4: . . A . . . . . A . .
Row 5: A . X . . . . . X . .
Row 6: . . X . . A A . X . .
Row 7: . . X . . . . . X . .
Row 8: . . A . A . . . A . .
Row 9: . A . . . . . . A A .
Row 10: (not given? Wait there are 9 rows? Let's check: The input shows 9 lines? Actually the input shows 9 lines: lines 1-9. Let's recount: Provided input:

```
. A . . . . . . . . . .
. . A . . . A . . . A
. . . . . . . . . A A
. . A . . . . . A . .
A . X . . . . . X . .
. . X . . A A . X . .
. . X . . . . . X . .
. . A . A . . . A . .
. A . . . . . . A A .
```

Yes 9 rows, 12 columns.

Output grid:

```
A . . . . . A
X . . . . . X
X . . A A . X
X . . . . . X
A . A . . . A
```

That's 5 rows, 7 columns.

So transformation reduces grid size. We need to find rule.

Let's analyze input: The metaphor: "dark ocean with azure bioluminescent plankton drifting randomly. A rectangular porthole: grey iron frame on left and right sides, azure brass fittings along top and bottom edges and at the four corners. Through the glass, azure sea-lights and dark water are visible. Find the porthole — grey iron sides and azure brass fittings — and capture only the sea view framed within. Bioluminescence outside the porthole is hull-side scatter; ignore it."

So we need to find a rectangular region defined by grey iron sides (X) on left and right sides, azure brass fittings (A) along top and bottom edges and at four corners. The view inside is azure (A) and black (.).

So we need to locate a rectangle where the border is X on left/right sides and A on top/bottom edges and corners. Then output the interior of that rectangle (including the border? The output includes A and X? Let's examine output: It contains A and X. The output grid includes A and X. The outp

... [9154 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "dark hall dotted with glowing gems. Most gems are solitary wanderers—red, green, magenta, maroon, grey—content in their loneliness. But two pairs of gems share an ancient bond: orange and yellow are kindred flames, and azure and blue are kindred waters. Sometimes both halves of a bonded pair find themselves stranded in the same corridor, separated by stretches of darkness. When two bonded gems discover they share the same corridor, the one closer to the western wall plants its feet and calls out. Its distant partner cannot resist the pull—it abandons its post and rushes across the darkness to nestle into the space just to the east of its anchor. The spot it fled goes dark, as if it were never there. Unbonded gems feel no such pull and remain perfectly still. Each corridor resolves its reunions independently."

We have training example 1. Let's parse it.

Input grid 10x10. Output grid 10x10. We need to deduce rule.

We have colors: . = black, B=blue, R=red, G=green, Y=yellow, X=grey, M=magenta, O=orange, A=azure, W=maroon.

Bonded pairs: orange and yellow; azure and blue. So O-Y pair, A-B pair. The rule: When two bonded gems are in same corridor (row?), separated by stretches of darkness, the one closer to western wall (left side) anchors, the other moves to the space just to the east of anchor, leaving its original spot dark. Unbonded gems remain.

We need to confirm that "corridor" refers to a row. The puzzle says "Each corridor resolves its reunions independently." So each row is a corridor. So we look at each row: if there are two gems of a bonded pair in same row, they will move accordingly. The one closer to western wall (leftmost) stays, the other moves to the cell immediately to the right of the anchor. The cell it left becomes black. The anchor remains. The moved gem may replace a black cell or maybe a gem? But the rule says "nestle into the space just to the east of its anchor." That space might be empty (black). But what if it's occupied by another gem? The rule might not allow that because there is at most one gem of each color per corridor. But the moved gem might be moving into a cell that is currently black. But if it's not black, maybe it's not allowed? But the rule says "the spot it fled goes dark, as if it were never there." So the moved gem leaves its original spot black. It moves to the cell just east of anchor. That cell might be black or maybe something else? But the rule might not consider collisions because there is at most one gem of each color per corridor. But there could be other gems of other colors in that cell. But the rule might override them? Let's examine training example to confirm.

Example 1 Input:

Row 1: ". . A . . . . W . ." (positions 1-10). Row 2: ". . M . . . . O . ." Row 3: ". O . . . . . . . Y" Row 4: ". . . R . Y . . . ." Row 5: ". . . . B . . . . A" Row 6: ". . G . . . W . . ." Row 7: "M . . . . . . Y

... [12267 chars truncated]

We need to solve a grid transformation puzzle. The description: "What you see: A golden river runs across the middle of the battlefield, dividing two kingdoms. Above the river, the Red Army has pitched its tents on certain squares. Below the river, the Blue Army holds its own positions. The rest of the land lies empty and dark. What to do: The war is over — the golden river dries up, and the two kingdoms merge into one. Wherever either army had claimed ground, the united banner of green now flies. Only the squares that neither army ever touched remain barren darkness. Every soldier, red or blue, becomes green in the new alliance. Grid details: The golden river is a single row splitting the world in half. The united kingdom is exactly the size of one half. Every plot of land answers one question: did anyone fight here? If so, it blooms green."

So the transformation: We have a grid with a "golden river" row that splits the grid into two halves. The top half contains red army positions (R). The bottom half contains blue army positions (B). The rest of the grid is empty (.). The output grid is the union of the two halves: any cell that had R or B becomes G. The rest remains . (black). The output grid size is the same as the input? Wait: The description says "The united kingdom is exactly the size of one half." That might mean the output grid is half the size of the input grid? Let's examine training examples to confirm.

Example 1 Input: Let's parse. Input grid lines:

1: . . . . .
2: . R R R .
3: . R . . .
4: R R R . R
5: Y Y Y Y Y
6: B B . . B
7: B B . B B
8: B . B . B
9: . B . B B

So input grid is 9 rows by 5 columns. The golden river is a single row splitting the world in half. Which row is the river? In the input, row 5 is Y Y Y Y Y. That seems to be the golden river row. So the top half is rows 1-4 (4 rows). The bottom half is rows 6-9 (4 rows). The output grid is 4 rows by 5 columns. Indeed, the output grid in Example 1 is:

G G . . G
G G G G G
G G G . G
G G G G G

That's 4 rows by 5 columns. So the output grid is the top half? Wait, the output grid is 4 rows by 5 columns. Which half? The top half? Let's check: The output grid's first row: G G . . G. Let's compare with the top half of input: rows 1-4. Row 1: . . . . . -> no R or B. But output row 1: G G . . G. That doesn't match. Let's examine the transformation: The output grid is the union of red and blue positions from both halves, but the output grid is the size of one half. But which half? The output grid seems to be the size of the top half (4 rows). But the output grid's first row has G G . . G. Let's see if that matches the union of red positions from top half and blue positions from bottom half, but projected onto the top half? Let's analyze.

We need to understand the mapping. The description: "The united kingdom is exactly the size of one half." That suggests that the output grid is the size of one half of the input grid. But which half? Possibly the top half? Or maybe th

... [9640 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the transformation rule. The puzzle description: "What you see: A nautical chart torn along a gold latitude line. The upper half marks reefs in red from one captain's survey; the lower marks reefs in blue from another's. Uncharted waters are blank on both. What to do: Stitch the charts together along the gold line and project both surveys onto a single map. Every cell where either captain spotted a reef is marked green for danger. Only waters clear on both surveys remain unmarked. The merged chart is the size of one half. Hazard cells are green; safe waters are blank."

So we have two halves: upper half (red cells) and lower half (blue cells). The input grid is a full grid that contains both halves? Let's examine training examples.

Example 1 Input: 10 rows? Let's count. Provided:

Input:
. . . . .
. R R R .
. R . . .
R R R . R
Y Y Y Y Y
B B . . B
B B . B B
B . B . B
. B . B B

Wait that's 9 rows? Let's count: row1: . . . . . (5 columns)
row2: . R R R . (5)
row3: . R . . . (5)
row4: R R R . R (5)
row5: Y Y Y Y Y (5)
row6: B B . . B (5)
row7: B B . B B (5)
row8: B . B . B (5)
row9: . B . B B (5)

So 9 rows, 5 columns. Output:

G G . . G
G G G G G
G G G . G
G G G G G

Output has 4 rows, 5 columns. So output is half the number of rows (9 -> 4? Actually 9/2 = 4.5, but output has 4 rows). So maybe the input grid is 2 halves stacked vertically: top half (rows 1-4) are red cells, bottom half (rows 5-8?) Actually bottom half maybe rows 5-8? But we have 9 rows, so maybe the middle row is the gold line? Wait the description: "nautical chart torn along a gold latitude line. The upper half marks reefs in red from one captain's survey; the lower marks reefs in blue from another's. Uncharted waters are blank on both." So the input grid might contain both halves: top half (rows 1-? maybe 4) with red cells, bottom half (rows 5-? maybe 8) with blue cells. The middle row (row 5) might be the gold line? But row 5 is Y Y Y Y Y. That is all Y's. Y is yellow. The color key: Y=yellow. So maybe Y indicates the gold line. So the input grid has a row of Y's that marks the gold line. The top half (rows above Y) contains red cells (R). The bottom half (rows below Y) contains blue cells (B). The Y row is the gold line. The output grid is the size of one half (i.e., the number of rows above Y). The hazard cells are green where either captain spotted a reef. So we need to overlay the red cells from the top half and the blue cells from the bottom half onto the same grid of size equal to the top half. For each cell, if either the red cell or the blue cell is present (i.e., R or B), then output G. If both are absent (i.e., '.' in both), output '.'.

But we need to align the bottom half onto the top half. The bottom half might be reversed? Let's examine Example 1 to confirm.

Example 1 Input: 9 rows, 5 columns. Row 5 is Y Y Y Y Y. So top half rows 1-4: rows 1-4. Bottom half rows 6-9: row

... [8615 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the rule. Let's parse the problem statement.

We have a metaphorical description: "What you see: A circuit board split by a golden bus bar. The upper channel carries red HIGH signals at certain nodes; the lower carries blue HIGH signals at others. Unpowered nodes sit at LOW on both sides. What to do: The bus bar routes both channels into a shared OR gate array. Each gate outputs green HIGH if either input is HIGH. Only nodes where both inputs are LOW remain off. Grid details: The output array matches one channel's dimensions. HIGH outputs are green; LOW nodes are black."

So we have two channels: upper channel (red) and lower channel (blue). The grid input includes both channels? The input grid includes both red and blue cells. The output grid is green where either red or blue is present (i.e., OR). But the output grid matches one channel's dimensions. Which channel? The output array matches one channel's dimensions. The output grid is smaller than the input? Let's examine training examples.

Example 1 Input grid: Let's list coordinates. The input grid appears to be 9 rows? Let's count: Provided lines:

1: . . . . .
2: . R R R .
3: . R . . .
4: R R R . R
5: Y Y Y Y Y
6: B B . . B
7: B B . B B
8: B . B . B
9: . B . B B

So 9 rows, each row has 5 columns. So input grid is 9x5. Output grid: Provided lines:

1: G G . . G
2: G G G G G
3: G G G . G
4: G G G G G

So output grid is 4x5. So output grid has 4 rows, 5 columns. So output grid matches one channel's dimensions. Which channel? The upper channel maybe? Let's examine the input: The first 4 rows (rows 1-4) contain red cells (R). The next row (row 5) is Y Y Y Y Y (yellow). Then rows 6-9 contain blue cells (B). So the input grid is split by a golden bus bar: row 5 is Y Y Y Y Y (gold). So the upper channel is rows 1-4 (red). The lower channel is rows 6-9 (blue). The bus bar is row 5 (yellow). So the output grid matches one channel's dimensions: maybe the upper channel's dimensions: 4 rows x 5 columns. Indeed output grid is 4x5. So output grid is the OR of the red and blue channels, but only for the positions that correspond to the upper channel? Wait, but the lower channel has 4 rows as well (rows 6-9). So both channels have 4 rows each. So output grid matches one channel's dimensions: either upper or lower. But the output grid is 4x5. So we need to compute OR of red and blue at each corresponding position? But the red and blue are in separate halves of the grid. So we need to overlay them? The bus bar routes both channels into a shared OR gate array. Each gate outputs green HIGH if either input is HIGH. Only nodes where both inputs are LOW remain off. So we need to align the two channels: The upper channel's nodes correspond to the lower channel's nodes? The bus bar splits them but then routes them into a shared OR gate array. So we need to overlay the two halves: For each position (i,j) in the output grid, w

... [9639 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A kitchen counter divided by a strip of saffron garnish. Above it, dollops of paprika reduction sit in some compartments of a mold; below, pools of blueberry coulis fill other compartments. Some compartments on each side are empty. What to do: Remove the saffron divider and fold both sauces into a single mold of the same compartment layout. Any compartment that received flavor from either sauce turns into a mature green pesto. Only compartments that were empty in both halves remain clean. The resulting mold has half the rows. Filled compartments are green; empty ones are bare."

We have training example 1: Input grid and output grid. We need to deduce transformation rule.

We have test input grid. We need to produce output grid.

We need to parse the training example to understand mapping.

Let's analyze training example 1.

Input grid:

```
. . . . .
. R R R .
. R . . .
R R R . R
Y Y Y Y Y
B B . . B
B B . B B
B . B . B
. B . B B
```

We need to interpret grid: Each cell is a color code: '.' black, 'R' red, 'Y' yellow, 'B' blue, etc. The grid is 9 rows? Let's count: Provided lines: 9 lines. Each line has 5 columns? Let's check: first line ". . . . ." -> 5 columns. So grid is 9x5.

Output grid:

```
G G . . G
G G G G G
G G . G
G G G G G
```

Wait output grid lines: 4 lines? Let's count: Provided lines: "G G . . G" (5 columns), "G G G G G" (5 columns), "G G . G" (4 columns?), "G G G G G" (5 columns). That seems inconsistent. Let's double-check: The output grid lines: "G G . . G" (5 columns). "G G G G G" (5). "G G . G" (4). "G G G G G" (5). That seems wrong. Maybe there is a formatting issue. Let's examine the training example again: Provided:

```
Output:
G G . . G
G G G G G
G G . G
G G G G G
```

It might be that the output grid is 4 rows, but the third row has only 4 columns? That seems unlikely. Maybe there is a missing space or a misprint. Let's analyze the transformation conceptually: The metaphor says: "kitchen counter divided by a strip of saffron garnish. Above it, dollops of paprika reduction sit in some compartments of a mold; below, pools of blueberry coulis fill other compartments. Some compartments on each side are empty. Remove the saffron divider and fold both sauces into a single mold of the same compartment layout. Any compartment that received flavor from either sauce turns into a mature green pesto. Only compartments that were empty in both halves remain clean. The resulting mold has half the rows. Filled compartments are green; empty ones are bare."

So we have a grid that is split horizontally by a saffron divider (maybe a row of 'X' or something). The top half has some colored cells (paprika reduction) and bottom half has some colored cells (blueberry coulis). We need to combine them: For each cell, if either top or bottom cell is colored (i.e., not '.'), then output cell is green 'G'. If both are '.' then output cell remains '

... [10856 chars truncated]

We need to parse the problem. We have a grid transformation puzzle. The description: "Two architectural floor plans separated by a golden binding strip. The upper plan draws walls in red drafting ink; the lower plan draws walls in blue. Open spaces in each plan are empty. Remove the binding and overlay the plans on the light table. Any cell where either plan specifies a wall becomes solid green in the composite. Only spaces open in both plans remain empty. The composite plan has the footprint of one floor. Solid walls are green; open spaces are unmarked."

So we have two input grids? Wait: The training example shows Input: a grid of 10 rows? Let's examine Example 1 Input:

```
. . . . .
. R R R .
. R . . .
R R R . R
Y Y Y Y Y
B B . . B
B B . B B
B . B . B
. B . B B
```

Wait that's 9 rows? Let's count: Row1: ". . . . ." (5 columns). Row2: ". R R R ." (5). Row3: ". R . . ." (5). Row4: "R R R . R" (5). Row5: "Y Y Y Y Y" (5). Row6: "B B . . B" (5). Row7: "B B . B B" (5). Row8: "B . B . B" (5). Row9: ". B . B B" (5). So 9 rows, 5 columns.

Output:

```
G G . . G
G G G G G
G G G . G
G G G G G
```

That's 4 rows, 5 columns. So the output is smaller. So the transformation is not just overlaying two grids of same size. The input seems to contain two floor plans separated by a golden binding strip. The golden binding strip might be the row of Y's? Wait Y is yellow. In the input, row5 is "Y Y Y Y Y". That might be the golden binding strip. The upper plan is above that row, the lower plan is below that row. The upper plan uses red walls (R). The lower plan uses blue walls (B). The Y row is the binding strip. The output is the composite plan: any cell where either plan has a wall becomes green. Only cells open in both remain empty. So we overlay the two plans ignoring the binding row. But the output grid is smaller: we need to combine the two halves into one grid. But the output grid has 4 rows, not 8. Wait the upper plan has 4 rows (rows 1-4). The lower plan has 4 rows (rows 6-9). So overlaying them would produce 4 rows? But we need to overlay them: For each cell position (i,j) in the output, we look at the corresponding cell in the upper plan (row i) and the lower plan (row i). But the lower plan's rows are offset? Wait the lower plan has 4 rows, but we overlay them onto the same positions as the upper plan. So we need to align them row-wise: row1 of upper plan with row1 of lower plan? But the lower plan's row1 is row6 of input. So we overlay row1 of upper plan with row1 of lower plan. That yields 4 rows. That matches output: 4 rows. So the output grid is the overlay of the two halves, ignoring the binding row. So we overlay each cell: if either is a wall (R or B), output G. If both are empty (.), output . (empty). But we also need to consider that the lower plan may have B walls, but the upper plan may have R walls. So we treat both as walls. So the rule: For each cell (i,j) in the output, if either the upper plan cell (i,j) is R or the lower plan cell (i

... [10355 chars truncated]

We need to solve a grid transformation puzzle. The description: "What you see: A war table split by a gold command ribbon. Above, one scout's report marks enemy positions in red. Below, the other scout's report marks positions in blue. Unobserved cells are blank in both. What to do: Remove the ribbon and merge both intelligence reports onto one tactical map. Every cell flagged by at least one scout turns green for 'confirmed presence.' Only cells missed by both remain unmarked. The tactical map matches one scout report's dimensions. Occupied cells are green; unconfirmed cells are blank."

So we have two grids: one above the ribbon (red cells) and one below (blue cells). The output grid is the same size as one of the scout reports (the top or bottom? The description says "The tactical map matches one scout report's dimensions." So the output grid is the same size as the top or bottom grid. The input grid is a single grid that contains both top and bottom parts separated by a row of Y's? Wait, the training examples show input grids that have a row of Y's in the middle. Let's examine Example 1 input:

Example 1 Input:
```
. . . . .
. R R R .
. R . . .
R R R . R
Y Y Y Y Y
B B . . B
B B . B B
B . B . B
. B . B B
```
So the input grid is 9 rows by 5 columns. The first 4 rows are the red scout's report (top). Then a row of Y Y Y Y Y (the gold command ribbon). Then 5 rows of blue scout's report (bottom). The output grid is 4 rows by 5 columns: 
```
G G . . G
G G G G G
G G G . G
G G G G G
```
So the output grid is the same size as the top part (4 rows). The output grid shows green cells where either red or blue had a cell. But note that the bottom part has 5 rows, but the output only has 4 rows. So we only consider the top part's dimensions. But we need to merge the two reports onto one map of that size. So we overlay the bottom part onto the top part, aligning them by columns but maybe aligning rows? Wait, the bottom part has 5 rows, but the top part has 4 rows. So how do we overlay? The output grid has 4 rows. So we need to overlay the bottom part onto the top part by aligning the bottom part's rows with the top part's rows? But the bottom part has 5 rows, so maybe we only consider the first 4 rows of the bottom part? Or maybe we consider the bottom part's rows that correspond to the top part's rows? Let's examine Example 1 to deduce the overlay logic.

Example 1 Input: top 4 rows, bottom 5 rows. Output 4 rows. Let's overlay bottom part onto top part by aligning the bottom part's rows with the top part's rows starting from the top? That would mean we overlay bottom rows 1-4 onto top rows 1-4. But bottom part has 5 rows, so row 5 of bottom part is not used. Let's test: bottom part rows:

Row 5: B B . . B
Row 6: B B . B B
Row 7: B . B . B
Row 8: . B . B B

Wait, bottom part has 5 rows: rows 6-10? Actually the input grid has 9 rows: rows 1-4 top, row 5 Y's, rows 6-10 bottom. So bottom part rows 6-10: 5 rows. Let's index them as bottom row 1 = row 6 of inpu

... [9719 chars truncated]

We need to solve the puzzle. Let's parse the description and training example to deduce transformation rule.

We have a 11x11 grid. Grey stone walls (X) form a tic-tac-toe frame: full rows and columns of stone dividing everything into a 3x3 arrangement of small 3x3 rooms. So the grid is 11x11: there are 3 rows of rooms each 3 cells tall, separated by 1 cell of walls (X). Similarly columns. So the pattern: rows 0-2 are first room row, row 3 is wall, rows 4-6 second room row, row 7 wall, rows 8-10 third room row. Similarly columns: columns 0-2 first room column, column 3 wall, columns 4-6 second room column, column 7 wall, columns 8-10 third room column. So the grid is 11x11 with X at row 3,7 and column 3,7. So the 3x3 rooms are at coordinates: (room row index 0-2, room col index 0-2). Each room is 3x3 cells.

The description: "What you see: A tic-tac-toe mansion of nine rooms separated by grey stone walls. Each room is cluttered with colorful furniture — but somewhere in the mansion, a single golden firefly (Y) flickers. Everything else is just set dressing. What to do: The firefly knows two things: which room it lives in, and where it's hovering within that room. Its position inside its room is a secret address — coordinates that point to one of the nine rooms in the mansion. The firefly sends its entire room — furniture, colors, and all — flying across the mansion to land in the addressed room. Every other room goes dark, its contents swept clean. Only the delivered room and the stone walls remain."

So the transformation: The Y cell indicates the "firefly" location. It knows which room it lives in (the room containing Y). And where it's hovering within that room: the coordinates of Y relative to the room (i.e., row and column within the 3x3 subgrid). That coordinate is used as an address to one of the nine rooms in the mansion. The firefly sends its entire room (the 3x3 subgrid containing Y) to that addressed room. All other rooms become dark (filled with .). Only the delivered room and the stone walls remain. So the output grid will have the 3x3 subgrid that was originally the Y's room moved to the target room location, with all other cells (except X walls) set to '.'.

We need to confirm with training example.

Let's analyze Example 1.

Input grid 11x11. Let's parse.

I'll rewrite the input grid with coordinates. Use 0-indexed rows 0-10, columns 0-10.

Input Example 1:

Row0: ". O . X . M . X O . ."
Row1: "A G M X . . . X . A ."
Row2: ". . . X . G . X . . ."
Row3: "X X X X X X X X X X X"
Row4: ". A O X . G . X . . O"
Row5: ". . . X A . . X . A M"
Row6: ". . M X . . . X G . ."
Row7: "X X X X X X X X X X X"
Row8: ". M . X . A . X . . ."
Row9: "A . . X G . . X Y . A"
Row10: ". O . X . M . X . M O"

We need to identify the Y cell. Let's find Y: row9 col? Row9: "A . . X G . . X Y . A". So Y at row9 col? Let's index: columns 0-10. Row9: col0 'A', col1 '.', col2 '.', col3 'X', col4 'G', col5 '.', col6 '.', col7 'X', col8 'Y',

... [8483 chars truncated]

We need to solve a grid transformation puzzle. The description: "Scattered across a dark landscape, small herds of mysterious grey animals huddle together. Some travel in pairs, some in trios, and some in groups of four. Each herd keeps to itself, never touching another. What to do: A naturalist arrives to catalog the wildlife. She identifies each herd by counting its members, then paints them with a tag color revealing their species: the smallest pairs share one color, the middle-sized trios another, and the largest bands of four a third. The empty wilderness stays untouched. Grid details: The dark terrain remains as-is. Every grey animal receives its species tag — a new coat color determined solely by how many companions share its herd. No creatures appear or vanish; only their coats change."

So we have a grid with '.' representing black (dark terrain). 'X' representing grey animals. We need to identify connected components of X's (connected orthogonally? Likely orthogonal adjacency). Each component size: 2, 3, or 4. Then we recolor each X in that component to a color based on size: pairs -> one color, trios -> another, groups of four -> another. The colors used in example: In Example 1, input had X's. Output shows R, G, B. Let's analyze mapping.

Example 1 Input grid 10x10. Let's parse.

Input grid lines:

1: . . . . . . . . . .
2: . . . . . . . . . .
3: . X X X . . . X . .
4: . . . . . . . X . .
5: . . . . . . . . . .
6: . . . X X . . . . .
7: . . . X . . . . . .
8: . . . . . . . X . .
9: . X X . . . X X X .
10: . X X . . . . . . .

Output grid lines:

1: . . . . . . . . . .
2: . . . . . . . . . .
3: . R R R . . . G . .
4: . . . . . . . G . .
5: . . . . . . . . . .
6: . . . R R . . . . .
7: . . . R . . . . . .
8: . . . . . . . B . .
9: . B B . . . B B B .
10: . B B . . . . . . .

We need to map each component.

Let's identify components in input.

Input X positions:

Row3: col2,3,4 (three X's contiguous horizontally). Row3 col8 (X). Row4 col8 (X). Row6 col4,5 (two X's). Row7 col4 (X). Row8 col8 (X). Row9 col2,3 (two X's). Row9 col7,8,9 (three X's). Row10 col2,3 (two X's).

Also Row3 col8 and Row4 col8 are adjacent vertically, so they form a component of size 2? Wait Row3 col8 and Row4 col8 are adjacent vertically, yes. So component of size 2.

Row6 col4 and Row6 col5 adjacent horizontally, size 2. Row7 col4 adjacent to Row6 col4 vertically, so that extends component to size 3? Wait Row6 col4 is part of component with Row6 col5. Row7 col4 is adjacent to Row6 col4, so component size 3. So that component is 3 X's: (6,4), (6,5), (7,4). Good.

Row9 col2,3 adjacent horizontally, size 2. Row10 col2,3 adjacent horizontally, and also adjacent vertically to row9 col2,3? Row9 col2 adjacent to row10 col2, row9 col3 adjacent to row10 col3. So all four X's (9,2),(9,3),(10,2),(10,3) form a component of size 4. Good.

Row9 col7,8,9 adjacent horizontally, size 3. Row8 col8 adjacent to row9 col8 vertically, so that extends component to size 4? 

... [8469 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A dark slide dotted with pale, unstained cell colonies of varying sizes. What to do: Apply the appropriate fluorescent marker to each colony based on the number of cells it contains. Smaller fusions glow one hue, mid-sized another, and the largest yet another. Grid details: Grid dimensions match the input. Black background remains. Each pale colony is recolored with its size-appropriate fluorescent dye."

We have training example 1: Input grid 10x10 with '.' and 'X' cells. Output grid has '.' and colored cells: R, G, B. So we need to map each connected component of X's to a color based on size. The mapping: small -> R? mid -> G? large -> B? Let's analyze.

Example 1 Input:

Row 0: . . . . . . . . . .
Row 1: . . . . . . . . . .
Row 2: . X X X . . . X . .
Row 3: . . . . . . . X . .
Row 4: . . . . . . . . . .
Row 5: . . . X X . . . . .
Row 6: . . . X . . . . . .
Row 7: . . . . . . . X . .
Row 8: . X X . . . X X X .
Row 9: . X X . . . . . . .

Let's identify connected components of X's. Use 4-neighbor connectivity? Likely 4-neighbor (up/down/left/right). Let's map.

Component 1: At (2,1),(2,2),(2,3) contiguous horizontally. Also (3,7) is separate? Wait (2,7) is X. Let's list all X coordinates:

Row 2: (2,1),(2,2),(2,3),(2,7)
Row 3: (3,7)
Row 5: (5,3),(5,4)
Row 6: (6,3)
Row 7: (7,7)
Row 8: (8,1),(8,2),(8,6),(8,7),(8,8)
Row 9: (9,1),(9,2)

Also maybe (8,6) is X. Yes.

Now connectivity:

Component A: (2,1),(2,2),(2,3) are connected horizontally. Are they connected to any other X? Check adjacency: (3,1) is ., (1,1) ., (2,0) ., (2,4) . So isolated component of size 3.

Component B: (2,7),(3,7),(7,7),(8,6),(8,7),(8,8),(7,7) etc. Let's see connectivity: (2,7) adjacent to (3,7). (3,7) adjacent to (2,7) and (4,7) ., (3,6) ., (3,8) . So component B includes (2,7),(3,7). Also (7,7) is far away, not connected. So component B size 2.

Component C: (5,3),(5,4),(6,3). These are connected: (5,3) adjacent to (5,4) and (6,3). (6,3) adjacent to (5,3). So component C size 3.

Component D: (7,7) alone? Wait (7,7) is X. Adjacent to (6,7) ., (8,7) X, (7,6) ., (7,8) . So (7,7) connects to (8,7). So component D includes (7,7),(8,7). Also (8,6) and (8,8) adjacent to (8,7). So component D includes (7,7),(8,7),(8,6),(8,8). Also (8,6) adjacent to (8,7). (8,8) adjacent to (8,7). So component D size 4.

Component E: (8,1),(8,2),(9,1),(9,2). These are connected: (8,1) adjacent to (8,2),(9,1). (8,2) adjacent to (8,1),(9,2). (9,1) adjacent to (8,1),(9,2). (9,2) adjacent to (8,2),(9,1). So component E size 4.

So we have components sizes: 3,2,3,4,4. Output grid shows colors:

Let's map output grid:

Row 0: all .
Row 1: all .
Row 2: . R R R . . . G . .
Row 3: . . . . . . . G . .
Row 4: all .
Row 5: . . . R R . . . . .
Row 6: . . . R . . . . . .
Row 7: . . . . . . . B . .
Row 8: . B B . . . B B B .
Row 9: . B B . . . . . . .

So mapping: component A (size 3) at (2,1-3) is colored R

... [7822 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the rule. Let's analyze.

We have a grid of 10x10 (since examples show 10 rows, 10 columns). Input uses '.' for black (empty). 'X' for grey. Output uses colors: R, G, B, etc. The rule: "Count the stars in each cluster and render them in the false-color palette assigned to that membership tier." The metaphor: "dark sky field with faint grey star clusters of various sizes. Count the stars in each cluster and render them in the false-color palette assigned to that membership tier." So we need to identify clusters of X's (connected components). Count number of X's in each cluster. Then assign a color based on membership tier. The membership tier likely refers to cluster size categories. The palette mapping: maybe small clusters -> B, medium -> G, large -> R, etc. Let's analyze training examples to deduce mapping.

Example 1 Input: Let's parse.

Example 1 Input grid:

Row1: . . . . . . . . . .
Row2: . . . . . . . . . .
Row3: . X X X . . . X . .
Row4: . . . . . . . X . .
Row5: . . . . . . . . . .
Row6: . . . X X . . . . .
Row7: . . . X . . . . . .
Row8: . . . . . . . X . .
Row9: . X X . . . X X X .
Row10: . X X . . . . . . .

Let's mark coordinates (row, col). We'll index 1-10.

Row3: X at (3,2),(3,3),(3,4). Also X at (3,8).
Row4: X at (4,8).
Row6: X at (6,4),(6,5).
Row7: X at (7,4).
Row8: X at (8,8).
Row9: X at (9,2),(9,3),(9,7),(9,8),(9,9).
Row10: X at (10,2),(10,3).

Now we need to identify clusters: adjacency likely 4-neighbor (up/down/left/right). Let's find clusters.

Cluster A: The group at (3,2),(3,3),(3,4) maybe connected to (6,4),(6,5),(7,4)? Let's check connectivity: (3,4) is at row3 col4. (4,4) is '.'; (5,4) '.'; (6,4) X. So there is a vertical gap of 2 rows. So not connected. So cluster A is just the three X's at row3 col2-4. That's size 3.

Cluster B: The group at (3,8),(4,8),(8,8). Wait (4,8) is adjacent to (3,8). (5,8) '.'; (6,8) '.'; (7,8) '.'; (8,8) X. So (3,8) and (4,8) are connected; (8,8) is separate. So cluster B: (3,8),(4,8) size 2.

Cluster C: The group at (6,4),(6,5),(7,4). Let's check connectivity: (6,4) adjacent to (6,5) horizontally; (6,4) adjacent to (7,4) vertically. So cluster size 3.

Cluster D: The group at (9,2),(9,3),(10,2),(10,3). These four X's form a 2x2 block. So cluster size 4.

Cluster E: The group at (9,7),(9,8),(9,9). These three X's adjacent horizontally. So cluster size 3.

Cluster F: The group at (9,7),(9,8),(9,9) we counted. Wait we also have (9,7),(9,8),(9,9). That's cluster E. Are there any other X's? Let's check: (9,7),(9,8),(9,9). That's cluster E. Are there any X's at (9,7) etc. Already counted. So cluster E size 3.

Also cluster at (9,7),(9,8),(9,9) is separate from cluster at (9,2),(9,3),(10,2),(10,3). Yes.

Also cluster at (9,7),(9,8),(9,9) maybe also adjacent to (8,8)? Wait (8,8) is X but not adjacent to (9,7) or (9,8) or (9,9) because adjacency is 4-neighbor. (8,8) is at row8 col8. (9,8) is at row

... [7484 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "Dark open water with clusters of grey vessels rafted together at scattered anchorages. Count the boats in each raft-up and repaint them in the harbor signal color for that raft size." So we have a grid with '.' representing black (dark water). 'X' representing grey vessels (boats). We need to count the boats in each raft-up (connected group of X's). Then repaint them in the harbor signal color for that raft size. The output shows colors: R, G, B, etc. We need to map group size to color. Let's analyze training example 1.

Input grid 10x10. Output grid 10x10. Let's parse.

Input Example 1:

Row1: . . . . . . . . . .
Row2: . . . . . . . . . .
Row3: . X X X . . . X . .
Row4: . . . . . . . X . .
Row5: . . . . . . . . . .
Row6: . . . X X . . . . .
Row7: . . . X . . . . . .
Row8: . . . . . . . X . .
Row9: . X X . . . X X X .
Row10: . X X . . . . . . .

Output Example 1:

Row1: . . . . . . . . . .
Row2: . . . . . . . . . .
Row3: . R R R . . . G . .
Row4: . . . . . . . G . .
Row5: . . . . . . . . . .
Row6: . . . R R . . . . .
Row7: . . . R . . . . . .
Row8: . . . . . . . B . .
Row9: . B B . . . B B B .
Row10: . B B . . . . . . .

We need to map each group of X's to a color. Let's identify groups in input.

Group 1: Row3 columns 2-4: X X X contiguous horizontally. Also check adjacency: Are there any other X's adjacent? Row4 col8 is separate. So group 1 size = 3. Output: those positions become R R R. So size 3 -> R.

Group 2: Row3 col8: X. Row4 col8: X. Row5 none. Row6 none. So vertical pair of X's at (3,8) and (4,8). That's size 2. Output: those positions become G G. So size 2 -> G.

Group 3: Row6 col4-5: X X. Row7 col4: X. So group of 3? Let's check connectivity: Row6 col4 adjacent to Row6 col5 horizontally. Row7 col4 adjacent vertically to Row6 col4. So group size 3. Output: those positions become R R R. Yes.

Group 4: Row8 col8: X. Row9 col8-10: X X X. Row10 col2-3: X X. Wait check connectivity: Row8 col8 adjacent to Row9 col8 vertically. Row9 col8 adjacent to Row9 col9 horizontally, and to Row9 col10 horizontally. Row9 col8 also adjacent to Row10 col8? Row10 col8 is '.' so no. Row9 col8 also adjacent to Row10 col8? no. Row9 col8 adjacent to Row10 col8? no. Row9 col8 adjacent to Row10 col8? no. Row9 col8 adjacent to Row10 col8? no. Row9 col8 adjacent to Row10 col8? no. Row9 col8 adjacent to Row10 col8? no. So group 4 includes Row8 col8, Row9 col8-10. That's 4 cells. Output: those positions become B B B B? Let's check output: Row8 col8: B. Row9 col8-10: B B B. Yes. So size 4 -> B.

Group 5: Row9 col2-3: X X. Row10 col2-3: X X. That's a 2x2 block of 4 cells. Are they connected? Yes. So group size 4. Output: those positions become B B B B. Row9 col2-3: B B. Row10 col2-3: B B. Yes.

So mapping: size 3 -> R, size 2 -> G, size 4 -> B. What about size 1? Not present. But we might need to map size 1 to some color maybe Y? Let's examine color key: . = black, B=b

... [8878 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "dark divination cloth with clusters of pale bone fragments of varying group sizes. Count the touching shards in each cluster to determine which deity claims the omen, then let that patron's sacred color suffuse the bones." So we have a grid with '.' representing black (empty cloth). 'X' representing grey bone fragments. The transformation: For each cluster of X's (connected orthogonally? maybe 4-neighbor connectivity), we count the number of touching shards in each cluster. That is, the size of the cluster (# of X cells). Then we determine which deity claims the omen. The output shows colored cells: R, G, B, etc. The mapping from cluster size to color is likely predetermined. We need to deduce mapping from training example.

We have Example 1 input and output. Let's analyze.

Example 1 Input grid 10x10. Let's parse.

Input grid lines:

1: . . . . . . . . . .
2: . . . . . . . . . .
3: . X X X . . . X . .
4: . . . . . . . X . .
5: . . . . . . . . . .
6: . . . X X . . . . .
7: . . . X . . . . . .
8: . . . . . . . X . .
9: . X X . . . X X X .
10: . X X . . . . . . .

Let's mark coordinates (row, col). We'll identify clusters of X's.

We need to determine connectivity: likely 4-neighbor (up, down, left, right). Let's examine.

Row3: positions (3,2),(3,3),(3,4) are X. Row3 col8 is X. Row4 col8 is X. Row6 col4, col5 are X. Row7 col4 is X. Row8 col8 is X. Row9 col2, col3 are X. Row9 col7, col8, col9 are X. Row10 col2, col3 are X.

Also row3 col8 and row4 col8 are adjacent vertically, so cluster. Row8 col8 is separate? Wait row8 col8 is X, but row7 col8? Row7 col8 is '.'; row9 col8 is X. So row8 col8 is adjacent to row9 col8? Yes, row8 col8 is above row9 col8, so they are connected. So cluster includes row3 col8, row4 col8, row8 col8, row9 col7,8,9? Wait row9 col7,8,9 are X. Row8 col8 is adjacent to row9 col8. Row9 col7 adjacent to row9 col8. Row9 col9 adjacent to row9 col8. So cluster includes all those. Also row3 col8 and row4 col8 are connected to row8 col8? They are separated by rows 5 and 6 and 7. Are there any X's in between? Row5 col8 is '.'; row6 col8 '.'; row7 col8 '.'; row8 col8 X. So no connectivity. So cluster of X's at col8 row3 and row4 is separate from cluster at row8 col8 and row9 col7-9. So we have at least two clusters in that vertical column.

Also cluster at row3 col2-4: positions (3,2),(3,3),(3,4). Are there any adjacent X's below? Row4 col2-4 are '.'; row2 col2-4 '.'; row3 col2-4 are only cluster. So cluster size 3.

Cluster at row6 col4-5: (6,4),(6,5). Row7 col4 is X adjacent to (6,4). So cluster includes (6,4),(6,5),(7,4). Are there any other X's adjacent? Row5 col4-5 '.'; row8 col4-5 '.'; row6 col4-5 adjacent to each other. So cluster size 3.

Cluster at row9 col2-3 and row10 col2-3: (9,2),(9,3),(10,2),(10,3). Are they connected? Yes, (9,2) adjacent to (10,2); (9,3) adjacent to (10,3); (9,2) adjacent to (9,3). So cluster size 4.

Cluster at row8 co

... [8989 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A dark stage floor with clusters of dancers (grey) holding various small formations. What to do: Count the dancers in each formation and assign them the costume color designated for that formation size. Grid details: Same stage. Empty floor stays dark. Each dancer group appears in their formation-size costume color."

We have training example 1: Input grid 10x10 with '.' and 'X' (grey). Output grid 10x10 with '.' and colors R, G, B. The rule: Count the dancers in each formation and assign them the costume color designated for that formation size. So we need to identify clusters of X's (connected components). For each cluster, count the number of X's. Then assign a color based on cluster size. The mapping from size to color: we need to deduce from example.

Let's analyze example 1.

Input grid:

Row indices 0-9, columns 0-9.

I'll rewrite input grid with coordinates.

Input:

Row0: . . . . . . . . . .
Row1: . . . . . . . . . .
Row2: . X X X . . . X . .
Row3: . . . . . . . X . .
Row4: . . . . . . . . . .
Row5: . . . X X . . . . .
Row6: . . . X . . . . . .
Row7: . . . . . . . X . .
Row8: . X X . . . X X X .
Row9: . X X . . . . . . .

Let's mark X positions:

Row2: col1,2,3; col7
Row3: col7
Row5: col3,4
Row6: col3
Row7: col7
Row8: col1,2; col6,7,8
Row9: col1,2

We need to find connected components. Connectivity likely 4-directional (up, down, left, right). Let's analyze.

Component A: cluster around (2,1),(2,2),(2,3). Are they connected to others? (2,1) adjacent to (3,1) none; (2,2) adjacent to (2,1),(2,3),(1,2),(3,2). None of those are X except (2,1),(2,3). So cluster of size 3 at top left. Output shows R R R at row2 col1-3. Yes output row2: . R R R . . . G . . Wait output row2: ". R R R . . . G . ." Actually output row2: ". R R R . . . G . ." Let's check. Output row2: ". R R R . . . G . ." So cluster of size 3 turned to R. So size 3 -> R.

Component B: cluster at (2,7),(3,7),(7,7),(8,6),(8,7),(8,8). Wait check connectivity: (2,7) adjacent to (3,7). (3,7) adjacent to (2,7),(4,7),(3,6),(3,8). None of those are X except (2,7). So cluster of size 2? Wait (2,7) and (3,7) only. But there are also X at (7,7) and (8,6),(8,7),(8,8). Are they connected? Let's check connectivity: (7,7) adjacent to (6,7),(8,7),(7,6),(7,8). (6,7) none; (8,7) is X; (7,6) none; (7,8) none. So (7,7) connected to (8,7). (8,7) adjacent to (8,6),(8,8),(7,7),(9,7). So (8,6) and (8,8) are X. So cluster of size 4? Wait we have X at (2,7),(3,7),(7,7),(8,6),(8,7),(8,8). Are (3,7) connected to (7,7)? No, because there is a gap of rows 4-6. So they are separate clusters. So cluster B1: (2,7),(3,7) size 2. Output row2 col7: G? Wait output row2 col7: G. Output row3 col7: G. So size 2 -> G.

Cluster B2: (7,7),(8,6),(8,7),(8,8). That's 4 X's. Output row7 col7: B? Wait output row7 col7: B? Let's check output row7: ". . . . . . . X . ." Actually output row7: ". . . . . . . X . ." Wait output ro

... [7812 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A cutting board (black surface) scattered with clusters of raw mushrooms (grey) of varying bunch sizes. What to do: Weigh each connected bunch by counting its pieces, then coat it in the sauce assigned to that weight class. Grid details: Same board layout. Background unchanged. Each mushroom cluster takes on the color of its assigned marinara."

We have training example 1: Input grid 10x10 with '.' and 'X' cells. Output grid 10x10 with '.' and colors R, G, B. The transformation: For each connected component of X's (connected orthogonally? likely 4-neighbor connectivity), count the number of cells. Then assign a color based on weight class. The mapping from size to color: In example 1, we need to deduce mapping.

Let's analyze example 1.

Input grid:

Row indices 0-9, columns 0-9.

I'll rewrite input grid with coordinates.

Input:

Row0: . . . . . . . . . .
Row1: . . . . . . . . . .
Row2: . X X X . . . X . .
Row3: . . . . . . . X . .
Row4: . . . . . . . . . .
Row5: . . . X X . . . . .
Row6: . . . X . . . . . .
Row7: . . . . . . . X . .
Row8: . X X . . . X X X .
Row9: . X X . . . . . . .

Let's mark X positions.

Row2: col1,2,3 are X. Also col7 is X.
Row3: col7 is X.
Row5: col3,4 are X.
Row6: col3 is X.
Row7: col7 is X.
Row8: col1,2 are X. col6,7,8 are X.
Row9: col1,2 are X.

So we have several clusters.

Let's identify connected components (4-neighbor adjacency). We'll list each cluster.

Cluster A: The group at top-left: Row2 col1-3. Are they connected to any other X? Let's check adjacency: Row2 col1 adjacent to row1 col1 (.), row3 col1 (.), row2 col0 (.), row2 col2 (X). So cluster includes col1,2,3. Row2 col3 adjacent to row1 col3 (.), row3 col3 (.), row2 col2 (X). So cluster A size 3.

Cluster B: The group at top-right: Row2 col7, Row3 col7, Row7 col7, Row8 col6-8? Wait check connectivity: Row2 col7 adjacent to Row3 col7 (down). Row3 col7 adjacent to Row2 col7 (up) and Row4 col7 (.), Row3 col6 (.), Row3 col8 (.). So cluster includes Row2 col7 and Row3 col7. Row7 col7 is far away: row4-6 col7 are '.'; row7 col7 is isolated? But maybe connected via row8 col7? Let's check: Row7 col7 adjacent to Row6 col7 (.), Row8 col7 (X). Row8 col7 adjacent to Row7 col7 (up), Row9 col7 (.), Row8 col6 (X), Row8 col8 (X). So cluster includes Row7 col7, Row8 col6,7,8. Row8 col6 adjacent to Row7 col6 (.), Row9 col6 (.), Row8 col5 (.), Row8 col7 (X). So cluster includes Row8 col6,7,8. Row9 col6? no. So cluster B includes Row2 col7, Row3 col7, Row7 col7, Row8 col6,7,8. Are they connected? Let's check connectivity: Row2 col7 to Row3 col7 is connected. Row3 col7 to Row4 col7 (.) no. Row3 col7 to Row2 col7 (connected). Row3 col7 to Row3 col6 (.) no. Row3 col7 to Row3 col8 (.) no. So cluster B currently includes Row2 col7 and Row3 col7. Row7 col7 is not connected to them because there is a gap of rows 4-6. So cluster B splits into two separate clusters: cluster B1: Row2 col7,

... [8399 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: An empty field (black) with clusters of unassigned players (grey) standing in small groups. What to do: Count the members of each group and issue them the jersey color designated for that squad size. Grid details: Same field. Empty grass stays black. Each group now wears their size-assigned jersey color."

We have training example 1: Input grid 10x10 with '.' and 'X' (grey). Output grid has '.' and colors: R, G, B. So transformation: For each cluster of X's (connected components), count the number of cells in the cluster. Then assign a color based on cluster size. The mapping from size to color: We need to deduce from example.

Let's analyze Example 1.

Input grid:

Row1: . . . . . . . . . .
Row2: . . . . . . . . . .
Row3: . X X X . . . X . .
Row4: . . . . . . . X . .
Row5: . . . . . . . . . .
Row6: . . . X X . . . . .
Row7: . . . X . . . . . .
Row8: . . . . . . . X . .
Row9: . X X . . . X X X .
Row10: . X X . . . . . . .

Let's mark coordinates (row, col). We'll identify clusters of X's. Connectivity: likely 4-directional (up, down, left, right). Let's examine.

Cluster 1: Row3 col2-4: X X X contiguous horizontally. Also Row4 col8: X? Wait row4 col8 is X but not connected to row3 col2-4. Let's examine each cluster.

Let's list all X positions:

Row3: col2, col3, col4, col8
Row4: col8
Row6: col4, col5
Row7: col4
Row8: col8
Row9: col2, col3, col7, col8, col9
Row10: col2, col3

Now cluster connectivity:

Cluster A: Row3 col2-4 (3 cells). Are there any adjacent X's? Row4 col2? No. Row3 col2 adjacent to row2 col2? No. Row3 col4 adjacent to row4 col4? No. So cluster A size 3.

Cluster B: Row3 col8 and Row4 col8 and Row8 col8? Wait Row4 col8 adjacent to Row3 col8 (vertical). Row8 col8 is far away (row8). Row4 col8 adjacent to Row5 col8? Row5 col8 is '.'; Row4 col8 adjacent to Row3 col8 (connected). Row4 col8 adjacent to Row5 col8 '.'; Row4 col8 adjacent to Row4 col7 '.'; Row4 col8 adjacent to Row4 col9 '.'; Row4 col8 adjacent to Row3 col8 (connected). Row8 col8 is not adjacent to Row4 col8 (distance 4). So cluster B: Row3 col8 + Row4 col8 = 2 cells.

Cluster C: Row6 col4, col5, Row7 col4. Let's examine connectivity: Row6 col4 adjacent to Row6 col5 (horizontal). Row6 col4 adjacent to Row7 col4 (vertical). Row6 col5 adjacent to Row7 col5? Row7 col5 '.'; Row6 col5 adjacent to Row5 col5 '.'; Row6 col5 adjacent to Row6 col6 '.'; Row6 col5 adjacent to Row7 col5 '.'; So cluster C size 3 cells: (6,4), (6,5), (7,4).

Cluster D: Row9 col2, col3, Row10 col2, col3. Let's examine connectivity: Row9 col2 adjacent to Row9 col3 (horizontal). Row9 col2 adjacent to Row10 col2 (vertical). Row9 col3 adjacent to Row10 col3 (vertical). So cluster D size 4 cells: (9,2),(9,3),(10,2),(10,3).

Cluster E: Row9 col7, col8, col9. Are they connected? Row9 col7 adjacent to Row9 col8 (horizontal). Row9 col8 adjacent to Row9 col9 (horizontal). Row9 col7 adjacent to Row8 col7 '.'; Row9 col

... [8510 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A dark radar screen with scattered grey storm cells of varying extent. What to do: Measure each connected weather system by its cell count, then paint it in the alert color assigned to that severity tier. Grid details: Same radar dimensions. Clear sky stays dark. Each storm system is recolored by its size-based alert level."

We have training example 1: Input grid 10x10 with '.' and 'X' cells. Output grid has '.' and colored cells: R, G, B. So we need to map each connected component of X's to a color based on its size. The mapping: small components -> B? Or maybe B for small, G for medium, R for large? Let's analyze.

We need to parse the training example. Let's reconstruct the input grid coordinates. We'll index rows 0-9, columns 0-9.

Input Example 1:

Row0: . . . . . . . . . .
Row1: . . . . . . . . . .
Row2: . X X X . . . X . .
Row3: . . . . . . . X . .
Row4: . . . . . . . . . .
Row5: . . . X X . . . . .
Row6: . . . X . . . . . .
Row7: . . . . . . . X . .
Row8: . X X . . . X X X .
Row9: . X X . . . . . . .

Let's mark X positions:

Row2: col1,2,3; col7
Row3: col7
Row5: col3,4
Row6: col3
Row7: col7
Row8: col1,2; col6,7,8
Row9: col1,2

So we have several connected components. Let's identify them.

Component A: The cluster at top-left: row2 col1-3. Are they connected to any other X? Let's check adjacency: 4-neighbor connectivity (likely). Row2 col1-3 are adjacent horizontally. Are they connected to any other X? Row3 col? Row3 col7 is far. Row5 col3? Row5 col3 is two rows below row3 col3? Wait row3 col3 is '.'; row4 col3 '.'; row5 col3 X. So not connected. So component A is just the 3 X's at row2 col1-3. Size = 3.

Component B: The vertical line at col7: row2 col7, row3 col7, row7 col7. Are they connected? Row2 col7 adjacent to row3 col7 (vertical). Row3 col7 adjacent to row4 col7 '.'; row5 col7 '.'; row6 col7 '.'; row7 col7 X. So row3 col7 not adjacent to row7 col7 because there is a gap of 3 rows. So they are separate components: row2-3 col7 is a component of size 2. Row7 col7 is a single X component of size 1.

Component C: The cluster at row5-6 col3-4: row5 col3,4; row6 col3. Are they connected? Yes: row5 col3 adjacent to row5 col4; row5 col3 adjacent to row6 col3. So component size = 3.

Component D: The cluster at bottom-left: row8 col1,2; row9 col1,2. Are they connected? Yes: row8 col1 adjacent to row8 col2; row8 col1 adjacent to row9 col1; row8 col2 adjacent to row9 col2. So component size = 4.

Component E: The cluster at row8 col6,7,8: row8 col6,7,8. Are they connected? Yes horizontally. So component size = 3.

So we have component sizes: 3, 2, 1, 3, 4, 3. Wait we also have maybe other components? Let's double-check: Did we miss any X? Row2 col7, row3 col7, row7 col7. Row5 col3,4; row6 col3. Row8 col1,2; row9 col1,2. Row8 col6,7,8. That's all.

Now output grid:

Row0: . . . . . . . . . .
Row1: . . . . . . . . . .
Row2: . R R R . . . G . .

... [8726 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A blank city grid (black) with grey building footprints of varying sizes scattered across it. What to do: Count the lots each footprint covers, then color-code it according to the zoning designation for that building class. Grid details: Same city grid. Empty lots remain black. Each footprint takes its zoning color."

We have training example 1: Input grid 10x10 with '.' and 'X' cells. Output grid 10x10 with '.' and colors: R, G, B. The mapping: The 'X' cells in input represent building footprints. In output, each contiguous region of X's is replaced by a color: R, G, B. The color depends on the size of the region? The description says: "Count the lots each footprint covers, then color-code it according to the zoning designation for that building class." So maybe the color depends on the number of cells in the region. Let's analyze training example 1.

Input grid:

Row1: . . . . . . . . . .
Row2: . . . . . . . . . .
Row3: . X X X . . . X . .
Row4: . . . . . . . X . .
Row5: . . . . . . . . . .
Row6: . . . X X . . . . .
Row7: . . . X . . . . . .
Row8: . . . . . . . X . .
Row9: . X X . . . X X X .
Row10: . X X . . . . . . .

Let's mark coordinates (row, col). We'll index 1-10.

Let's identify contiguous regions of X's (connected orthogonally? Usually 4-neighbor connectivity). Let's find each region.

Region A: Starting at (3,2). Let's trace: (3,2),(3,3),(3,4) contiguous horizontally. Also (4,8) is separate? Wait (3,8) is X. Let's list all X coordinates:

Row3: col2,3,4,8
Row4: col8
Row6: col4,5
Row7: col4
Row8: col8
Row9: col2,3,7,8,9
Row10: col2,3

Also row3 col8, row4 col8, row8 col8: these are vertical cluster? Let's check connectivity: (3,8) adjacent to (4,8) vertical. (4,8) adjacent to (8,8)? No, there is a gap: rows 5,6,7 between 4 and 8. So not connected. So (3,8) and (4,8) are a cluster of size 2. (8,8) is isolated? Wait (8,8) is X but adjacent to (9,8) which is X. So (8,8) and (9,8) are connected. Also (9,7) and (9,9) are X. So cluster at bottom right: (8,8),(9,7),(9,8),(9,9). Also (10,2),(10,3) are X. They are adjacent to (9,2),(9,3) which are X. So cluster at bottom left: (9,2),(9,3),(10,2),(10,3). Also (6,4),(6,5),(7,4) cluster: (6,4) adjacent to (6,5) and (7,4). So cluster of size 3. Also cluster at top left: (3,2),(3,3),(3,4) cluster of size 3. Also cluster at (3,8),(4,8) cluster of size 2. So we have clusters of sizes: 3,3,2,3,4? Wait bottom right cluster size 4? Let's count: (8,8),(9,7),(9,8),(9,9) = 4. So cluster sizes: 3,3,2,3,4,4? Wait bottom left cluster size 4? Let's count: (9,2),(9,3),(10,2),(10,3) = 4. So cluster sizes: 3,3,2,3,4,4. Actually we have 6 clusters: cluster1 size3 (top left), cluster2 size3 (middle left), cluster3 size2 (top right), cluster4 size3 (bottom left), cluster5 size4 (bottom right). Wait we counted 5 clusters? Let's recount: cluster1: (3,2),(3,3),(3,4) size3. cluster2: (6,4),(6,5),(7,4) size3. cluster3: (3,8)

... [8642 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A dark tactical map with grey markers indicating enemy positions, each cluster representing a unit of unknown strength. What to do: Assess each unit's strength by counting its connected positions, then replace the grey markers with the colored pin designated for that unit size. Grid details: Same map. Unmarked terrain stays dark. Each unit's markers are replaced with their strength-coded color."

We have training example 1: Input grid 10x10 with '.' and 'X' markers. Output grid has '.' and colored letters: R, G, B. The mapping: clusters of X's replaced by colors based on cluster size. Let's analyze.

Input Example 1:

Row1: . . . . . . . . . .
Row2: . . . . . . . . . .
Row3: . X X X . . . X . .
Row4: . . . . . . . X . .
Row5: . . . . . . . . . .
Row6: . . . X X . . . . .
Row7: . . . X . . . . . .
Row8: . . . . . . . X . .
Row9: . X X . . . X X X .
Row10: . X X . . . . . . .

Output Example 1:

Row1: . . . . . . . . . .
Row2: . . . . . . . . . .
Row3: . R R R . . . G . .
Row4: . . . . . . . G . .
Row5: . . . . . . . . . .
Row6: . . . R R . . . . .
Row7: . . . R . . . . . .
Row8: . . . . . . . B . .
Row9: . B B . . . B B B .
Row10: . B B . . . . . . .

So we need to map cluster sizes to colors: R, G, B. Let's identify clusters.

We need to consider connectivity: likely 4-directional adjacency (up, down, left, right). Let's find clusters of X's.

Input grid coordinates: Let's index rows 1-10, columns 1-10.

Row3: positions (3,2),(3,3),(3,4) are X. Also (3,8) is X.

Row4: (4,8) is X.

Row6: (6,4),(6,5) are X.

Row7: (7,4) is X.

Row8: (8,8) is X.

Row9: (9,2),(9,3) are X; (9,7),(9,8),(9,9) are X.

Row10: (10,2),(10,3) are X.

Also row3 col8, row4 col8, row8 col8, row9 col7-9, etc.

Let's identify clusters:

Cluster A: The group at top left: (3,2),(3,3),(3,4). Are they connected? Yes horizontally. Are there any other X's adjacent? (4,2) is '.'; (2,2) '.'; (3,1) '.'; (3,5) '.'; So cluster size 3.

Cluster B: The group at (3,8),(4,8),(8,8),(9,7),(9,8),(9,9),(8,8) etc. Wait we need to check connectivity. Let's list all X's in that region:

(3,8)
(4,8)
(8,8)
(9,7),(9,8),(9,9)
(10,2),(10,3) are separate.

But (8,8) is far from (4,8). Are they connected via vertical adjacency? Let's check: (4,8) is at row4 col8. (5,8) is '.'; (6,8) '.'; (7,8) '.'; (8,8) is X. So there is a vertical gap of 3 rows. So they are not connected. So cluster B: (3,8),(4,8) maybe cluster size 2? Wait (3,8) adjacent to (4,8) vertically. So cluster size 2.

But output shows G at (3,8) and (4,8). Yes G at those positions. So cluster size 2 maps to G.

But we also have cluster at (8,8) alone? Let's check: (8,8) is X. Are there any adjacent X's? (7,8) '.'; (9,8) X; (8,7) '.'; (8,9) '.'; So (8,8) adjacent to (9,8). So cluster includes (8,8),(9,8). Also (9,7),(9,9) are adjacent to (9,8). So cluster includes (9,7),(9,8),(9,9). So cluster size 4? Let's count: (8,8),(9,7),(9,8),(9,9). That's 4 ce

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We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A dark garden bed with clusters of grey seedlings of varying group sizes poking through the soil. What to do: Count the sprouts in each cluster and tie the ribbon color that corresponds to that count around the group. Grid details: Same bed dimensions. Bare soil stays dark. Each seedling cluster displays its count-assigned ribbon color."

We have training example 1: Input grid with '.' and 'X' cells. Output grid with '.' and colored cells: R, G, B. The mapping: clusters of X's are counted, and each cluster gets a color based on the count. The color mapping: maybe 3 clusters of size 3 -> R? Let's analyze.

We need to deduce the rule: For each cluster of X's (connected components), count the number of X cells. Then assign a color based on the count. The mapping from count to color: maybe 1->? 2->? 3->? 4->? 5->? 6->? 7->? 8->? 9->? But we only see R, G, B in example. Let's analyze the example.

Example 1 Input grid: 10x10. Let's map coordinates. I'll index rows 0-9, columns 0-9.

Input:

Row0: . . . . . . . . . .
Row1: . . . . . . . . . .
Row2: . X X X . . . X . .
Row3: . . . . . . . X . .
Row4: . . . . . . . . . .
Row5: . . . X X . . . . .
Row6: . . . X . . . . . .
Row7: . . . . . . . X . .
Row8: . X X . . . X X X .
Row9: . X X . . . . . . .

Let's identify clusters of X's. Connectivity: likely orthogonal adjacency (4-neighbor). Let's find clusters.

Cluster A: Row2 col1-3: X X X contiguous horizontally. Also check adjacency to other X's: Row3 col7 is far. Row2 col7 is X. So cluster A is the group at (2,1),(2,2),(2,3). That's 3 cells.

Cluster B: Row2 col7: X. Row3 col7: X. Row7 col7: X. Row8 col6-8: X X X. Row9 col1-2: X X. Wait we need to check connectivity.

Let's list all X coordinates:

(2,1),(2,2),(2,3)
(2,7)
(3,7)
(5,3),(5,4)
(6,3)
(7,7)
(8,1),(8,2),(8,6),(8,7),(8,8)
(9,1),(9,2)

Now cluster connectivity:

- Cluster 1: (2,1),(2,2),(2,3) are connected horizontally. Are they connected to any other X? Check adjacency: (3,1) is ., (1,1) is ., (2,0) is ., (2,4) is . So cluster 1 is isolated. Size 3.

- Cluster 2: (2,7),(3,7),(7,7),(8,6),(8,7),(8,8). Are they connected? Let's see adjacency: (2,7) adjacent to (3,7). (3,7) adjacent to (2,7) and (4,7) is ., (3,6) is ., (3,8) is . So cluster includes (2,7),(3,7). (7,7) is far: row difference 4. Not connected. (8,6),(8,7),(8,8) are adjacent horizontally. Are they connected to (7,7)? (7,7) adjacent to (8,7). Yes, (7,7) adjacent to (8,7). So cluster includes (7,7),(8,6),(8,7),(8,8). Are they connected to (2,7),(3,7)? No. So cluster 2 is (2,7),(3,7). Size 2.

- Cluster 3: (5,3),(5,4),(6,3). These are connected: (5,3) adjacent to (5,4) and (6,3). (6,3) adjacent to (5,3). So cluster size 3.

- Cluster 4: (8,1),(8,2),(9,1),(9,2). These are connected: (8,1) adjacent to (8,2) and (9,1). (8,2) adjacent to (8,1),(9,2). (9,1) adjacent to (8,1),(9,2). (9,2) adjacent to (8,2),(9,1). So cl

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We need to solve a grid transformation puzzle. We have a metaphorical description, training examples, and a test input grid. We need to produce the output grid.

We have a color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

We have a metaphorical description: "What you see: A few luminous sparks float in a dark room — scattered embers of a single hue glowing against the void. What to do: Develop the photographic negative: the bright sparks burn out and go dark, while every shadow blooms into light. But the light that emerges is not the same color that vanished — each ember leaves behind its complementary ghost. Grey ash resurrects as golden flame, cool azure surfaces as warm crimson, and forest green is reborn as deep ocean blue. The darkness and the light trade places, and the color transforms into its secret twin. Grid details: The photograph and its negative are the same size. Every point in the image is either spark or shadow — nothing is left unexposed. The developed negative is a perfect inversion: crowded where the original was sparse, empty where it was full."

We have training examples. Example 1:

Input:
X X X
. . X
. . .

Output:
. . .
Y Y .
Y Y Y

Test Input:
. X .
X X .
. . X

We need to produce output grid.

We need to parse the puzzle. The puzzle is about a grid transformation. The input grid uses characters: X, ., maybe other colors. The output grid uses Y, maybe other colors. The transformation seems to involve complement colors, negative, etc.

We need to identify the CAST: roles of grid elements. AFFORDANCES: what each element can do or have done to it. TRANSFORMATION RULE: precise rule mapping input to output.

We have only one training example. Let's analyze it.

Example 1:

Input grid (3x3):
Row1: X X X
Row2: . . X
Row3: . . .

Output grid (3x3):
Row1: . . .
Row2: Y Y .
Row3: Y Y Y

We need to interpret the transformation.

Input uses X and . only. Output uses Y and . only. So maybe X is a color (grey) and . is black. Output uses Y (yellow) and . (black). So maybe the transformation is: X (grey) becomes Y (yellow). And . (black) remains .? But output has . in some places where input had X? Let's check.

Input positions:
(1,1) X -> output (1,1) . (so X turned to .)
(1,2) X -> output (1,2) . (X turned to .)
(1,3) X -> output (1,3) . (X turned to .)
(2,1) . -> output (2,1) Y (so . turned to Y)
(2,2) . -> output (2,2) Y
(2,3) X -> output (2,3) . (X turned to .)
(3,1) . -> output (3,1) Y
(3,2) . -> output (3,2) Y
(3,3) . -> output (3,3) Y

So transformation: X -> . (X becomes black). . -> Y (black becomes yellow). So it's like a negative: X (grey) becomes black, black becomes Y (yellow). But why Y? The description says: "each ember leaves behind its complementary ghost. Grey ash resurrects as golden flame, cool azure surfaces as warm crimson, and forest green is reborn as deep ocean blue." So grey (X) becomes golden flame (Y). But in the e

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We need to solve a grid transformation puzzle. The description: "frames" are colored borders of rectangles. Inside each frame, there is empty canvas (black cells). The rule: if the frame encloses a single bare point of wall (i.e., the interior is a single cell), fill that cell with grey (X). If the frame encloses more than one cell, fill all interior cells with orange (O). The frames themselves are never touched; only the void within is transformed.

We have training examples to confirm.

Example 1: Input grid: 6x6. There is a Y rectangle: Y Y Y on row 1? Let's parse.

Input Example 1:

Row1: . . . . . .
Row2: Y Y Y . . .
Row3: Y . Y . . .
Row4: Y . Y . . .
Row5: Y Y Y . . .
Row6: . . . . . .

So Y rectangle: 3x3? Actually Y border: top row Y Y Y, left column Y Y Y Y? Wait row2 col1 Y, row3 col1 Y, row4 col1 Y, row5 col1 Y. Right column Y at col3 rows 2-5. Bottom row Y Y Y at row5 col1-3. So it's a 4x3 rectangle? Let's map coordinates: rows 2-5, cols 1-3. So interior cells: rows 3-4, cols 2. That's two cells: (3,2) and (4,2). In input, those are '.' (black). Output: those cells become O. Indeed output shows Y O Y at rows 3-4. So rule: interior >1 cell => fill with O.

Example 2: Input: 6x6. A rectangle of A: rows 2-4, cols 2-4. Interiors: row3 col3 only one cell. Input: '.' at (3,3). Output: X at (3,3). So rule: interior single cell => X.

Example 3: More complex. There are multiple frames: Y, G, R. Interiors: Y rectangle: rows 2-4, cols 2-5? Let's parse. Input: row2: . Y Y Y Y . . . . . . . (col2-5 Y). Row3: . Y . . Y . . G G G . . (col2 Y, col5 Y). Row4: . Y Y Y Y . . G . G . . (col2-5 Y). So Y rectangle: rows 2-4, cols 2-5. Interiors: rows 3, cols 3-4. That's 2 cells. Output: row3 col3-4 become O. Indeed output shows Y O O Y. Row4 interior col3-4? Wait row4 interior col3-4? But row4 is bottom row of Y rectangle, so interior is only row3. So Y rectangle interior cells become O.

G rectangle: appears at rows 3-6, cols 7-9? Let's parse: row3: . Y . . Y . . G G G . . (col7-9 G). Row4: . Y Y Y Y . . G . G . . (col7 G, col9 G). Row5: . . . . . . . G . G . . (col7 G, col9 G). Row6: . . . . . . . G G G . . (col7-9 G). So G rectangle: rows 3-6, cols 7-9. Interiors: rows 4-5, cols 8. That's 2 cells. Output: row4 col8 becomes O, row5 col8 becomes O. Indeed output shows G O G at row4, G O G at row5.

R rectangle: appears at rows 10-12, cols 10-13? Let's parse: row10: . . . G G G . . R R R R (col10-13 R). Row11: . . . G . G . . R . . R (col10 R, col13 R). Row12: . . . G G G . . R R R R (col10-13 R). So R rectangle: rows 10-12, cols 10-13. Interiors: row11, cols 11-12. That's 2 cells. Output: row11 col11-12 become O. Indeed output shows R O O R.

Also there is a small R rectangle at rows 15-17, cols 6-8? Let's parse: row15: . . . . . R R R . . . . (col6-8 R). Row16: . . . . . R . R . . . . (col6 R, col8 R). Row17: . . . . . R R R . . . . (col6-8 R). So R rectangle: rows 15-17, cols 6-8. Interiors: row16, col7. That's 1 cell. Output: row16 col7 beco

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We need to solve a grid transformation puzzle. We have a metaphorical description, training examples, and a test input grid. We need to produce the output grid.

We have a description: "What you see: A stone wall of grey cuts across the earth, dividing a garden into a shady upper plot and a sunlit lower plot. Two rival vines — one red, one yellow — climb through both plots, their stems rising as colored cells in fixed columns. The black soil surrounds them, empty and waiting. What to do: Each vine is hungrier in the lower plot, stretching toward the sun. Measure how much each vine has flourished below the wall compared to above it — that ambition, that extra reach, is its growth. The vine that grew more aggressively in the sunny plot claims victory and plants its flag. Grid details: The victor's flag is a small 2×2 patch of earth, dyed entirely in the winning vine's color — a tiny trophy garden announcing which rival thrived more."

We have training example 1: Input grid and output grid. We need to deduce the rule.

Let's parse the training example.

Input grid: 11 rows? Let's count. Provided:

```
. . R . . . Y . .
. . . . . . Y . .
. . . . . . Y . .
. . . . . . . . .
. . . . . . . . .
X X X X X X X X X
. . R . . . Y . .
. . R . . . Y . .
. . R . . . Y . .
. . R . . . Y . .
. . . . . . Y . .
```

So 11 rows, each row has 9 columns? Let's count columns: first row: ". . R . . . Y . ." that's 9 tokens. So grid is 11x9.

The wall of grey: "X X X X X X X X X" is a row of X's. That is row 6 (index 5 if 0-based). So the wall divides the grid into upper part (rows 0-4) and lower part (rows 6-10). Row 5 is the wall.

The vines: red (R) and yellow (Y). They appear in columns? Let's see positions: In the input, there are R's in column 2 (0-indexed 2). Y's in column 6 (0-indexed 6). They appear in both upper and lower parts. The R's appear in rows 0, 6, 7, 8, 9? Wait let's list:

Rows 0: ". . R . . . Y . ." -> R at col 2, Y at col 6.
Row 1: ". . . . . . Y . ." -> Y at col 6.
Row 2: ". . . . . . Y . ." -> Y at col 6.
Row 3: ". . . . . . . . ." -> none.
Row 4: ". . . . . . . . ." -> none.
Row 5: "X X X X X X X X X" -> wall.
Row 6: ". . R . . . Y . ." -> R at col 2, Y at col 6.
Row 7: ". . R . . . Y . ." -> R at col 2, Y at col 6.
Row 8: ". . R . . . Y . ." -> R at col 2, Y at col 6.
Row 9: ". . R . . . Y . ." -> R at col 2, Y at col 6.
Row 10: ". . . . . . Y . ." -> Y at col 6.

So R appears in rows 0, 6, 7, 8, 9. Y appears in rows 0, 1, 2, 6, 7, 8, 9, 10. So Y appears more in lower part? Let's count above wall (rows 0-4) and below wall (rows 6-10). For R: above wall: row 0 has R. That's 1. Below wall: rows 6-10: R at rows 6,7,8,9. That's 4. So R has 4 below, 1 above. For Y: above wall: rows 0-4: Y at rows 0,1,2. That's 3. Below wall: rows 6-10: Y at rows 6,7,8,9,10. That's 5. So Y has 5 below, 3 above.

Now the rule: "Each vine is hungrier in the lower plot, stretching toward the sun. Measure how 

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We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A black cross cuts through the grid like a windowframe, creating four small panes. Behind each pane, colored tiles form a tiny mosaic. Three of the panes show the same scene — as if copied from the same memory. But one pane remembers things differently. What to do: Interview all four witnesses. The three who tell the same story cancel each other out — their agreement makes them unremarkable. The lone dissenter, the one whose testimony doesn't match, is the one worth listening to. Pull that voice out of the crowd. Grid details: The windowframe is always the same: a vertical and horizontal bar of darkness splitting the world into four equal chambers. What you're left with after removing the frame is always a single small pane — the rebel's version of events."

We have training examples. Let's analyze them.

Example 1:

Input grid:
```
B . . B .
. B . . B
. . . . .
B . . B .
B B . . B
```
Output:
```
B .
B B
```

We need to understand the transformation. The input grid is 5x5? Let's check: The input lines: "B . . B ." (5 columns), ". B . . B" (5), ". . . . ." (5), "B . . B ." (5), "B B . . B" (5). So 5x5 grid.

Output grid: "B ." (2 columns), "B B" (2 columns). So output is 2x2 grid.

So the transformation reduces a 5x5 grid to a 2x2 grid. The description says: "The windowframe is always the same: a vertical and horizontal bar of darkness splitting the world into four equal chambers." So the cross is a vertical and horizontal bar of darkness (black). In the input, the black cells are '.'? Wait, '.' is black. So the cross is formed by '.' cells? Let's examine the input: The cross is at row 3 (index 2) all '.'? Actually row 3 is ". . . . .", all '.' (black). That is the horizontal bar. The vertical bar is column 3? Let's check column 3 (index 2). In each row, column 3 is '.'? Row 1: "B . . B ." -> column 3 is '.' (index 2). Row 2: ". B . . B" -> column 3 is '.' (index 2). Row 3: ". . . . ." -> column 3 is '.' (index 2). Row 4: "B . . B ." -> column 3 is '.' (index 2). Row 5: "B B . . B" -> column 3 is '.' (index 2). So yes, column 3 is all '.'.

Thus the cross is at row 3 and column 3, both all '.' (black). So the cross splits the grid into four equal chambers: top-left 2x2, top-right 2x2, bottom-left 2x2, bottom-right 2x2. Indeed, the grid is 5x5, cross at center splits into 4 quadrants of size 2x2 each. The cross cells themselves are black ('.').

Now, behind each pane, colored tiles form a tiny mosaic. The three panes show the same scene, but one pane remembers things differently. The rule: "Interview all four witnesses. The three who tell the same story cancel each other out — their agreement makes them unremarkable. The lone dissenter, the one whose testimony doesn't match, is the one worth listening to. Pull that voice out of the crowd. Grid details: The windowframe is always the same: a vertical and horizontal

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We need to solve a grid transformation puzzle. We have a metaphorical description, training examples, and test input. We need to deduce the transformation rule. Let's parse the problem carefully.

We have a 7x7 grid input. Output is a 3x3 grid. The description: "What you 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. What to 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 details: 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."

So we need to find the color that appears most frequently in the 7x7 grid. That color is the "loudest voice". Then we need to output a 3x3 grid that is the "pose" of that color. The pose is predetermined for each color. The description says: "Each color-voice has rehearsed its own distinctive pose: one stands bold as a horizon line, another rises like a bent elbow, another traces a zigzag path." So each color has a unique 3x3 pattern. The output grid is that pattern. The pattern is in azure (A) on a dark stage (black). So the output grid is 3x3 with azure cells (A) and black cells (.). The pattern is predetermined for each color. We need to deduce the mapping from color to pattern from the training examples.

We have two training examples. Let's analyze them.

Example 1 Input:

Row1: B . B . O . .
Row2: B B W B . B .
Row3: . . B B . R .
Row4: . . . . G . B
Row5: . Y . B . . B
Row6: . . B . R . A
Row7: . . B . O G B

Output:
. . A
A A .
. A .

So the output is a 3x3 grid:

Row1: . . A
Row2: A A .
Row3: . A .

We need to find the dominant color in the input. Let's count each color frequency.

Colors present: B, O, W, R, G, Y, A. Let's count.

I'll parse each row:

Row1: B . B . O . . => B:2, O:1
Row2: B B W B . B . => B:4, W:1
Row3: . . B B . R . => B:2, R:1
Row4: . . . . G . B => G:1, B:1
Row5: . Y . B . . B => Y:1, B:2
Row6: . . B . R . A => B:1, R:1, A:1
Row7: . . B . O G B => B:2, O:1, G:1

Now sum B: row1 2 + row2 4 + row3 2 + row4 1 + row5 2 + row6 1 + row7 2 = 14 B's. O: row1 1 + row7 1 = 2. W: 1. R: row3 1 + row6 1 = 2. G: row4 1 + row7 1 = 2. Y: 1. A: 1.

So B is the dominant color with 14 occurrences. So the output pattern corresponds to color B. The output p

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We need to solve a grid transformation puzzle. We have training examples with input 7x7 grids and output 3x3 grids. The description: "What you see: A crowded culture plate where several species of microorganism vie for resources. One species vastly outnumbers the rest, while rare mutant strains appear as isolated specimens. What to do: Identify which colony has achieved dominance through sheer population. Each dominant species, when it wins, expresses a unique molecular signature — a small, fixed fold pattern. Read off the winning species' signature. Grid details: The petri dish is a 7×7 field. The diagnostic result is always a 3×3 protein fold rendered in azure against a dark background."

So we need to find the dominant species (color) that has the largest population in the 7x7 grid. Then we need to output a 3x3 pattern of azure (A) that is the "signature" of that species. The pattern is fixed for each species? The output is always a 3x3 grid of azure (A) and black (.)? Wait, the output examples show azure (A) and black (.) only. Let's examine the training examples.

Example 1 Input: 7x7 grid with many colors: B, O, W, R, G, Y, A, X. Output: 3x3 grid with azure (A) and black (.). Let's examine the output:

Example 1 Output:
. . A
A A .
. A .

So 3x3 grid with azure at positions: (0,2), (1,0),(1,1),(2,1). That's a pattern.

Example 2 Output:
. A A
. A .
. A .

Positions: (0,1),(0,2),(1,1),(2,1). That's a different pattern.

Example 3 Output:
. . .
A A A
. . .

Positions: (1,0),(1,1),(1,2). That's a horizontal line.

So each species has a unique 3x3 pattern of azure. The pattern is fixed for each species. The output is the pattern for the dominant species.

Thus we need to determine which color appears most in the input grid. Then output the pattern associated with that color.

We need to deduce the mapping from color to pattern from the training examples.

We have 3 training examples. Let's analyze each.

Example 1 Input: Let's count each color.

Input grid:

Row0: B . B . O . .
Row1: B B W B . B .
Row2: . . B B . R .
Row3: . . . . G . B
Row4: . Y . B . . B
Row5: . . B . R . A
Row6: . . B . O G B

Let's count:

Colors: B, O, W, R, G, Y, A, X? Actually X appears? In example 1, I don't see X. Wait, there is no X in example 1. Colors present: B, O, W, R, G, Y, A. Let's count each:

- B: Let's count. Row0: B at (0,0) and (0,2) => 2. Row1: B at (1,0),(1,1),(1,3),(1,5) => 4. Row2: B at (2,2),(2,3) => 2. Row3: B at (3,6) => 1. Row4: B at (4,3),(4,6) => 2. Row5: B at (5,2) => 1. Row6: B at (6,2),(6,6) => 2. Total B = 2+4+2+1+2+1+2 = 14.

- O: Row0: O at (0,4) => 1. Row6: O at (6,5) => 1. Total O = 2.

- W: Row1: W at (1,2) => 1. Total W = 1.

- R: Row2: R at (2,5) => 1. Row5: R at (5,4) => 1. Total R = 2.

- G: Row3: G at (3,4) => 1. Row6: G at (6,5) => 1? Wait, row6 has G at (6,5). But we already counted O at (6,5). Actually row6: ". . B . O G B" => positions: (6,0)=., (6,1)=., (6,2)=B, (6,3)

... [8233 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the rule. Let's analyze.

We have a 7x7 input grid, and a 3x3 output grid. The output grid uses only a subset of colors: In example 1, output uses '.' and 'A' only. In example 2, output uses '.' and 'A' only. So output is a 3x3 grid of '.' and 'A' only. So the transformation likely selects a 3x3 subgrid from the input, or maybe a pattern of 'A's based on some rule.

The description: "What you see: A dense star field with stars of various spectral types. One class of star vastly outnumbers the rest, which appear as rare scattered points. What to do: Classify the stars and determine which spectral type dominates. Each dominant class triggers a specific constellation projection — a fixed pattern. Display it on the dome. Grid details: The star field is 7×7. The constellation projection is 3×3, illuminated in azure on the dark dome."

So we have a 7x7 grid of stars of various spectral types (colors). One class of star vastly outnumbers the rest, which appear as rare scattered points. So we need to find the dominant color (most frequent). Then each dominant class triggers a specific constellation projection — a fixed pattern. So for each dominant color, there is a fixed 3x3 pattern of azure (A) and black (.)? The output uses azure 'A' for the pattern. So the output is a 3x3 pattern of azure (A) and black (.) that corresponds to the dominant color.

Thus the rule: Determine the most frequent color in the 7x7 grid. Then output a 3x3 pattern that is predetermined for that color. The pattern is likely the same across all examples? But we only have two examples. Let's analyze the patterns.

Example 1 Input: 7x7 grid. Let's list the colors:

Row1: B . B . O . .
Row2: B B W B . B .
Row3: . . B B . R .
Row4: . . . . G . B
Row5: . Y . B . . B
Row6: . . B . R . A
Row7: . . B . O G B

We need to count each color frequency. Let's count:

Colors: B, O, W, R, G, Y, A, . (black). But '.' is background? The description says '.' = black. So black cells are background. The stars are colored cells. So we count only colored cells? But maybe we count all cells including '.'? But the dominant class likely refers to colored stars, not background. But we need to confirm.

Let's count colored cells:

Row1: B, B, O => 3 colored cells
Row2: B, B, W, B, B => 5 colored cells
Row3: B, B, R => 3 colored cells
Row4: G, B => 2 colored cells
Row5: Y, B, B => 3 colored cells
Row6: B, R, A => 3 colored cells
Row7: B, O, G, B => 4 colored cells

Total colored cells: 3+5+3+2+3+3+4 = 23 colored cells.

Now count each color:

B: Let's count. Row1: 2 B. Row2: 4 B. Row3: 2 B. Row4: 1 B. Row5: 2 B. Row6: 1 B. Row7: 3 B. Total B = 2+4+2+1+2+1+3 = 15 B.

O: Row1: 1 O. Row7: 1 O. Total O = 2.

W: Row2: 1 W. Total W = 1.

R: Row3: 1 R. Row6: 1 R. Total R = 2.

G: Row4: 1 G. Row7: 1 G. Total G = 2.

Y: Row5: 1 Y. Total Y = 1.

A: Row6: 1 A. Total A = 1.

So B is domi

... [10189 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the rule. Let's parse the problem.

We have a 7x7 input grid, and a 3x3 output grid. The description: "What you see: A busy harbor where ships fly flags of many nations. One fleet vastly outnumbers the others, while a few foreign vessels dot the anchorage. What to do: Survey the harbor and identify the dominant fleet by flag count. Each fleet has a unique signal pennant pattern. The harbormaster hoists that pennant. Grid details: The harbor is 7×7. The signal pennant is 3×3, stitched in azure on a dark field."

So we have a 7x7 grid of colors. We need to find the dominant fleet by flag count. Each fleet has a unique signal pennant pattern. The harbormaster hoists that pennant. The output is a 3x3 grid of colors, presumably the pattern of the dominant fleet's pennant. The output is azure (A) on a dark field? Wait: "The signal pennant is 3×3, stitched in azure on a dark field." So the output is a 3x3 grid with azure (A) and dark field (maybe black '.'? But the output examples show '.' and 'A' only. Let's examine training examples.

Example 1 Input: 7x7 grid with many colors: B, ., O, W, R, G, Y, A. Output: 3x3 grid with '.' and 'A' only. Let's examine the output:

Example 1 Output:
. . A
A A .
. A .

So output grid has '.' and 'A' only. So azure 'A' cells correspond to the pattern of the dominant fleet's pennant. The rest of the output cells are '.' (black). So the output is a 3x3 pattern of azure cells (A) and black cells (.) representing the pennant.

Thus the rule: find the color that appears most frequently in the 7x7 grid (dominant fleet). Then find the 3x3 pattern of that color in the grid? Wait: The output pattern is azure on a dark field. The azure cells correspond to the pattern of the dominant fleet's pennant. But the output pattern is not necessarily the same as the arrangement of that color in the input grid. It might be the shape of the dominant color's cluster? Let's analyze.

Example 1 Input: Let's list coordinates of each color. We'll need to parse the grid.

Example 1 Input grid:

Row1: B . B . O . .
Row2: B B W B . B .
Row3: . . B B . R .
Row4: . . . . G . B
Row5: . Y . B . . B
Row6: . . B . R . A
Row7: . . B . O G B

Let's index rows 1-7, columns 1-7.

We need to find the dominant color. Let's count each color:

Colors present: B, O, W, R, G, Y, A. Also '.' (black). Let's count.

We'll count each color:

Initialize counts: B:0, O:0, W:0, R:0, G:0, Y:0, A:0.

Row1: B . B . O . . => B:2, O:1
Row2: B B W B . B . => B:5 (2+3?), let's count: B at col1, col2, col4, col6 => 4 B's. So B:2+4=6. W:1
Row3: . . B B . R . => B at col3, col4 => +2 => B:8. R:1
Row4: . . . . G . B => G:1, B:1 => B:9
Row5: . Y . B . . B => Y:1, B at col4, col7 => +2 => B:11
Row6: . . B . R . A => B:1 => B:12, R:1 => R:2, A:1
Row7: . . B . O G B => B at col3, col7 => +2 => B:14, O:1 => O:2, G:1 => G:2



... [8228 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the rule. Let's analyze.

We have 7x7 input grids and 3x3 output grids. The output grid is 3x3. The output grid uses only colors A, B, G, R, Y, X, etc? Let's check training outputs.

Example 1 output:
```
. . A
A A .
. A .
```
So output uses only A and . (black). Example 2 output:
```
. A A
. A .
. A .
```
Also only A and . . So output is a 3x3 pattern of A's and . (black). So the output is a pattern of azure (A) lights on a dark panel. The puzzle description: "diagnostic display is 3×3, lit in azure on a dark panel." So output is azure pattern.

So the rule: from 7x7 input grid, we need to produce a 3x3 pattern of azure (A) lights. The azure pattern corresponds to the dominant frequency? The metaphor: "What you see: A noisy circuit board carrying signals across many frequency bands. One frequency appears on far more traces than the others, which register as faint noise. What to do: Analyze the signal spectrum and identify the dominant frequency. Each frequency is mapped to a unique diagnostic LED pattern — a fixed indicator shape. Light up that pattern."

So we need to identify the dominant frequency among the colors? The input grid has many colors: B, R, G, Y, X, M, O, A, W. The output pattern is a 3x3 pattern of azure (A). The azure pattern corresponds to the dominant frequency. So we need to find which color appears most frequently in the input grid. Then map that color to a 3x3 pattern. The mapping is fixed: each color maps to a unique 3x3 pattern of azure lights. The output pattern is the pattern for the dominant color.

Thus we need to deduce the mapping from colors to 3x3 patterns from the training examples.

We have two training examples. In each, we can compute the frequency of each color in the input grid. Then find the dominant color. Then see the output pattern. That will give us mapping for that color.

Let's analyze Example 1.

Example 1 Input grid (7x7):

Row1: B . B . O . .
Row2: B B W B . B .
Row3: . . B B . R .
Row4: . . . . G . B
Row5: . Y . B . . B
Row6: . . B . R . A
Row7: . . B . O G B

Let's count each color: B, O, W, R, G, Y, A. Also maybe . (black). Let's count.

I'll write coordinates. Let's count manually.

Row1: B . B . O . . => B:2, O:1
Row2: B B W B . B . => B:4, W:1
Row3: . . B B . R . => B:2, R:1
Row4: . . . . G . B => G:1, B:1
Row5: . Y . B . . B => Y:1, B:2
Row6: . . B . R . A => B:1, R:1, A:1
Row7: . . B . O G B => B:2, O:1, G:1

Now sum:

B: row1 2 + row2 4 + row3 2 + row4 1 + row5 2 + row6 1 + row7 2 = 14? Let's sum: 2+4=6, +2=8, +1=9, +2=11, +1=12, +2=14. Yes B=14.

O: row1 1 + row7 1 = 2.

W: row2 1 = 1.

R: row3 1 + row6 1 = 2.

G: row4 1 + row7 1 = 2.

Y: row5 1 = 1.

A: row6 1 = 1.

So B is dominant with 14 occurrences. So the output pattern corresponds to color B.

Now the output pattern is:

```
. . A
A A .
. A .
```

So the pattern for B is that shape.

Now Example 2.

Example 2 

... [5799 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the rule. Let's analyze.

We have 7x7 input grids and 3x3 output grids. The output grid is 3x3. The description: "What you see: A sacred grove alive with many spiritual presences. One spirit manifests far more intensely than the others, whose traces are faint and scattered. What to do: Sense which spirit dominates the grove. Each spirit, when it prevails, inscribes its personal rune on the altar — a compact, fixed glyph. Read the glowing rune. Grid details: The grove is 7×7. The altar rune is 3×3, glowing azure on dark stone."

So we need to find which spirit dominates the grove. Each spirit, when it prevails, inscribes its personal rune on the altar — a compact, fixed glyph. So the output is a 3x3 glyph that corresponds to the dominant spirit. The glyph is "glowing azure" (color A). So the output grid is 3x3 with azure cells? Wait the output examples show azure cells (A) and black cells (.). Let's examine Example 1 output:

Example 1 Output:
. . A
A A .
. A .

So 3x3 grid with azure cells at positions: (0,2), (1,0),(1,1),(2,1). That's a shape. Example 2 Output:
. A A
. A .
. A .

Positions: (0,1),(0,2),(1,1),(2,1). That's a shape similar but rotated? Let's compare shapes.

Example 1 shape: coordinates (0,2),(1,0),(1,1),(2,1). Example 2 shape: (0,1),(0,2),(1,1),(2,1). So they differ: Example 1 has an extra cell at (1,0) and missing at (0,1). Example 2 has extra at (0,1) and missing at (1,0). So shapes differ. So the glyph depends on which spirit dominates. So we need to identify the dominant spirit in the input grid. The dominant spirit is the one that manifests far more intensely than others, whose traces are faint and scattered. So we need to find which color appears most frequently? But the description says "One spirit manifests far more intensely than the others, whose traces are faint and scattered." So maybe the dominant spirit is the one that appears most often in the grid. But we need to confirm with training examples.

Let's analyze Example 1 input grid:

Example 1 Input (7x7):
Row0: B . B . O . .
Row1: B B W B . B .
Row2: . . B B . R .
Row3: . . . . G . B
Row4: . Y . B . . B
Row5: . . B . R . A
Row6: . . B . O G B

Let's count each color frequency:

Colors: B, O, W, R, G, Y, A. Let's count.

Row0: B, B, O => B:2, O:1
Row1: B,B,W,B,B => B:4, W:1
Row2: B,B,R => B:2, R:1
Row3: G,B => G:1, B:1
Row4: Y,B,B => Y:1, B:2
Row5: B,R,A => B:1, R:1, A:1
Row6: B,O,G,B => B:2, O:1, G:1

Now sum B: 2+4+2+1+2+1+2 = 14? Wait let's sum carefully: Row0 B:2, Row1 B:4 => 6, Row2 B:2 => 8, Row3 B:1 => 9, Row4 B:2 => 11, Row5 B:1 => 12, Row6 B:2 => 14. So B appears 14 times.

O: Row0 1, Row6 1 => 2
W: Row1 1 => 1
R: Row2 1, Row5 1 => 2
G: Row3 1, Row6 1 => 2
Y: Row4 1 => 1
A: Row5 1 => 1

So B is dominant with 14 occurrences. So the dominant spirit is B (blue). The output glyph shape for B i

... [10043 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the rule. Let's analyze.

We have a 7x7 input grid, and a 3x3 output grid. The output grid uses only a subset of colors: A, maybe others? In example 1 output: 
```
. . A
A A .
. A .
```
So output uses only '.' and 'A'. Example 2 output:
```
. A A
. A .
. A .
```
Also only '.' and 'A'.

So the transformation likely selects a 3x3 subgrid from the 7x7 input, maybe based on some rule, and then transforms it to output. The output uses only '.' and 'A', maybe representing presence of a particular color in the subgrid? The description: "What you see: A geological cross-section showing many mineral types embedded in rock. One mineral is pervasive throughout the sample, while others appear as rare inclusions. What to do: Examine the sample and identify the dominant mineral by abundance. Each mineral, when dominant, produces a characteristic crystal habit — a fixed geometric form. Sketch it in the notebook. Grid details: The core sample is 7×7. The crystal habit sketch is 3×3, drawn in azure on a dark page."

Interpretation: The input grid is a 7x7 cross-section with many colors representing minerals. One mineral is pervasive throughout the sample, while others appear as rare inclusions. The task: identify the dominant mineral by abundance. Each mineral, when dominant, produces a characteristic crystal habit — a fixed geometric form. Sketch it in the notebook. The output grid is 3x3, drawn in azure on a dark page. So the output grid is a 3x3 representation of the crystal habit of the dominant mineral, drawn in azure (color A). The output grid uses '.' for background (dark page) and 'A' for azure lines. So the output is a 3x3 pattern of azure cells representing the crystal habit shape of the dominant mineral.

Thus the transformation: find the color that appears most frequently in the 7x7 input grid. Then find the 3x3 pattern that best matches the arrangement of that color in the input? Or maybe the 3x3 pattern is the shape of the dominant mineral's crystal habit, which is predetermined for each color. But we only have two training examples, so we need to deduce the mapping from color to 3x3 pattern. The output patterns are:

Example 1 output:
```
. . A
A A .
. A .
```
Example 2 output:
```
. A A
. A .
. A .
```

We need to see which color is dominant in each input, and then see if the output pattern corresponds to that color's predetermined habit.

Let's analyze Example 1 input:

Example 1 Input grid (7x7):
Row1: B . B . O . .
Row2: B B W B . B .
Row3: . . B B . R .
Row4: . . . . G . B
Row5: . Y . B . . B
Row6: . . B . R . A
Row7: . . B . O G B

Let's count each color frequency:

Colors: B, O, W, R, G, Y, A. Also '.'.

Count B: Let's count manually.

Row1: B at col1, B at col3 => 2
Row2: B at col1, col2, col4, col6 => 4
Row3: B at col3, col4 => 2
Row4: B at col8? Wait row4 has 7 columns: row4: . . . . G . B. So B at col7 => 1
Row5: 

... [7554 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A bubbling pot with many ingredients, but one flavor dominates the broth. Other seasonings — a pinch here, a dash there — are barely noticeable by comparison. What to do: Taste the stew and identify the overwhelming ingredient. Each dominant flavor has a traditional plating style — a specific arrangement of garnish on a small square plate. Present the garnish that corresponds to whatever took over the dish. Grid details: The stew pot is a 7×7 arrangement of ingredients. The plate is always 3×3, garnished in azure on a clean dark surface."

We have training examples. We need to deduce the transformation rule. Let's analyze the training examples.

Example 1:

Input grid 7x7:

Row1: B . B . O . .
Row2: B B W B . B .
Row3: . . B B . R .
Row4: . . . . G . B
Row5: . Y . B . . B
Row6: . . B . R . A
Row7: . . B . O G B

Output grid 3x3:

Row1: . . A
Row2: A A .
Row3: . A .

We need to find rule mapping input to output. Let's analyze colors: B=blue, W=maroon? Wait W=maroon. Actually W=maroon. But we have W in input. Also O=orange, Y=yellow, R=red, G=green, X=grey, A=azure. Output uses only A and . (black). So output is 3x3 with azure cells and black cells. The output pattern seems to be a shape of azure cells. The azure cells correspond to something in input. The metaphor: "dominant flavor" is the color that dominates the broth. The output is a 3x3 plate garnished in azure on a clean dark surface. So the output is a 3x3 grid with azure cells representing the garnish arrangement for the dominant flavor. So we need to find the dominant color in the input grid, then produce a 3x3 pattern that corresponds to that color. The pattern is predetermined for each color. The output pattern is the "traditional plating style" for that dominant flavor. So we need to deduce mapping from color to 3x3 pattern.

We have two training examples. Let's analyze them.

Example 1: Input grid has many colors: B, O, W, R, G, Y, A. We need to find the dominant color. Let's count occurrences of each color.

We'll parse the grid:

Row1: B . B . O . . => B:2, O:1
Row2: B B W B . B . => B:4, W:1
Row3: . . B B . R . => B:2, R:1
Row4: . . . . G . B => G:1, B:1
Row5: . Y . B . . B => Y:1, B:2
Row6: . . B . R . A => B:1, R:1, A:1
Row7: . . B . O G B => B:2, O:1, G:1

Now sum:

B: 2+4+2+1+2+1+2 = 14? Let's compute: Row1 2, Row2 4 => 6, Row3 2 => 8, Row4 1 => 9, Row5 2 => 11, Row6 1 => 12, Row7 2 => 14. Yes B=14.

O: Row1 1, Row7 1 => 2.

W: Row2 1 => 1.

R: Row3 1, Row6 1 => 2.

G: Row4 1, Row7 1 => 2.

Y: Row5 1 => 1.

A: Row6 1 => 1.

So B is dominant with 14 occurrences. So the dominant flavor is blue (B). The output pattern is azure cells arranged in a shape. But azure is A. So the output uses azure cells to represent the garnish for the dominant flavor. So the output pattern is predetermined for blue. Let's

... [10227 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A chaotic warm-up where many instruments play simultaneously. One instrumental section is far louder and more numerous than the scattered soloists from other sections. What to do: Listen for which section dominates the soundscape. The conductor responds with a specific baton gesture — a compact motion pattern unique to that instrument family. Transcribe the gesture. Grid details: The orchestra pit is 7×7. The conductor's gesture is a 3×3 notation in azure on silence."

We have training examples. We need to deduce the transformation rule. Let's analyze the examples.

Example 1:

Input grid 7x7:

Row1: B . B . O . .
Row2: B B W B . B .
Row3: . . B B . R .
Row4: . . . . G . B
Row5: . Y . B . . B
Row6: . . B . R . A
Row7: . . B . O G B

Output grid 3x3:

. . A
A A .
. A .

We need to find rule mapping input to output. The output is 3x3 azure (A) pattern on silence (.). The output pattern is a 3x3 shape of azure cells. The output pattern appears to be a shape of azure cells that correspond to something in the input. The description: "One instrumental section is far louder and more numerous than the scattered soloists from other sections." So we need to find the color that appears most frequently in the input grid. That color is the dominant instrument. Then we need to produce a 3x3 pattern that is a "compact motion pattern unique to that instrument family." So maybe we need to produce a 3x3 pattern that is the shape of the most frequent color's arrangement? Or maybe we need to produce a 3x3 pattern that is the shape of the most frequent color's bounding box? Or maybe we need to produce a 3x3 pattern that is the shape of the most frequent color's "motion pattern" (like a 3x3 pattern that is the most common 3x3 subgrid of that color?). Let's analyze.

We need to examine the input grid for Example 1. Let's count each color frequency.

Colors: B, O, W, R, G, Y, A, X? Actually X appears? In Example 1, I see B, O, W, R, G, Y, A. No X. Let's count.

Row1: B . B . O . . => B:2, O:1
Row2: B B W B . B . => B:4, W:1
Row3: . . B B . R . => B:2, R:1
Row4: . . . . G . B => G:1, B:1
Row5: . Y . B . . B => Y:1, B:2
Row6: . . B . R . A => B:1, R:1, A:1
Row7: . . B . O G B => B:2, O:1, G:1

Now sum B: row1 2 + row2 4 + row3 2 + row4 1 + row5 2 + row6 1 + row7 2 = 14 B's. O: row1 1 + row7 1 = 2 O's. W: 1. R: row3 1 + row6 1 = 2 R's. G: row4 1 + row7 1 = 2 G's. Y: 1. A: 1. So B is dominant with 14. So the dominant color is B.

Now the output grid is 3x3 with azure (A) cells. So azure is the output color. The output pattern is:

Row1: . . A
Row2: A A .
Row3: . A .

So azure cells at positions: (1,3), (2,1), (2,2), (3,2). That's a shape like a small cross? Actually shape: coordinates (row, col) 1-indexed: (1,3), (2,1), (2,2), (3,2). That's like a shape of 4 cells forming a "T" shape rotated? Let's visualize:

Row1: . . A
Row2: A A .
Row3: .

... [9605 chars truncated]

We need to solve a puzzle. We have a grid transformation puzzle. The description: "What you see: A satellite view shows a region with many competing weather systems. One type of front covers far more area than the scattered pockets of other conditions. What to do: Read the dominant weather pattern across the map. Each type of dominant front produces a characteristic forecast symbol — a compact icon. Display that icon on the forecast board. Grid details: The weather map spans a 7×7 region. The forecast icon is a 3×3 symbol rendered in azure on a dark bulletin board."

We have training examples. We need to deduce the transformation rule. Let's analyze the training examples.

We have 7x7 input grids, and 3x3 output grids. The output grid uses only '.' and 'A' in examples? Let's check.

Example 1 Input: 7x7 grid with colors: B, ., O, W, R, G, Y, X, A. Output: 3x3 grid with '.' and 'A' only. Example 2: Output also '.' and 'A'. Example 3: Output also '.' and 'A'. So output is a 3x3 grid of '.' and 'A' only. So the transformation reduces the 7x7 grid to a 3x3 grid of azure (A) and black (.) cells. The azure cells correspond to the dominant weather pattern across the map. The description: "Read the dominant weather pattern across the map. Each type of dominant front produces a characteristic forecast symbol — a compact icon. Display that icon on the forecast board." So we need to find the dominant weather pattern across the map. The dominant front type covers far more area than the scattered pockets of other conditions. So we need to find the color that appears most frequently in the 7x7 grid. That is the dominant front. Then we need to produce a 3x3 icon that corresponds to that front type. Each type of dominant front produces a characteristic forecast symbol — a compact icon. So each color has a unique 3x3 pattern of azure cells. The output is that pattern. So we need to map each color to a 3x3 pattern. The training examples show patterns for some colors. Let's analyze.

Example 1 Input: Let's count colors. Input grid:

Row1: B . B . O . .
Row2: B B W B . B .
Row3: . . B B . R .
Row4: . . . . G . B
Row5: . Y . B . . B
Row6: . . B . R . A
Row7: . . B . O G B

Let's count each color: B, O, W, R, G, Y, A. Let's count B: row1: 2 B; row2: 4 B? Wait row2: B B W B . B . => B at positions 1,2,4,6 => 4 B. Row3: . . B B . R . => 2 B. Row4: . . . . G . B => 1 B. Row5: . Y . B . . B => 2 B. Row6: . . B . R . A => 1 B. Row7: . . B . O G B => 2 B. Total B = 2+4+2+1+2+1+2 = 14 B. O: row1: O at col5 => 1. Row7: O at col5 => 1. So O=2. W: row2: W at col3 => 1. R: row3: R at col6 => 1. Row6: R at col5 => 1. So R=2. G: row4: G at col5 => 1. Row7: G at col6 => 1. So G=2. Y: row5: Y at col2 => 1. A: row6: A at col7 => 1. So B is dominant with 14 cells. So the output pattern should correspond to B. The output grid is:

. . A
A A .
. A .

Let's write that as 3x3:

Row1: . . A
Row2: A A .
Row3: . A .


... [6851 chars truncated]

We need to solve a grid transformation puzzle. We have training examples with input 7x7 grids and output 3x3 grids. The puzzle description: "What you see: An aerial view of a city block with structures made of various materials. One material overwhelmingly dominates the landscape, while rare materials appear in isolated buildings. What to do: Survey the block and identify the prevailing construction material. Each material is associated with a specific zoning stamp — a small blueprint mark. Stamp the permit with the appropriate mark. Grid details: The city block is 7×7. The zoning stamp is 3×3, inked in azure on a dark permit."

So we need to find the "prevailing construction material" in the 7x7 grid. That is the color that appears most frequently? Then we need to produce a 3x3 grid that is "inked in azure on a dark permit." The output examples show 3x3 grids with '.' and 'A' characters. 'A' stands for azure. The output grid seems to have 'A's in some pattern. The pattern likely corresponds to the shape of the most frequent color's arrangement? Or maybe the shape of the largest contiguous region of that color? Let's analyze training examples.

We have 5 training examples. Let's parse each.

Example 1 Input (7x7):

Row1: B . B . O . .
Row2: B B W B . B .
Row3: . . B B . R .
Row4: . . . . G . B
Row5: . Y . B . . B
Row6: . . B . R . A
Row7: . . B . O G B

Output 3x3:

. . A
A A .
. A .

So output grid has A's in positions: (1,3), (2,1),(2,2),(3,2). Let's index rows 1-3, columns 1-3.

Positions with A: (1,3), (2,1),(2,2),(3,2). That's a shape like a rotated L? Let's map coordinates: row1 col3; row2 col1, col2; row3 col2. So shape: top right, middle left, middle center, bottom center. That's like a cross shape missing top left, top center, bottom left, bottom right. Actually shape: a 3x3 with A's at positions: (1,3), (2,1),(2,2),(3,2). So pattern:

Row1: . . A
Row2: A A .
Row3: . A .

Ok.

Now we need to deduce rule: maybe we find the most frequent color in input. Let's count colors in Example 1.

Input grid:

Row1: B . B . O . . => B appears 2 times, O 1.
Row2: B B W B . B . => B 4, W 1.
Row3: . . B B . R . => B 2, R 1.
Row4: . . . . G . B => G 1, B 1.
Row5: . Y . B . . B => Y 1, B 2.
Row6: . . B . R . A => B 1, R 1, A 1.
Row7: . . B . O G B => B 2, O 1, G 1.

Count B: row1 2, row2 4, row3 2, row4 1, row5 2, row6 1, row7 2 => total B = 14? Let's sum: 2+4=6, +2=8, +1=9, +2=11, +1=12, +2=14. Yes B=14.

Count O: row1 1, row7 1 => 2.

Count W: row2 1 => 1.

Count R: row3 1, row6 1 => 2.

Count G: row4 1, row7 1 => 2.

Count Y: row5 1 => 1.

Count A: row6 1 => 1.

So B is overwhelmingly dominant. So the "prevailing construction material" is B. The output grid is azure (A) marks. So we need to produce a 3x3 grid of azure marks that correspond to something about B. Maybe we need to find the shape of the largest contiguous region of B? Let's examine B's arrangement in the 7x7 grid. Let's mark B posit

... [7525 chars truncated]

We need to solve a grid transformation puzzle. We have training examples with input and output. We need to deduce the rule. The puzzle description: "What you see: A contested field where many factions have deployed forces. One faction vastly outnumbers the others, whose scattered units are too few to matter. What to do: Count the forces and determine which faction holds numerical superiority. Each faction carries a unique battle standard — a small, fixed emblem. Reproduce that emblem on the strategic map. Grid details: The battlefield is a 7×7 grid. The war room emblem is a 3×3 mark in azure on a dark map."

So we have a 7x7 input grid with colors. Output is a 3x3 grid with azure (A) and black (.)? Let's examine training examples.

Example 1 Input: 7x7 grid. Output: 3x3 grid with azure and black. Let's analyze.

Example 1 Input:

Row1: B . B . O . .
Row2: B B W B . B .
Row3: . . B B . R .
Row4: . . . . G . B
Row5: . Y . B . . B
Row6: . . B . R . A
Row7: . . B . O G B

Output:
. . A
A A .
. A .

So output is 3x3 grid with azure (A) and black (.) only. So the output is a 3x3 pattern of azure and black. The puzzle says "war room emblem is a 3×3 mark in azure on a dark map." So the output is a 3x3 azure pattern on a dark map (black). So we need to produce a 3x3 azure pattern that corresponds to something derived from the input.

The description: "What you see: A contested field where many factions have deployed forces. One faction vastly outnumbers the others, whose scattered units are too few to matter. What to do: Count the forces and determine which faction holds numerical superiority. Each faction carries a unique battle standard — a small, fixed emblem. Reproduce that emblem on the strategic map."

So we need to count the number of each color in the input grid. The one with the most units is the majority. Then we need to reproduce that faction's emblem (a small fixed emblem) on the output grid. The emblem is a 3x3 pattern of azure? Wait, the output is azure pattern. But the emblem is a small fixed emblem that each faction carries. So each color has a unique emblem. The output is the emblem of the majority color. But the output is azure? Wait, the output uses azure (A) for the emblem. But the emblem is a small fixed shape that is unique to each faction. But the output uses azure for the emblem. So maybe the output is the emblem of the majority color, but drawn in azure. So the shape of the emblem is fixed for each color. So we need to know the emblem shapes for each color. But we only have examples. We need to deduce the emblem shapes from the outputs.

Let's analyze each example to deduce the majority color and the output pattern.

Example 1 Input: Let's count colors.

Colors: B, O, W, R, G, Y, A. Let's count each.

I'll parse each row:

Row1: B . B . O . . => B:2, O:1
Row2: B B W B . B . => B:4, W:1
Row3: . . B B . R . => B:2, R:1
Row4: . . . . G . B => G:1, B:1
Row5: . Y . B . . B => Y:1, B:2
Row6: . .

... [8671 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A casting call where many performers appear on stage. One performer keeps showing up in scene after scene, while others make only fleeting cameos. What to do: Review the audition log and identify the performer with the most appearances. Each lead actor is known for a unique mask silhouette. Display that mask on the marquee. Grid details: The stage is 7×7. The marquee mask is 3×3, rendered in azure against a dark backdrop."

We have training examples. We need to deduce the transformation rule. Let's analyze the training examples.

Example 1:

Input grid 7x7:

Row1: B . B . O . .
Row2: B B W B . B .
Row3: . . B B . R .
Row4: . . . . G . B
Row5: . Y . B . . B
Row6: . . B . R . A
Row7: . . B . O G B

Output grid 3x3:

. . A
A A .
. A .

We need to find rule mapping input to output. The description: "identify the performer with the most appearances. Each lead actor is known for a unique mask silhouette. Display that mask on the marquee." So we need to find the color that appears most frequently in the input grid? Then output a 3x3 mask of that color? But output grid is 3x3 with azure (A) and black (.)? Wait azure is A. The output grid has A's and .s. So maybe we need to output a 3x3 mask of the most frequent color, but the mask shape is unique to each color? The description: "Each lead actor is known for a unique mask silhouette." So each color has a unique 3x3 pattern? The output shows a pattern of A's and .s. So maybe the pattern is the silhouette of the most frequent color. But we need to deduce the pattern for each color. Let's analyze Example 1: Input has many colors: B, O, W, R, G, Y, A. We need to find the most frequent color. Let's count.

Input grid:

Row1: B . B . O . . => B appears 2 times, O 1
Row2: B B W B . B . => B 4, W 1
Row3: . . B B . R . => B 2, R 1
Row4: . . . . G . B => G 1, B 1
Row5: . Y . B . . B => Y 1, B 2
Row6: . . B . R . A => B 1, R 1, A 1
Row7: . . B . O G B => B 2, O 1, G 1

Let's sum B: Row1 2, Row2 4, Row3 2, Row4 1, Row5 2, Row6 1, Row7 2 => total B = 14? Let's sum: 2+4=6, +2=8, +1=9, +2=11, +1=12, +2=14. Yes B=14.

O: Row1 1, Row7 1 => 2
W: Row2 1 => 1
R: Row3 1, Row6 1 => 2
G: Row4 1, Row7 1 => 2
Y: Row5 1 => 1
A: Row6 1 => 1

So B is most frequent. Output grid is 3x3 with A's and .s. But B is most frequent, not A. So maybe the output is the silhouette of the most frequent color, but the silhouette is represented in azure (A). So we output the shape of B's positions? But the output grid is 3x3, not 7x7. So maybe we need to find the 3x3 subgrid that contains the most B's? Or maybe we need to find the 3x3 mask that matches the shape of the most frequent color's pattern? Let's analyze the output pattern: . . A / A A . / . A . . Wait output is 3x3:

Row1: . . A
Row2: A A .
Row3: . A .

Let's write coordinates (row, col) 1-indexed:

(1,3) A
(2,1) A
(2,2) A
(3,2) A

So shape:

... [7051 chars truncated]

We need to solve a grid transformation puzzle. The description: "What you see: A warrior carries two shields stacked one behind the other — the front shield is forged from green iron, the rear from blue steel. Each shield has gaps where the metal was never filled in, leaving dark empty spaces. What to do: An archer fires arrows at the paired shields. Where both shields have holes — where neither green iron nor blue steel stands guard — the arrow passes clean through and leaves a red wound on the wall behind. Wherever at least one shield holds firm, the arrow is deflected and the wall stays unmarked. Grid details: The two shields sit one atop the other in the input, each a square slab four units across. The wall behind them, revealed in the output, is the same size as a single shield, dark except where it bleeds red."

So we have two shields stacked: front shield is green, rear shield is blue. Each shield is a 4x4 grid? The input grid likely contains both shields stacked vertically? The output grid is a 4x4 grid representing the wall behind them, with red where both shields have holes (i.e., both are empty at that position). The input grid likely contains a 8x4 grid? Actually, the input grid might be 8 rows by 4 columns: first 4 rows are the front shield (green), next 4 rows are the rear shield (blue). But the example input shows 9 rows? Let's examine the training example.

Example 1 Input:
```
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
```
Wait, that's 9 rows? Let's count: Row1: ". G G .", Row2: ". G . G", Row3: ". . G .", Row4: "G G G G", Row5: "B B B B", Row6: "B B . .", Row7: "B B . .", Row8: ". B B .". That's 8 rows. Actually, I miscounted: Let's list them:

1. ". G G ."
2. ". G . G"
3. ". . G ."
4. "G G G G"
5. "B B B B"
6. "B B . ."
7. "B B . ."
8. ". B B ."

Yes, 8 rows. So the input grid is 8 rows by 4 columns. The first 4 rows are the front shield (green). The next 4 rows are the rear shield (blue). But the first 4 rows contain both green and maybe some black? Wait, the first 4 rows contain G and . only? Let's check: Row1: ". G G .": has '.' and 'G'. Row2: ". G . G": '.' 'G' '.' 'G'. Row3: ". . G .": '.' '.' 'G' '.'. Row4: "G G G G": all G. So yes, first 4 rows are green shield with holes ('.').

Rows 5-8: "B B B B", "B B . .", "B B . .", ". B B .": these contain B and '.' only. So second shield is blue with holes.

So the input grid is 8x4: top 4 rows are green shield, bottom 4 rows are blue shield. The output grid is 4x4: "wall behind them" with red where both shields have holes. The output grid in example 1 is:

```
. . . .
. . R .
. . . R
. . . .
```

Wait, that's 4 rows by 4 columns. Let's check: Row1: ". . . .", Row2: ". . R .", Row3: ". . . R", Row4: ". . . .". So indeed 4x4.

So the rule: For each cell position (i,j) in the 4x4 grid, if the corresponding cell in the green shield (top 4 rows) is '.' (hole) AND the corresponding cell in the blue shield (bottom 4 rows) is '.' (hole), then outpu

... [10284 chars truncated]

We need to solve a grid transformation puzzle. The description: "What you see: A specimen slide divided into two layered membranes—one stained green, one stained blue—each with gaps in their coverage. What to do: Overlay the two membranes and find where both leave the tissue exposed. The dye penetrates only through shared openings, marking those sites red. Grid details: The input is 4 columns by 8 rows, two 4×4 membrane layers stacked. The output is a single 4×4 tissue sample. Background is unstained black."

We have training example 1: Input grid 4 columns by 8 rows? Let's examine. Example 1 Input:

```
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
```

That's 8 rows, each row has 4 columns. So yes 4x8 grid. The first 4 rows correspond to green membrane? The next 4 rows correspond to blue membrane? The description says two 4x4 membrane layers stacked. So the first 4 rows are green membrane, next 4 rows are blue membrane. The output is a single 4x4 tissue sample. The rule: overlay the two membranes and find where both leave the tissue exposed. The dye penetrates only through shared openings, marking those sites red. So we need to find cells where both membranes have a gap (i.e., '.' maybe indicates gap). But the description says "background is unstained black." The output grid uses '.' for black. The output example:

```
. . . .
. . R .
. . . R
. . . .
```

Let's analyze the input to confirm.

Input first 4 rows (green membrane):

Row1: . G G .
Row2: . G . G
Row3: . . G .
Row4: G G G G

So green membrane has '.' at positions: (1,1), (1,4), (2,1), (2,3), (3,1), (3,2), (3,4), (4,1?) Wait row4 has G G G G, so no '.' in row4. So green gaps at positions: (row, col) coordinates 1-indexed: (1,1), (1,4), (2,1), (2,3), (3,1), (3,2), (3,4). That's 7 gaps.

Blue membrane (next 4 rows):

Row5: B B B B
Row6: B B . .
Row7: B B . .
Row8: . B B .

So blue gaps at positions: (row5? Actually row5 is first row of blue membrane, but we need to map to 4x4 grid coordinates. So row5 corresponds to row1 of blue membrane, row6 to row2, row7 to row3, row8 to row4. So blue gaps at: row6 col3, row6 col4, row7 col3, row7 col4, row8 col1, row8 col4. So positions: (1,3), (1,4), (2,3), (2,4), (3,1), (3,4). Wait careful: row6 is second row of blue membrane: B B . . => gaps at col3, col4. Row7: B B . . => gaps at col3, col4. Row8: . B B . => gaps at col1, col4. So yes.

Now overlay: We need to find positions where both membranes have a gap. That is intersection of green gaps and blue gaps. Let's list green gaps: (1,1), (1,4), (2,1), (2,3), (3,1), (3,2), (3,4). Blue gaps: (1,3), (1,4), (2,3), (2,4), (3,1), (3,4). Intersection: (1,4), (2,3), (3,1), (3,4). That's 4 positions. The output grid shows red at positions: row2 col3? Wait output grid:

```
. . . .
. . R .
. . . R
. . . .
```

Let's map coordinates: row1: all '.'; row2: '.' '.' 'R' '.' => red at (2,3). row3: '.' '.' '.' 'R' => red at (3,4). row4: all '.'.

But we also ex

... [11274 chars truncated]

We need to solve a grid transformation puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid.

Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

## Metaphorical Description

What you see: A telescope view showing two overlapping nebula layers, one glowing green and one blue, each with dark gaps in their gas clouds.
What to do: Where both nebulae have voids at the same position, the background red dwarf's light is visible. Mark those sightlines red in the observation chart.
Grid details: Input is 4 wide by 8 tall, two 4×4 nebula maps. Output is a 4×4 stellar visibility chart. Background is empty space (black).

Before predicting the output, perform a Conceptual Digestion:
1. Identify the CAST: What roles do different grid elements play?
2. Identify the AFFORDANCES: What can each element do or have done to it?
3. Identify the TRANSFORMATION RULE: What is the precise rule that maps input to output?

Then apply the rule to the test input to predict the output grid.

## Training Examples

Example 1:
Input:
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
Output:
. . . .
. . R .
.. etc.

Example 2, Example 3.

Test Input:
. G . G
G G G .
. . . G
G G G .
. . B B
. . B B
. B . .
B B . .

We need to produce output grid 4x4.

We need to deduce transformation rule from training examples.

Let's parse training examples carefully.

We have input grids of size 4x8? Wait: The description says Input is 4 wide by 8 tall, two 4×4 nebula maps. So input grid is 4 columns by 8 rows. The first 4 rows correspond to green nebula map? The next 4 rows correspond to blue nebula map? Let's examine Example 1 input:

Example 1 Input:
```
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
```
Let's count rows: 8 rows. Each row has 4 characters. So yes 4x8 grid.

We can think of first 4 rows as green map, next 4 rows as blue map. But we need to confirm.

Let's label rows 0-7. Row 0: ". G G ."
Row 1: ". G . G"
Row 2: ". . G ."
Row 3: "G G G G"
Row 4: "B B B B"
Row 5: "B B . ."
Row 6: "B B . ."
Row 7: ". B B ."

Now output grid is 4x4:

```
. . . .
. . R .
. . . R
. . . .
```

So output has red cells at positions (1,2) and (2,3) (0-indexed). Let's analyze.

The metaphor: "two overlapping nebula layers, one glowing green and one blue, each with dark gaps in their gas clouds. Where both nebulae have voids at the same position, the background red dwarf's light is visible. Mark those sightlines red in the observation chart."

So we have two maps: green and blue. Each has voids (dark gaps). Where both have voids at same position, we mark red. So we need to find positions where both maps have '.'? Wait: The maps are 4x4 each. The input grid is 4x8: first 4 rows are green map, next 4 rows are blue map. The cells in each map can be '.' (empty) or 'G' or 'B'? Actually the green map u

... [7955 chars truncated]

We need to parse the problem. The puzzle: "grid transformation puzzle" with metaphorical description. We have training examples. We need to deduce transformation rule. Input grid: 4 wide by 8 tall, two 4×4 masks. Output is a 4×4 wafer surface. Background is unetched silicon (black). The description: "What you see: A fabrication stack showing two photolithography masks, one green-tinted and one blue-tinted, each with opaque and transparent zones. What to do: Align the masks. Where both are transparent at the same cell, the laser etches through and marks the wafer red. All other positions remain unetched."

So we have two masks: green mask and blue mask. Each mask is 4x4. The input grid is 4 wide by 8 tall, so presumably the first 4 rows correspond to green mask, next 4 rows correspond to blue mask. The output is 4x4 wafer surface. The rule: For each cell, if both masks have transparent (i.e., not opaque) at that cell, then output is red. Else output remains black (unetched). Transparent vs opaque: In the input, we have characters: '.' (black), 'G' (green), 'B' (blue). But we need to interpret which are transparent and which are opaque. The description: "two photolithography masks, one green-tinted and one blue-tinted, each with opaque and transparent zones." So each mask has transparent and opaque zones. The input uses 'G' and 'B' to represent the mask color? Wait: The input grid uses '.' for black, 'G' for green, 'B' for blue. But we need to interpret which cells are transparent or opaque. In the example, we need to deduce mapping.

Let's analyze Example 1.

Example 1 Input:

```
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
```

We need to parse: 4 wide by 8 tall. So first 4 rows (rows 0-3) are green mask. Next 4 rows (rows 4-7) are blue mask.

Let's write them:

Green mask (rows 0-3):
Row0: . G G .
Row1: . G . G
Row2: . . G .
Row3: G G G G

Blue mask (rows 4-7):
Row4: B B B B
Row5: B B . .
Row6: B B . .
Row7: . B B .

Now output is 4x4 wafer surface:

```
. . . .
. . R .
. . . R
. . . .
```

We need to see how this output arises.

We need to interpret transparent vs opaque. Usually in photolithography, transparent zones allow light to pass through, opaque zones block. The mask color indicates the mask type: green mask or blue mask. But the color might not indicate transparency. The input uses '.' for black (maybe representing transparent? Or maybe black is background? Wait: The color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon. So '.' is black. But in the input, '.' appears in both masks. But the description says "two photolithography masks, one green-tinted and one blue-tinted, each with opaque and transparent zones." So each mask is tinted green or blue. So the mask color indicates the mask type. Transparent zones might be represented by '.'? But '.' is black, not green or blue. But maybe the mask color indicates the color of the mask, but the mask's transparent zones are r

... [11525 chars truncated]

We need to solve a grid transformation puzzle. The description: "What you see: A threshold woven with two layers of magical protection, one shimmering green and one blue, each with unprotected gaps. What to do: Where both enchantments are absent at the same spot, infernal red flame breaks through the threshold. Mark those breaches red. Grid details: Input is 4 columns by 8 rows, two 4×4 ward layers. Output is a 4×4 threshold map. Background is sealed stone (black)."

We have training example 1: Input grid 4 columns by 8 rows? Let's examine. Example 1 Input:

```
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
```

That's 8 rows, each row has 4 columns. So yes 4x8 grid. Output:

```
. . . .
. . R .
. . . R
. . . .
```

So output is 4x4 grid. The rule: Where both enchantments are absent at the same spot, mark red. The two enchantments are green and blue layers. The input grid has two layers: first 4 rows are green layer? Actually first 4 rows: rows 1-4: . G G ., . G . G, . . G ., G G G G. That seems to be green layer. Next 4 rows: B B B B, B B . ., B B . ., . B B . . That seems to be blue layer. So each layer is 4x4. The output is 4x4 threshold map. The rule: For each cell (i,j) in 4x4, if both layers have no protection at that spot (i.e., both are '.'?), then mark red. But the output shows red at positions (2,3) and (3,4) (1-indexed). Let's check: In input, green layer at (2,3) is '.'? Let's index rows 1-4, columns 1-4. Green layer:

Row1: . G G . => col1 '.', col2 'G', col3 'G', col4 '.'
Row2: . G . G => col1 '.', col2 'G', col3 '.', col4 'G'
Row3: . . G . => col1 '.', col2 '.', col3 'G', col4 '.'
Row4: G G G G => col1 'G', col2 'G', col3 'G', col4 'G'

Blue layer rows 5-8:

Row5: B B B B => col1 'B', col2 'B', col3 'B', col4 'B'
Row6: B B . . => col1 'B', col2 'B', col3 '.', col4 '.'
Row7: B B . . => col1 'B', col2 'B', col3 '.', col4 '.'
Row8: . B B . => col1 '.', col2 'B', col3 'B', col4 '.'

Now, for each cell, we check if both layers are '.'? Let's compute:

Cell (1,1): green '.'; blue 'B' => not both '.' => no red
Cell (1,2): green 'G'; blue 'B' => no
Cell (1,3): green 'G'; blue 'B' => no
Cell (1,4): green '.'; blue 'B' => no

Cell (2,1): green '.'; blue 'B' => no
Cell (2,2): green 'G'; blue 'B' => no
Cell (2,3): green '.'; blue '.' => both '.' => red
Cell (2,4): green 'G'; blue '.' => no

Cell (3,1): green '.'; blue 'B' => no
Cell (3,2): green '.'; blue 'B' => no
Cell (3,3): green 'G'; blue '.' => no
Cell (3,4): green '.'; blue '.' => both '.' => red

Cell (4,1): green 'G'; blue '.' => no
Cell (4,2): green 'G'; blue 'B' => no
Cell (4,3): green 'G'; blue '.' => no
Cell (4,4): green 'G'; blue '.' => no

Thus red at (2,3) and (3,4). Output shows red at those positions. Yes.

So rule: For each cell in 4x4, if both layers have '.' (no protection), output 'R', else output '.' (black). That matches description: "Where both enchantments are a

... [9186 chars truncated]

We need to solve a grid transformation puzzle. The description: "What you see: A rehearsal floor divided into two practice sessions viewed from above, one troupe in green and one in blue, each occupying certain tiles. What to do: Compare both formations. Where neither troupe occupies a tile, the choreographer marks it with a red rose for the final number. Grid details: Input is 4 wide by 8 tall, two 4×4 floor plans. Output is a 4×4 rose placement map. Background is bare floor (black)."

So we have an input grid of 4 columns by 8 rows. The first 4 rows correspond to the green troupe's floor plan? Actually the description says "two 4×4 floor plans" meaning the input grid is 4 wide by 8 tall, representing two 4x4 grids stacked vertically: top 4 rows for green, bottom 4 rows for blue. The output is a 4x4 grid of red roses placed where neither troupe occupies a tile. So we need to compute the intersection of the two sets? Wait: "Where neither troupe occupies a tile, the choreographer marks it with a red rose for the final number." That means we need to find cells that are empty (.) in both the green and blue floor plans. Those cells become red (R) in the output. All other cells remain black (.)? But the output examples show only '.' and 'R' cells. Let's examine training examples to confirm.

Example 1 Input:

```
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
```

Let's parse: 8 rows, 4 columns each. Top 4 rows (rows 0-3) are green plan. Bottom 4 rows (rows 4-7) are blue plan.

Let's label coordinates: row 0-3 for green, row 4-7 for blue. Each row has 4 columns.

Green plan:

Row0: . G G .
Row1: . G . G
Row2: . . G .
Row3: G G G G

Blue plan:

Row4: B B B B
Row5: B B . .
Row6: B B . .
Row7: . B B .

Now we need to produce output 4x4 grid of red roses where neither troupe occupies a tile. That means we need to find cells that are '.' in both green and blue at the same coordinates (i.e., same row and column). Let's compute.

We need to align the two 4x4 grids: top 4 rows vs bottom 4 rows. So we compare row0 of green with row0 of blue? Wait, the bottom 4 rows are rows 4-7. So row4 of input corresponds to row0 of blue plan. So we need to map row index: row i of green (0-3) corresponds to row i of blue (4-7). So we compare each cell at (i,j) for i=0..3, j=0..3.

Let's compute:

Green grid G[i][j], Blue grid B[i][j] (i=0..3). We'll compute.

Row0: G[0] = . G G .
Row0 of blue: B[0] = B B B B

Positions:
- (0,0): G '.' ; B 'B' -> not both '.' -> no rose.
- (0,1): G 'G'; B 'B' -> no.
- (0,2): G 'G'; B 'B' -> no.
- (0,3): G '.' ; B 'B' -> no.

Row1: G[1] = . G . G
Blue row1: B[1] = B B . .

Positions:
- (1,0): G '.' ; B 'B' -> no.
- (1,1): G 'G'; B 'B' -> no.
- (1,2): G '.' ; B '.' -> both '.' -> rose.
- (1,3): G 'G'; B '.' -> no.

Row2: G[2] = . . G .
Blue row2: B[2] = B B . .

Positions:
- (2,0): G '.' ; B 'B' -> no.
- (2,1): G '.' ; B 'B' -> no.
- (2,2): G 'G'; B '.' -> no.
- (2,3): G '.'

... [8448 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A geological cross-section showing two rock layers, one green-mineralized and one blue, each with fissures and solid sections. What to do: Where fractures in both strata align at the same position, magma erupts through, marking those surface vents red. Grid details: Input is 4 columns by 8 rows, two 4×4 rock strata. Output is a 4×4 surface eruption map. Background is solid crust (black)."

We have training examples. Example 1: Input grid 4x8? Let's examine. Provided Input:

```
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
```

That's 8 rows, each row has 4 columns. So yes 4x8. Output:

```
. . . .
. . R .
. . . R
. . . .
```

So output is 4x4. The rule: Where fractures in both strata align at the same position, magma erupts through, marking those surface vents red. So we need to find positions where both strata have a fracture (i.e., a '.' maybe?) at the same column and row? But the strata are two 4x4 layers stacked vertically: top 4 rows are green layer, bottom 4 rows are blue layer. The output is 4x4 surface eruption map: each cell corresponds to a column and row of the strata? But the output is 4x4, same as each layer. So we need to map each column and row of the strata to a cell in output. The rule: Where fractures in both strata align at the same position, magma erupts through, marking those surface vents red. So we need to check for each column and row (i.e., each cell in the 4x4 grid) if both the green layer and blue layer have a fracture at that position. But the strata are 4x4 each. The green layer occupies rows 0-3, columns 0-3. The blue layer occupies rows 4-7, columns 0-3. So we need to check for each column j (0-3) and row i (0-3) if the cell at (i,j) in the green layer is '.' (fracture) and the cell at (i+4,j) in the blue layer is '.' (fracture). If both are '.' then output cell (i,j) is 'R' (red). Else output cell (i,j) is '.' (black). That seems plausible.

Let's test with Example 1. We'll parse the input:

Row 0: ". G G ."
Row 1: ". G . G"
Row 2: ". . G ."
Row 3: "G G G G"
Row 4: "B B B B"
Row 5: "B B . ."
Row 6: "B B . ."
Row 7: ". B B ."

Let's index rows 0-7, columns 0-3.

Green layer rows 0-3:

- (0,0) = '.'
- (0,1) = 'G'
- (0,2) = 'G'
- (0,3) = '.'

- (1,0) = '.'
- (1,1) = 'G'
- (1,2) = '.'
- (1,3) = 'G'

- (2,0) = '.'
- (2,1) = '.'
- (2,2) = 'G'
- (2,3) = '.'

- (3,0) = 'G'
- (3,1) = 'G'
- (3,2) = 'G'
- (3,3) = 'G'

Blue layer rows 4-7:

- (4,0) = 'B'
- (4,1) = 'B'
- (4,2) = 'B'
- (4,3) = 'B'

- (5,0) = 'B'
- (5,1) = 'B'
- (5,2) = '.'
- (5,3) = '.'

- (6,0) = 'B'
- (6,1) = 'B'
- (6,2) = '.'
- (6,3) = '.'

- (7,0) = '.'
- (7,1) = 'B'
- (7,2) = 'B'
- (7,3) = '.'

Now we check each (i,j) for both '.':

- (0,0): green '.'; blue at (4,0) = 'B' -> not both '.' -> output '.'
- (0,1): green 'G'; blue (4,1) = 'B' -> not both '.' -> '.'
- (0,2): green 'G'; blue (4,2) = 'B' -> '.'
- (0,3): green

... [8393 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A playing field viewed from above, showing two defensive squads arranged in 4×4 zones—green defenders on one half, blue on the other—with gaps in their coverage. What to do: Overlay both formations. Where neither team has a defender stationed, the striker's shot blazes through, marked red in the goal grid. Grid details: Input is 4 wide by 8 tall, two 4×4 defensive zones stacked. Output is a 4×4 target grid. Background is empty pitch (black)."

We have training examples. Example 1: Input grid 4x8? Let's examine. Example 1 Input:

```
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
```

That's 8 rows, each 4 columns. Yes. Output:

```
. . . .
. . R .
. . . R
. . . .
```

So output is 4x4 grid. The rule: overlay both formations (green and blue). Where neither team has a defender stationed, the striker's shot blazes through, marked red in the goal grid. So we need to find cells that are empty (.) in both the green zone and the blue zone? But the input has two 4x4 zones stacked: top 4 rows are green zone? Actually the description: "two defensive squads arranged in 4×4 zones—green defenders on one half, blue on the other—with gaps in their coverage." So maybe the top 4 rows are green defenders, bottom 4 rows are blue defenders. But the input shows green cells in top rows, blue cells in bottom rows. Let's confirm: In input, first 4 rows: row1: . G G . ; row2: . G . G ; row3: . . G . ; row4: G G G G. These are green defenders. Bottom 4 rows: row5: B B B B ; row6: B B . . ; row7: B B . . ; row8: . B B . . Wait row8: . B B . . Actually row8: . B B . . Wait row8 has 4 columns: . B B . . Wait that's 5 columns? Let's check: The input lines: "B B . ." is 4 columns: B, space, B, space, ., space, .? Actually the input lines are separated by spaces? The example shows each row as " . G G . " etc. But the formatting might be ambiguous. Let's parse each row: The input lines are:

1. ". G G ."
2. ". G . G"
3. ". . G ."
4. "G G G G"
5. "B B B B"
6. "B B . ."
7. "B B . ."
8. ". B B ."

Wait row8: ". B B ." is 4 columns: ., B, B, . . Yes. So bottom 4 rows: rows 5-8. They contain B's and .s. So indeed top 4 rows are green zone, bottom 4 rows are blue zone.

Now the output: 4x4 grid. The rule: overlay both formations. Where neither team has a defender stationed, the striker's shot blazes through, marked red in the goal grid. So we need to find cells that are empty in both the green zone and the blue zone. But the output shows some R's. Let's compute.

We need to overlay the two 4x4 zones: For each cell (i,j) in 4x4 grid, we look at the cell in the green zone (top 4 rows) and the cell in the blue zone (bottom 4 rows). If both are empty (.), then we mark R in output. If either has a defender (G or B), then output is .? But the output shows some R's. Let's compute.

Let's index rows 1-4 for green zone, rows 5-8 for blue

... [9368 chars truncated]

We need to parse the problem. It's a grid transformation puzzle. We have a metaphorical description: "What you see: A cathedral window composed of two lattice screens stacked vertically, one of green glass and one of blue, each with certain panes absent. What to do: Align the two screens. Where both have absent panes at the same position, the rosy exterior light floods through, marking those floor tiles red. Grid details: Input is 4 wide by 8 tall, two 4×4 glass screens. Output is a 4×4 floor illumination pattern. Background is dark stone (black)."

We have training examples. Example 1: Input grid is 4 wide by 8 tall? Let's examine. Example 1 Input:

```
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
```

That's 8 rows, each 4 columns. So yes 4x8. The first 4 rows are the green screen? The next 4 rows are the blue screen? Let's check: The first 4 rows contain G and .; the next 4 rows contain B and .; yes. So the input is two 4x4 screens stacked vertically: top 4 rows are green screen, bottom 4 rows are blue screen. The output is 4x4 grid. Output:

```
. . . .
. . R .
. . . R
. . . .
```

So output has R at positions where both screens have absent panes (i.e., '.' in both). Let's verify: For each position (row, col) in 4x4, we look at top screen (row 0-3) and bottom screen (row 4-7). If both are '.' then output 'R', else '.'? Let's test with example.

Let's index rows 0-3 for green, 4-7 for blue. Let's create a table:

Row 0: ". G G ."
Row 1: ". G . G"
Row 2: ". . G ."
Row 3: "G G G G"

Row 4: "B B B B"
Row 5: "B B . ."
Row 6: "B B . ."
Row 7: ". B B ."

Now we need to compute output 4x4. Let's compute each cell:

- (0,0): green '.'; blue 'B' (row 4 col 0). Not both '.' => output '.'.
- (0,1): green 'G'; blue 'B' => '.'.
- (0,2): green 'G'; blue 'B' => '.'.
- (0,3): green '.'; blue 'B' => '.'.

Row 0 output: ". . . ."

- (1,0): green '.'; blue 'B' => '.'.
- (1,1): green 'G'; blue 'B' => '.'.
- (1,2): green '.'; blue '.' (row 5 col 2). Both '.' => 'R'.
- (1,3): green 'G'; blue '.' (row 5 col 3). Not both '.' => '.'.

Row 1 output: ". . R ."

- (2,0): green '.'; blue 'B' => '.'.
- (2,1): green '.'; blue 'B' => '.'.
- (2,2): green 'G'; blue '.' (row 6 col 2). Not both '.' => '.'.
- (2,3): green '.'; blue '.' (row 6 col 3). Both '.' => 'R'.

Row 2 output: ". . . R"

- (3,0): green 'G'; blue '.' (row 7 col 0). Not both '.' => '.'.
- (3,1): green 'G'; blue 'B' => '.'.
- (3,2): green 'G'; blue 'B' => '.'.
- (3,3): green 'G'; blue '.' (row 7 col 3). Not both '.' => '.'.

Row 3 output: ". . . ."

Matches output. So rule: For each cell, if both top and bottom screens have '.' (absent pane), output 'R', else '.'.

But we need to confirm that there are no other colors in output. The output only uses '.' and 'R'. So the transformation is: Align the two screens (top and bottom). Where both have absent panes at same position, mark that floor tile red. So yes.

Now we need to apply to test

... [10864 chars truncated]

We need to solve a grid transformation puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid.

Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

## Metaphorical Description

What you see: A fortification cross-section: two defensive walls, one greenstone and one bluestone, each with narrow openings scattered across their face.
What to do: Find positions where both walls have openings aligned. Fire arrows pass through these double slits and ignite the keep wall behind, marked red.
Grid details: Input is 4 columns by 8 rows, two 4×4 wall faces stacked. Output is a 4×4 keep wall. Background is unburnt stone (black).

Before predicting the output, perform a Conceptual Digestion:
1. Identify the CAST: What roles do different grid elements play?
2. Identify the AFFORDANCES: What can each element do or have done to it?
3. Identify the TRANSFORMATION RULE: What is the precise rule that maps input to output?

Then apply the rule to the test input to predict the output grid.

## Training Examples

Example 1:
Input:
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
Output:
. . . .
. . R .
.. . R
. . . .

Test Input:
. G . G
G G G .
. . . G
G G G .
. . B B
. . B B
. B . .
B B . .

Think step by step. After your reasoning, you MUST write out the complete predicted output grid using these single-character color codes:
Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

At the very end of your response, write the complete output grid inside a clearly labeled block like this:
ANSWER:
.. etc"

We need to produce the output grid for the test input. We have only one training example. We need to deduce the transformation rule.

Let's parse the training example.

Input grid: 4 columns by 8 rows. So 8 rows, each row has 4 characters. The input is:

Row1: . G G .
Row2: . G . G
Row3: . . G .
Row4: G G G G
Row5: B B B B
Row6: B B . .
Row7: B B . .
Row8: . B B .

Wait, the input lines: Let's list them:

1: . G G .
2: . G . G
3: . . G .
4: G G G G
5: B B B B
6: B B . .
7: B B . .
8: . B B .

But the example shows 8 rows? Let's check: The example input lines:

```
. G G .
. G . G
. . G .
G G G G
B B B B
B B . .
B B . .
. B B .
```

Yes, 8 rows. Good.

Output grid: 4 columns by 4 rows. Output lines:

```
. . . .
. . R .
. . . R
. . . .
```

Wait, the output lines: The example output shows:

```
. . . .
. . R .
. . . R
. . . .
```

But the example output in the prompt is:

```
. . . .
. . R .
. . . R
. . . .
```

But the prompt shows:

```
. . . .
. . R .
. . . R
. . . .
```

But the actual example output in the prompt is:

```
. . . .
. . R .
. . . R
. . . .
```

Wait, the prompt shows:

```
. . . .
. . R .
. . . R
. . . .
```

But the prompt shows:

```
. . . .
. . R .
. . . R
. . . .
```

But the prompt shows:

```
. . . .
. . R .
. . . R
. . . .

... [9329 chars truncated]

We need to solve a grid transformation puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid."

We have a color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

We have a metaphorical description: "What you see: An open orange field is enclosed by thick castle walls built from colored stone (maroon, grey, azure). Standing in the field is an archer — a red (R) figure — with a trail of magenta (M) banners streaming behind them like a wind sock, showing which way the wind blows. Somewhere along the castle wall, one stone block is a different color from its neighbors — a weak spot in the masonry. What to do: The archer looses an arrow in the direction the wind carries — away from the trailing banners, through the red archer, and onward across the open field. The arrow flies straight until it strikes the castle wall. Where it hits, the stone crumbles and reveals the orange earth beneath — one block of wall becomes part of the field. Nothing else in the kingdom changes."

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

We have training examples. Example 1: Input grid 14x14, Output grid 14x14. We need to deduce transformation rule.

Let's parse Example 1.

Input grid:

Row1: W W W W W W W W W W W W X X
Row2: X X O O O O O O O O O O X X
Row3: X X O O O O O O O M O O X X
Row4: W W O O O O O O O M O O X X
Row5: W W O O O O O O O M O O X X
Row6: X X O O O O O O O M O O X X
Row7: X X O O O O O O O R O O X X
Row8: X X O O O O O O O O O O X X
Row9: X X O O O O O O O O O O X X
Row10: X X O O O O O O O O O O X X
Row11: X X O O O O O O O O O O X X
Row12: X X O O O O O O O O O O X X
Row13: X X O O O O O O O O O O X X
Row14: X X A X X A A A A A A A A A

Output grid:

Row1: W W W W W W W W W W W W X X
Row2: X X O O O O O O O O O O X X
Row3: X X O O O O O O O M O O X X
Row4: W W O O O O O O O M O O X X
Row5: W W O O O O O O O M O O X X
Row6: X X O O O O O O O M O O X X
Row7: X X O O O O O O O R O O X X
Row8: X X O O O O O O O O O O X X
Row9: X X O O O O O O O O O O X X
Row10: X X O O O O O O O O O O X X
Row11: X X O O O O O O O O O O X X
Row12: X X O O O O O O O O O O X X
Row13: X X O O O O O O O O O O X X
Row14: X X A X X A A A A O A A A A

Comparing input and output: The only difference is at row14, column? Let's index columns 1-14. Input row14: X X A X X A A A A A A A A A. Output row14: X X A X X A A A A O A A A A. So at row14, column? Let's find the difference: Input row14: positions: 1 X, 2 X, 3 A, 4 X, 

... [8232 chars truncated]

We need to parse the puzzle. We have a metaphorical description: "What you 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. What to 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 details: 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."

We have training examples. Example 1: Input grid 9x9? Let's examine. Input:

Row1: . . . . . . . . .
Row2: . . . . . . . . .
Row3: . . X . . . X . .
Row4: . . X . . . X . .
Row5: . . X A A A X . .
Row6: . . X A A A X . .
Row7: . . X A A A X . .
Row8: . . X A A A X . .
Row9: . . X X X X X . .

Output:
A A .
. . .
. . .

So output is 3x3 grid: first row: A A . ; second row: . . . ; third row: . . .

We need to deduce transformation rule.

We have a 9x9 input grid with a pattern: a vertical column of X's at column 3 (0-index? Actually columns: 1-9). Let's index columns 1-9. Row3: . . X . . . X . . ; row4 same; row5: . . X A A A X . . ; row6 same; row7 same; row8 same; row9: . . X X X X X . . . Wait row9: . . X X X X X . . . Actually row9: . . X X X X X . . . Wait there are 9 columns: row9: . . X X X X X . . . Wait that's 10? Let's count: row9: . . X X X X X . . . Actually the input row9: ". . X X X X X . ." That's 9 tokens: ., ., X, X, X, X, X, ., . . Wait there are 9 tokens: ., ., X, X, X, X, X, ., . . Wait that's 9 tokens: 1: ., 2: ., 3: X, 4: X, 5: X, 6: X, 7: X, 8: ., 9: . . So row9 has X at columns 3-7 inclusive. So the shape is like a well: vertical walls of X at column 3 and column 7? Actually there is X at column 3 and column 7 in many rows. Let's examine each row:

Row1: . . . . . . . . . (no X)
Row2: . . . . . . . . . (no X)
Row3: . . X . . . X . . (X at col3 and col7)
Row4: . . X . . . X . . (same)
Row5: . . X A A A X . . (X at col3 and col7, A at col4-6)
Row6: . . X A A A X . . (same)
Row7: . . X A A A X . . (same)
Row8: . . X A A A X . . (same)
Row9: . . X X X X X . . (X at col3-7)

So the shape is like a rectangular well: vertical walls at col3 and col7, bottom row row9 has X across columns 3-7 forming the base. The interior columns 4-6 contain A's from rows 5-8. So the well is filled with A's from row5 to row8. The top of the well is rows 3-4, which are empty (no A). So the waterline is at row4? Actually the waterline is between row4 and row5: above row5 there is no A, below row5 there is A. So the waterline is at the top of the A region. The empty air

... [11701 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: An orange sky stretches above an azure launchpad. Clustered on or near the pad, colorful balloons of various shapes wait, freshly inflated and straining against the ground. Each balloon is a tight knot of same-colored or distinctly colored cells, full of lift. What to do: Release the balloons. Each one rises into the orange sky — the more air inside it, the higher it floats. A balloon's buoyancy is measured by its fullness: every breath of color it holds carries it one story higher. The launchpad stays bolted to the earth, and the sky fills in behind each balloon as it ascends. Grid details: The sky is 8 columns wide and 8 stories tall. The azure launchpad is the ground floor, permanent and immovable. The orange atmosphere fills every space not claimed by a balloon. Each balloon keeps its shape perfectly as it drifts upward — no stretching, no tumbling, just a clean vertical ascent."

We have training examples. Example 1: Input grid 8x8. Output grid 8x8. We need to deduce transformation rule.

Let's analyze Example 1.

Input grid:

Row1: O O O O O O O O
Row2: O O O O O O O O
Row3: O O O O O O O O
Row4: O O O O O O O O
Row5: O O O O O O O O
Row6: O W O O O O O O
Row7: W W W O O R R R
Row8: A A A A A A A A

Output grid:

Row1: O O O O O O O O
Row2: O W O O O O O O
Row3: W W W O O O O O
Row4: O O O O O R R R
Row5: O O O O O O O O
Row6: O O O O O O O O
Row7: O O O O O O O O
Row8: A A A A A A A A

We need to interpret. The input has some colored cells: W (maroon) at row6 col2, row7 col1-3, R (red) at row7 col6-8. The rest are O (orange). The bottom row (row8) is A (azure). The top rows are all O.

The output shows that the W cluster moved upward: originally at row6 col2, row7 col1-3. In output, W cluster is at row2 col2, row3 col1-3. So it moved up 4 rows? Let's check: The W cluster originally had shape: a 3x2 shape? Actually coordinates: (row6, col2), (row7, col1), (row7, col2), (row7, col3). That's a shape like a small cluster. In output, W cluster at (row2, col2), (row3, col1), (row3, col2), (row3, col3). So moved up 4 rows (row6->row2, row7->row3). Similarly, the R cluster originally at row7 col6-8. In output, R cluster at row4 col6-8. So moved up 3 rows? Wait row7->row4 is 3 rows up. But maybe the rule is that each balloon rises until it hits the top or until it would collide with other balloons? Let's analyze.

The input has a ground floor row8 of A. The sky is O. The balloons are W and R. The rule: release balloons, they rise until they hit the top? But the output shows W cluster moved up 4 rows, R cluster moved up 3 rows. Why different? Maybe because the W cluster had more cells (4 cells) so it rises higher? The metaphor says: "The more air inside it, the higher it floats. A balloon's buoyancy is measured by its fullness: every breath of color it holds carries it one story higher." So each cell of a balloon gives it one story 

... [11779 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: An azure dock line runs along the bottom of the harbor cross-section. Colored cargo bundles rest near the dock, submerged in the murky orange water of the harbor. What to do: Each cargo bundle floats upward — the more crates lashed together, the more trapped air buoys them higher. The dock stays anchored at the bottom. Each bundle rises intact through the orange water, preserving its packing arrangement. Grid details: 8-berth harbor, 8 fathoms deep. Azure bottom is the dock. Orange is harbor water. Colored clusters are cargo bundles."

We have training example 1. Input grid 8x8. Output grid 8x8. We need to deduce transformation rule.

Let's analyze training example 1.

Input grid:

Row1: O O O O O O O O
Row2: O O O O O O O O
Row3: O O O O O O O O
Row4: O O O O O O O O
Row5: O O O O O O O O
Row6: O W O O O O O O
Row7: W W W O O R R R
Row8: A A A A A A A A

Output grid:

Row1: O O O O O O O O
Row2: O W O O O O O O
Row3: W W W O O O O O
Row4: O O O O O R R R
Row5: O O O O O O O O
Row6: O O O O O O O O
Row7: O O O O O O O O
Row8: A A A A A A A A

We need to interpret. Input: bottom row (row8) is A A A A A A A A (azure). Row7: W W W O O R R R. Row6: O W O O O O O O. Others all O.

Output: bottom row remains A's. Row7 all O. Row6 all O. Row5 all O. Row4: O O O O O R R R. Row3: W W W O O O O O. Row2: O W O O O O O O. Row1 all O.

So basically the colored clusters (W and R) moved upward. The W cluster originally at row6 col2 and row7 col1-3. In output, W cluster moved to row3 col1-3 and row2 col2? Wait let's map coordinates.

Let's index rows 1-8 top to bottom, columns 1-8 left to right.

Input:

Row6: col1 O, col2 W, col3 O, col4 O, col5 O, col6 O, col7 O, col8 O.
Row7: col1 W, col2 W, col3 W, col4 O, col5 O, col6 R, col7 R, col8 R.

So W cluster: cells (6,2), (7,1),(7,2),(7,3). R cluster: cells (7,6),(7,7),(7,8).

Output:

Row2: col1 O, col2 W, col3 O, col4 O, col5 O, col6 O, col7 O, col8 O.
Row3: col1 W, col2 W, col3 W, col4 O, col5 O, col6 O, col7 O, col8 O.
Row4: col1 O, col2 O, col3 O, col4 O, col5 O, col6 R, col7 R, col8 R.

So W cluster moved up 4 rows: from row6 to row2? Actually (6,2) moved to (2,2). (7,1) moved to (3,1). (7,2) moved to (3,2). (7,3) moved to (3,3). So cluster shape preserved but moved upward by 4 rows. R cluster moved up 3 rows: from row7 to row4. (7,6) -> (4,6). (7,7) -> (4,7). (7,8) -> (4,8). So R cluster moved up 3 rows.

But why different distances? The rule might be: each cluster floats upward until it hits the top or another cluster? But the clusters are moving upward until they reach the top? Let's examine.

In input, W cluster is at rows 6-7. In output, W cluster is at rows 2-3. So it moved up until it reached row2? Actually row2 is second row from top. So W cluster moved up until it reached row2? But why not row1? Because maybe it stops when it would collide with another cluster? But there is no other cluste

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We need to solve a grid transformation puzzle. We have a metaphorical description, training examples, and test input. We need to deduce the transformation rule. Let's analyze the training example.

We have an 8x8 grid. Input and output grids are given. Let's rewrite them with coordinates. We'll use row 0 at top, row 7 at bottom. Columns 0-7 left to right.

Input Example 1:

Row0: O O O O O O O O
Row1: O O O O O O O O
Row2: O O O O O O O O
Row3: O O O O O O O O
Row4: O O O O O O O O
Row5: O W O O O O O O
Row6: W W W O O R R R
Row7: A A A A A A A A

Output Example 1:

Row0: O O O O O O O O
Row1: O W O O O O O O
Row2: W W W O O O O O
Row3: O O O O O R R R
Row4: O O O O O O O O
Row5: O O O O O O O O
Row6: O O O O O O O O
Row7: A A A A A A A A

We need to find transformation rule mapping input to output.

Observations: The bottom row (row7) remains unchanged: all A's. The top rows (rows0-4) remain unchanged except for some changes? Let's compare row by row.

Input row0: all O. Output row0: all O. unchanged.

Row1: all O. Output row1: O W O O O O O O. So at column1 (index1) changed from O to W. Input row1 had all O. So a W appears at (row1, col1). Where did that W come from? In input, there were W's at row5 col1, row6 col0-2. So maybe W's moved upward? Let's see.

Input row5: O W O O O O O O. Output row5: all O. So the W at (5,1) moved up to (1,1). Input row6: W W W O O R R R. Output row6: all O. So the W's at (6,0),(6,1),(6,2) moved up to (2,0),(2,1),(2,2)? Let's check output row2: W W W O O O O O. Yes, output row2 has W at columns 0,1,2. So W's moved upward by 4 rows? Wait: (6,0) -> (2,0) is up 4 rows. (6,1) -> (2,1) up 4 rows. (6,2) -> (2,2) up 4 rows. (5,1) -> (1,1) up 4 rows. So all W's moved up 4 rows. But also the R's at (6,5),(6,6),(6,7) moved up? Let's check output row3: O O O O O R R R. Yes, R's moved up 3 rows? Wait: (6,5) -> (3,5) is up 3 rows. (6,6) -> (3,6) up 3 rows. (6,7) -> (3,7) up 3 rows. So R's moved up 3 rows. But maybe they moved up until they hit something? Let's examine.

Input row6: W W W O O R R R. Output row3: O O O O O R R R. So R's moved up 3 rows. But why 3? Maybe they moved up until they hit the topmost row that is not O? But there is no other color above them. Let's check the top rows: row0-4 all O. So R's could have moved up 6 rows to row0? But they didn't. So maybe they moved up until they hit a row that contains a different color? But there is no other color. So maybe they moved up until they hit the first row that contains a non-O? But there is none. So maybe they moved up until they hit the first row that contains a W? But there is no W above them. So maybe they moved up until they hit the first row that contains a different color than themselves? But there is no other color. So maybe they moved up until they hit the first row that contains a color that is not O and not the same as them? But there is none. So maybe they moved up until they hit the first row that contains a color that is not O an

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We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: An azure bedrock layer lies at the base of the geological cross-section. Colored mineral deposits sit near the bedrock, each a different ore cluster, embedded in orange sedimentary matrix. What to do: Each mineral vein is thrust upward by tectonic forces — the more crystalline mass in the deposit, the greater the uplift. The bedrock stays immovable. Each deposit preserves its crystal structure as it's pushed through the sediment, orange matrix backfilling the void. Grid details: 8-column cross-section, 8 strata deep. Azure bottom is bedrock. Orange is sedimentary matrix. Colored clusters are mineral deposits."

We have training example 1. Input grid 8x8. Output grid 8x8. We need to deduce transformation rule.

Let's analyze training example 1.

Input grid:

Row1: O O O O O O O O
Row2: O O O O O O O O
Row3: O O O O O O O O
Row4: O O O O O O O O
Row5: O O O O O O O O
Row6: O W O O O O O O
Row7: W W W O O R R R
Row8: A A A A A A A A

So bottom row (row8) is all A (azure). Row7 has W W W O O R R R. Row6 has O W O O O O O O. Row1-5 all O.

Output grid:

Row1: O O O O O O O O
Row2: O W O O O O O O
Row3: W W W O O O O O
Row4: O O O O O R R R
Row5: O O O O O O O O
Row6: O O O O O O O O
Row7: O O O O O O O O
Row8: A A A A A A A A

So transformation: The colored clusters (W and R) moved upward? Let's examine.

Input: W cluster: at row6 col2 (W). Row7 col1-3 are W. So W cluster shape: a 3x2 block? Actually row6 col2 is W, row7 col1-3 are W. So shape: a 3x2 cluster with a missing at row6 col1? Wait row6 col1 is O. So shape: row6 col2 W; row7 col1-3 W. So shape like a "L" shape? Let's map coordinates: using 1-indexed rows from top.

Input coordinates:

Row6 col2: W
Row7 col1: W
Row7 col2: W
Row7 col3: W

So shape: a 3x2 cluster with missing at row6 col1 and row6 col3? Actually row6 col3 is O. So shape is like a "T" shape? Let's draw:

Row6: . W . . . . . .
Row7: W W W . . R R R

So W cluster is 4 cells: (6,2), (7,1),(7,2),(7,3). R cluster: row7 col5-7: R R R. So R cluster is 3 cells contiguous horizontally.

Now output: W cluster moved upward: row2 col2? Wait output row2 col2 is W. Row3 col1-3 are W. So W cluster moved up by 4 rows? Let's check: Input W cluster at rows 6-7. Output W cluster at rows 2-3. So moved up 4 rows. R cluster moved up: Input R cluster at row7 col5-7. Output R cluster at row4 col5-7. So moved up 3 rows. So each cluster moved upward by some amount. The bedrock (A) stays at bottom row 8. The orange matrix (O) remains at other cells? But in output, many O cells changed to O? Actually output row1-5 all O except where clusters moved. But input had O in all cells except clusters. So O remains O except where clusters moved. But also the clusters moved upward, leaving behind O. So the transformation is: each colored cluster moves upward until it hits bedrock? But bedrock is at bottom row 8. But clusters moved upward, not downward. Wait the me

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We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: An azure baking sheet sits at the bottom of the oven. Lumps of differently colored dough rest on or near the sheet, surrounded by the warm orange glow of the oven cavity. What to do: Each lump of dough rises — the more flour kneaded into it, the higher it climbs. Bigger lumps contain more yeast and lift proportionally higher. The baking sheet stays put, and the dough holds its shape as it ascends through the heat. Grid details: 8-wide, 8-tall oven interior. Azure bottom is the baking sheet. Orange is ambient heat. Colored lumps are the dough pieces."

We have training examples. Example 1: Input grid 8x8. Output grid 8x8. We need to deduce transformation rule.

Let's parse Example 1.

Input grid:

Row1: O O O O O O O O
Row2: O O O O O O O O
Row3: O O O O O O O O
Row4: O O O O O O O O
Row5: O O O O O O O O
Row6: O W O O O O O O
Row7: W W W O O R R R
Row8: A A A A A A A A

Output grid:

Row1: O O O O O O O O
Row2: O W O O O O O O
Row3: W W W O O O O O
Row4: O O O O O R R R
Row5: O O O O O O O O
Row6: O O O O O O O O
Row7: O O O O O O O O
Row8: A A A A A A A A

We need to see transformation: The input had W at (row6, col2) and W at (row7, col1-3). R at (row7, col6-8). Output moved W's upward? Let's index coordinates: 1-indexed rows from top. Input: row6 col2 has W. row7 col1-3 W. row7 col6-8 R. Output: row2 col2 has W. row3 col1-3 W. row4 col6-8 R. So W moved up 4 rows? Actually from row6 to row2: moved up 4 rows. W at row7 col1-3 moved to row3 col1-3: moved up 4 rows. R at row7 col6-8 moved to row4 col6-8: moved up 3 rows? Wait row7 to row4 is 3 rows up. But maybe R moved up 3? Let's check: Input row7 col6-8 R. Output row4 col6-8 R. That's 3 rows up. So W moved 4 rows up, R moved 3 rows up. But maybe the rule is that each colored lump rises until it hits something? The bottom row is azure (A). The top rows are orange (O). The lumps are W and R. They rise until they hit the top? But they don't go to top; they stop at some height. Maybe they rise until they hit the topmost row that is not orange? But top row is O. They might rise until they hit the first non-O cell above them? But above them there is only O. So they'd go to top row? But they didn't. So maybe they rise until they hit the first non-O cell above them, but there is none. So maybe they rise until they hit the first non-O cell below them? Wait they are moving upward, so they'd hit something above them. But there is nothing above them except O. So maybe they rise until they hit the first non-O cell below them? That would be downward movement. But they moved upward. So maybe they rise until they hit the first non-O cell below them? That would be downward movement. But they moved upward. So maybe they rise until they hit the first non-O cell above them? But there is none. So maybe they rise until they hit the first non-O cell below them? That would be downward. So not that.

Let's analyze th

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We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: An azure springboard stretches across the bottom of the arena. Teams of differently colored athletes stand huddled on or near the board, surrounded by the orange mat of the competition floor. What to do: Each team launches off the springboard in formation — the larger the squad, the higher their vault carries them. They hold their huddle shape mid-air. The springboard stays bolted to the floor, and the mat fills where they stood. Grid details: 8-lane arena, 8 rows high. Azure bottom is the springboard. Orange is the mat. Colored groups are athlete teams."

We have training examples. Example 1: Input grid 8x8. Output grid 8x8. We need to deduce transformation rule.

Let's parse Example 1.

Input grid:

Row1: O O O O O O O O
Row2: O O O O O O O O
Row3: O O O O O O O O
Row4: O O O O O O O O
Row5: O O O O O O O O
Row6: O W O O O O O O
Row7: W W W O O R R R
Row8: A A A A A A A A

Output grid:

Row1: O O O O O O O O
Row2: O W O O O O O O
Row3: W W W O O O O O
Row4: O O O O O R R R
Row5: O O O O O O O O
Row6: O O O O O O O O
Row7: O O O O O O O O
Row8: A A A A A A A A

We need to interpret transformation. Let's label coordinates: row 1 top, row 8 bottom. Column 1 left, column 8 right.

Input: There is a group of W (maroon) at row6 col2? Wait row6: "O W O O O O O O" so W at (row6, col2). Row7: "W W W O O R R R" so W at (row7, col1-3). R at (row7, col6-8). A at row8 all columns.

Output: Row2: "O W O O O O O O" so W at (row2, col2). Row3: "W W W O O O O O" so W at (row3, col1-3). Row4: "O O O O O R R R" so R at (row4, col6-8). Row5-7 all O. Row8 same A.

So transformation: The W group moved upward from rows 6-7 to rows 2-3. The R group moved upward from row7 col6-8 to row4 col6-8. The A group stayed at bottom row8. The O background remains O except where moved groups replaced O. The O at row5-7 become O again after groups moved.

Essentially, the groups (W and R) moved upward until they hit the top of the arena? But they didn't go all the way to top; they moved to row2-3 and row4. Let's analyze distances: W group originally at rows 6-7. After transformation, at rows 2-3. So moved up 4 rows. R group originally at row7 col6-8. After transformation, at row4 col6-8. Moved up 3 rows. So maybe they moved up until they hit the topmost non-O cell? But there is no other non-O cells above them except O. So maybe they moved up until they hit the top row? But they didn't go to row1. They ended at row2-3 for W, row4 for R. So maybe they moved up until they hit the next non-O cell (like the A row at bottom? No, that's below). Wait maybe they moved up until they hit the next non-O cell in the same column? But there is no other non-O cell above them. So maybe they moved up until they hit the topmost row that is not the bottom row? But that seems arbitrary.

Let's examine the metaphor: "An azure springboard stretches across the bottom of the arena. Teams of differently 

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We need to solve a grid transformation puzzle. We have a metaphorical description, training examples, and a test input grid. We need to produce the output grid.

We have to analyze the training example to deduce the transformation rule. Let's parse the training example.

We have an 8x8 grid. Input grid:

Row1: O O O O O O O O
Row2: O O O O O O O O
Row3: O O O O O O O O
Row4: O O O O O O O O
Row5: O O O O O O O O
Row6: O W O O O O O O
Row7: W W W O O R R R
Row8: A A A A A A A A

Output grid:

Row1: O O O O O O O O
Row2: O W O O O O O O
Row3: W W W O O O O O
Row4: O O O O O R R R
Row5: O O O O O O O O
Row6: O O O O O O O O
Row7: O O O O O O O O
Row8: A A A A A A A A

So the transformation moved some colored cells upward? Let's examine.

Input: Row6 has O W O O O O O O. So at row6, column2 is W. Row7 has W W W O O R R R. So row7 columns1-3 are W, columns6-8 are R. Row8 is all A.

Output: Row2 has O W O O O O O O. So the W from row6 moved up to row2. Row3 has W W W O O O O O. So the W's from row7 moved up to row3. Row4 has O O O O O R R R. So the R's from row7 moved up to row4. The rest of the grid is all O except bottom row A.

So the transformation seems to "lift" the colored shapes upward, maybe by a number of rows equal to something like the number of W's? Let's analyze.

Input: The W's are at row6 col2, row7 col1-3. The R's at row7 col6-8. The A's at row8 all columns. The O's fill the rest.

Output: The W's moved up to row2 and row3. The R's moved up to row4. The A's stayed at row8. The O's fill the rest.

So the transformation seems to "lift" each colored shape upward until it hits the top or until it collides with something? But the shapes moved upward by different amounts: W at row6 moved up 4 rows to row2. W at row7 moved up 4 rows to row3. R at row7 moved up 3 rows to row4. So maybe the rule is: For each colored shape (non-O), move it upward until it reaches the first row that is not occupied by the same color? But the shapes moved to different rows.

Let's examine the relative positions: In input, the W shape is a cluster of 4 cells: at (row6,col2), (row7,col1),(row7,col2),(row7,col3). The R shape is a cluster of 3 cells: at (row7,col6),(row7,col7),(row7,col8). The A shape is a cluster of 8 cells: at row8 all columns. The O shape is everything else.

In output, the W shape moved up to rows 2-3: at (row2,col2),(row3,col1),(row3,col2),(row3,col3). The R shape moved up to row4: at (row4,col6),(row4,col7),(row4,col8). The A shape stayed at row8.

So the W shape moved up 4 rows (from row6 to row2, and row7 to row3). The R shape moved up 3 rows (from row7 to row4). The A shape moved up 0 rows (stayed at row8). So maybe the rule is: Each shape moves upward by a number of rows equal to the number of rows it is above the bottom? But that doesn't match: W shape is at rows 6-7, so above bottom by 1-2 rows? Actually bottom row is row8. So W shape is 1-2 rows above bottom. But moved up 4 rows. R shape is also at row7, 1 row above bottom, moved up 3 row

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We need to solve a grid transformation puzzle. We have a metaphorical description, training examples, and a test input grid. We need to produce the output grid.

We have to analyze the transformation rule from the training example. Let's parse the training example.

We have an 8x8 grid. Input grid:

Row1: O O O O O O O O
Row2: O O O O O O O O
Row3: O O O O O O O O
Row4: O O O O O O O O
Row5: O O O O O O O O
Row6: O W O O O O O O
Row7: W W W O O R R R
Row8: A A A A A A A A

Output grid:

Row1: O O O O O O O O
Row2: O W O O O O O O
Row3: W W W O O O O O
Row4: O O O O O R R R
Row5: O O O O O O O O
Row6: O O O O O O O O
Row7: O O O O O O O O
Row8: A A A A A A A A

We need to understand the transformation. Let's label coordinates: rows 1-8 from top to bottom, columns 1-8 left to right.

Input: The bottom row (row8) is all A (azure). Row7 has W W W O O R R R. Row6 has O W O O O O O O. The rest rows 1-5 are all O.

Output: Row8 remains all A. Row7 becomes all O. Row6 becomes all O. Row5 becomes all O. Row4 has O O O O O R R R. Row3 has W W W O O O O O. Row2 has O W O O O O O O. Row1 remains all O.

So basically the pattern of W and R moved upward? Let's examine.

Input: Row6: O W O O O O O O. Row7: W W W O O R R R. Row8: A A A A A A A A.

Output: Row2: O W O O O O O O. Row3: W W W O O O O O. Row4: O O O O O R R R. Row5: O O O O O O O O. Row6: O O O O O O O O. Row7: O O O O O O O O. Row8: A A A A A A A A.

So the W cluster moved up from row6 to row2? Actually the W cluster originally at row6 col2 (W) moved to row2 col2. The W cluster originally at row7 col1-3 moved to row3 col1-3. The R cluster originally at row7 col6-8 moved to row4 col6-8. So the clusters moved upward by some amount. The bottom row remains unchanged. The top rows become O except where clusters moved.

It seems like the transformation is: For each colored cluster (non-O, non-A?), we "shoot upward" until we hit the top or until we hit something? The description: "Each seedling cluster shoots upward — the more roots in its mass, the taller it grows. The soil bed stays at the base. Each cluster maintains its leaf arrangement as it stretches skyward, orange mulch filling where stems once pressed." The metaphor: azure bottom is soil. Orange is mulch. Colored groups are seedling clusters. The transformation: each cluster shoots upward, the more roots in its mass, the taller it grows. The soil bed stays at the base. Each cluster maintains its leaf arrangement as it stretches skyward, orange mulch filling where stems once pressed.

So we have a bottom row of azure (soil). The clusters are colored groups. They shoot upward, meaning they move upward. The more roots in its mass, the taller it grows. That might mean that the cluster's vertical extent increases? Or the cluster's height increases? The cluster maintains its leaf arrangement as it stretches skyward, orange mulch filling where stems once pressed. So the cluster's shape remains the same relative arrangement, but it moves upward, an

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We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: On a dark stage, a colorful balloon floats — its skin one color, the air inside another. Somewhere nearby, a tiny azure pin glints under the spotlight. What to do: The balloon swells toward the pin, as if daring it to pop. It stretches its skin and fills with more colored air, reaching until its surface arrives exactly where the pin sits. The pin vanishes on contact, consumed by the balloon's expansion, while the far side of the balloon stays firmly anchored where it started. Grid details: The stage is black. The balloon is a bordered shape whose wall and filling are two distinct colors. The pin is always a lone azure dot lurking off to one side of the balloon, aligned with its body. Once the balloon has inflated to swallow the pin, no trace of azure remains."

We have training examples. Let's analyze them.

Example 1:

Input grid 11x11? Actually 11 columns? Let's count: Provided lines: 11 lines? Wait: The input shows 11 lines of 11 columns each? Let's count: first line: ". . . . . . . . . . ." that's 11 tokens. So grid is 11x11. Output also 11x11.

Input Example 1:

Row1: . . . . . . . . . . .
Row2: . G G G G G . . . . .
Row3: . G R R R G . . . . A
Row4: . G R R R G . . . . .
Row5: . G G G G G . . . . .
Row6-11: all dots.

So we have a shape: a rectangle of G border with R interior? Let's examine: The shape is a 5x5 square of G border with R interior? Actually rows 2-5, columns 2-6? Let's index: columns 1-11. Row2: . G G G G G . . . . . => G at columns 2-6. Row3: . G R R R G . . . . A => G at col2, R at 3-5, G at col6, A at col12? Wait there are 11 columns, but A at col12? Let's recount: Row3 tokens: ". G R R R G . . . . A" that's 11 tokens: positions: 1:., 2:G, 3:R, 4:R, 5:R, 6:G, 7:., 8:., 9:., 10:., 11:A. So A at column 11. Row4: . G R R R G . . . . . => G at col2, R at 3-5, G at col6. Row5: . G G G G G . . . . . => G at 2-6. So shape is a 4x4? Actually rows 2-5, columns 2-6: a 4x5? Wait rows 2-5 inclusive: 4 rows. Columns 2-6 inclusive: 5 columns. So shape is 4x5 rectangle: border G, interior R. So a rectangle of G border with R interior. The A is at row3 col11, far to the right. So the A is a single azure dot to the right of the shape, aligned with the shape's body? The shape's body is vertical? The shape's body is the rectangle. The A is to the right of the shape, maybe aligned with the shape's center row? Row3 is the third row of the shape (the second row of interior). So A is aligned horizontally with the shape's interior? The description says "aligned with its body" meaning the pin is somewhere near the shape, maybe along the same horizontal line as the shape's center? In this case, A is at row3, which is the middle row of the shape (since shape has 4 rows, middle rows are 2 and 3? Actually shape rows 2-5: row2 is top border, row3 interior, row4 interior, row5 bottom border. So row3 is interior row. So A is aligned with in

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We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A small stage with nine positions arranged in a square — some occupied by performers in colored costumes, others left dark and empty. Each performer is a distinct voice in the ensemble. What to do: The more voices present in the choir, the more space each one claims. Every performer swells in presence proportional to the total number of singers — as if each voice resonates with every other, amplifying itself. The empty seats swell too, but remain silent darkness. The chorus arranges itself exactly as they stood on the original stage, just grander. Grid details: The intimate 3×3 rehearsal stage becomes a full concert hall. Each performer's single seat blooms into a square throne whose size is dictated by the richness of the ensemble — a solo act barely grows, but a quintet commands enormous territory. The darkness between performers expands in kind, a respectful silence scaled to match the music."

We have training example 1: Input 3x3 grid, output 9x9 grid. The transformation seems to be scaling each cell into a block of size equal to number of distinct colors? Let's analyze.

Input Example 1:
Row1: . A .
Row2: . M M
Row3: W A .

So 3x3 grid. Output is 9x9 grid. Let's examine output:

Output:
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .

We can see that each input cell is expanded into a 3x3 block? Let's check: Input cell (1,1) is '.' (black). In output, the top-left 3x3 block is all '.'? Let's see: Output rows 1-3, columns 1-3: all '.'? Yes, output row1 col1-3: . . . ; row2 col1-3: . . . ; row3 col1-3: . . . . So yes, '.' expands to 3x3 block of '.'.

Input cell (1,2) is 'A'. In output, the block at rows 1-3, columns 4-6: all 'A'? Let's check: row1 col4-6: A A A ; row2 col4-6: A A A ; row3 col4-6: A A A. Yes.

Input cell (1,3) is '.' again, so block rows 1-3, columns 7-9: all '.'.

Input cell (2,1) is '.' -> block rows 4-6, columns 1-3: all '.'? Let's check: row4 col1-3: . . . ; row5 col1-3: . . . ; row6 col1-3: . . . . Yes.

Input cell (2,2) is 'M' -> block rows 4-6, columns 4-6: all 'M'? Let's check: row4 col4-6: M M M ; row5 col4-6: M M M ; row6 col4-6: M M M. Yes.

Input cell (2,3) is 'M' -> block rows 4-6, columns 7-9: all 'M'? Let's check: row4 col7-9: M M M ; row5 col7-9: M M M ; row6 col7-9: M M M. Yes.

Input cell (3,1) is 'W' -> block rows 7-9, columns 1-3: all 'W'? Let's check: row7 col1-3: W W W ; row8 col1-3: W W W ; row9 col1-3: W W W. Yes.

Input cell (3,2) is 'A' -> block rows 7-9, columns 4-6: all 'A'? Yes.

Input cell (3,3) is '.' -> block rows 7-9, columns 7-9: all '.'? Yes.

So the transformation is simply scaling each cell into a block of size equal to the number of distinct colors? Wait, but the scaling factor is 3. The input grid is 3x3, output is 9x9. So scaling factor i

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We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A petri dish of colored organisms scattered among empty medium, each species distinct. What to do: Each organism replicates itself into a colony whose size reflects the biodiversity of the dish — the richer the ecosystem, the larger every colony swells. Grid details: The dish scales outward uniformly; empty medium expands in lockstep with living colonies, preserving the original spatial arrangement of the culture."

We have training example 1: Input grid 3x3? Let's parse.

Example 1 Input:
```
. A .
. M M
W A .
```
So 3 rows, 3 columns. '.' is black? Actually '.' is black. Colors: B=blue, R=red, G=green, Y=yellow, X=grey, M=magenta, O=orange, A=azure, W=maroon. '.' is black.

So input grid:

Row1: . A .
Row2: . M M
Row3: W A .

Output grid is 9x9? Let's examine.

Output:
```
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .
```
So output grid is 9x9. So transformation: each cell in input expands to a 3x3 block? Let's check.

Input cell (1,1) is '.' (black). In output, top-left 3x3 block is all '.'? Let's see output rows 1-3, columns 1-3: all '.'? Output row1 col1-3: . . . ; row2 col1-3: . . . ; row3 col1-3: . . . . Yes, all '.'.

Input cell (1,2) is 'A'. In output, top-left 3x3 block? Actually the block for (1,2) would be rows 1-3, columns 4-6. Let's check: output rows 1-3, columns 4-6: A A A ; A A A ; A A A. Yes, all 'A'.

Input cell (1,3) is '.'; output rows 1-3, columns 7-9: . . . ; . . . ; . . . . Yes.

Input cell (2,1) is '.'; output rows 4-6, columns 1-3: . . . ; . . . ; . . . . Yes.

Input cell (2,2) is 'M'; output rows 4-6, columns 4-6: M M M ; M M M ; M M M. Yes.

Input cell (2,3) is 'M'; output rows 4-6, columns 7-9: M M M ; M M M ; M M M. Yes.

Input cell (3,1) is 'W'; output rows 7-9, columns 1-3: W W W ; W W W ; W W W. Yes.

Input cell (3,2) is 'A'; output rows 7-9, columns 4-6: A A A ; A A A ; A A A. Yes.

Input cell (3,3) is '.'; output rows 7-9, columns 7-9: . . . ; . . . ; . . . . Yes.

So transformation: each cell expands to a 3x3 block of the same color. So scaling factor 3. But the description says "Each organism replicates itself into a colony whose size reflects the biodiversity of the dish — the richer the ecosystem, the larger every colony swells. Grid details: The dish scales outward uniformly; empty medium expands in lockstep with living colonies, preserving the original spatial arrangement of the culture." That seems to match: each cell replicates into a colony of size equal to the number of distinct colors? Wait, "size reflects the biodiversity of the dish — the richer the ecosystem, the larger every colony swells." But in example, all colonies are same size 3x3. So maybe the size is constant? But the description might be generic. But we need to deduce rule: scaling factor maybe equal to number 

... [10949 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A small star chart with colored celestial objects and dark void between them. What to do: Each object and each void region expands into a square zone proportional to the count of distinct luminaries in the chart. Grid details: The star chart scales uniformly outward, preserving the original constellation pattern as each point becomes a block."

We have training example 1: Input grid 3x3? Let's examine.

Input:
. A .
. M M
W A .

So 3 rows, 3 columns. Represented as:

Row1: . A .
Row2: . M M
Row3: W A .

Output grid: 9x9? Let's examine output:

. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .

So output is 9x9. Each input cell expands into a 3x3 block? Let's check: Input cell at (1,1) is '.' (black). In output, the top-left 3x3 block is all '.'? Let's see: Output rows 1-3, columns 1-3: all '.'? Yes, first 3 rows, first 3 columns: all '.'.

Input cell at (1,2) is 'A' (azure). In output, the block at rows 1-3, columns 4-6: all 'A'? Yes, all 'A'.

Input cell at (1,3) is '.' again. Output block rows 1-3, columns 7-9: all '.'? Yes.

Input cell at (2,1) is '.' again. Output block rows 4-6, columns 1-3: all '.'? Wait, output rows 4-6, columns 1-3: all '.'? Let's check: rows 4-6, columns 1-3: all '.'? The output shows row4: . . . M M M M M M. So columns 1-3 are '.'? Yes, row4 columns 1-3: '.' '.' '.'. Row5: . . . M M M M M M. Row6: . . . M M M M M M. So yes, '.'.

Input cell at (2,2) is 'M' (magenta). Output block rows 4-6, columns 4-6: all 'M'? Let's check: row4 columns 4-6: M M M. Row5: M M M. Row6: M M M. Yes.

Input cell at (2,3) is 'M' again. Output block rows 4-6, columns 7-9: all 'M'? Row4 columns 7-9: M M M. Row5: M M M. Row6: M M M. Yes.

Input cell at (3,1) is 'W' (maroon). Output block rows 7-9, columns 1-3: all 'W'? Row7: W W W A A A . . . So columns 1-3: W W W. Row8: W W W. Row9: W W W. Yes.

Input cell at (3,2) is 'A'. Output block rows 7-9, columns 4-6: all 'A'? Row7 columns 4-6: A A A. Row8: A A A. Row9: A A A. Yes.

Input cell at (3,3) is '.' again. Output block rows 7-9, columns 7-9: all '.'? Row7 columns 7-9: . . . Row8: . . . Row9: . . . Yes.

So the transformation is: each input cell expands into a block of size N x N, where N is the number of distinct colors in the input grid? Wait, the description: "Each object and each void region expands into a square zone proportional to the count of distinct luminaries in the chart." The count of distinct luminaries in the chart: In the input, distinct colors: '.' (black), 'A', 'M', 'W'. That's 4 distinct colors. But the block size is 3x3, not 4x4. So maybe it's the number of distinct colors minus 1? Or maybe it's the number of distinct colors minus 1? Let's check: 4 distinct colors, minus 1 = 3. That matches block size 3. But is that always? Let's test with other examples.

We only have 

... [9937 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A small harbor chart with colored vessels and open water. What to do: Every ship and every stretch of open water swells into a square berth whose size matches the number of distinct flags flying in the harbor. Grid details: The harbor chart scales uniformly, each original position expanding into a square block while preserving the fleet's formation."

We have training example 1: Input grid 3x3? Let's parse.

Example 1 Input:
```
. A .
. M M
W A .
```
So 3 rows, 3 columns. '.' is black? Actually '.' is black. Colors: B=blue, R=red, G=green, Y=yellow, X=grey, M=magenta, O=orange, A=azure, W=maroon. '.' is black.

So input grid:

Row1: . A .
Row2: . M M
Row3: W A .

Output grid:
```
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .
```
So output grid is 9x9? Let's count columns: The first row: ". . . A A A . . ." that's 9 columns. So output is 9x9. So each input cell expands into a 3x3 block? Let's check: Input grid 3x3, output 9x9. So each cell expands into a 3x3 block. But the output shows that each cell's color is expanded into a 3x3 block of that color? Let's check.

Input cell (1,1) is '.' (black). Output block at top-left 3x3: all '.'? Let's check output first 3 rows, first 3 columns: Row1: . . . ; Row2: . . . ; Row3: . . . . Yes, all '.'.

Input cell (1,2) is 'A' (azure). Output block at top-left 3x3? Actually the block for (1,2) would be columns 4-6, rows 1-3. Let's check: Row1 columns 4-6: A A A ; Row2: A A A ; Row3: A A A. Yes, all 'A'.

Input cell (1,3) is '.' again. Output block at columns 7-9, rows 1-3: all '.'.

Input cell (2,1) is '.' again. Output block at rows 4-6, columns 1-3: all '.'? Let's check: Row4 columns 1-3: . . . ; Row5: . . . ; Row6: . . . . Yes.

Input cell (2,2) is 'M' (magenta). Output block at rows 4-6, columns 4-6: all 'M'? Let's check: Row4 columns 4-6: M M M ; Row5: M M M ; Row6: M M M. Yes.

Input cell (2,3) is 'M' again. Output block at rows 4-6, columns 7-9: all 'M'? Let's check: Row4 columns 7-9: M M M ; Row5: M M M ; Row6: M M M. Yes.

Input cell (3,1) is 'W' (maroon). Output block at rows 7-9, columns 1-3: all 'W'? Let's check: Row7 columns 1-3: W W W ; Row8: W W W ; Row9: W W W. Yes.

Input cell (3,2) is 'A' again. Output block at rows 7-9, columns 4-6: all 'A'? Row7 columns 4-6: A A A ; Row8: A A A ; Row9: A A A. Yes.

Input cell (3,3) is '.' again. Output block at rows 7-9, columns 7-9: all '.'? Row7 columns 7-9: . . . ; Row8: . . . ; Row9: . . . . Yes.

So the transformation is: each input cell expands into a square block of size equal to the number of distinct colors in the input? Wait, the description says: "Every ship and every stretch of open water swells into a square berth whose size matches the number of distinct flags flying in the harbor." So the size of each block is equal to the number of

... [9451 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A small PCB layout with colored components and empty pads. What to do: Each component and each empty pad scales into a square region whose side equals the number of unique part types on the board. Grid details: The PCB layout grows uniformly, maintaining the original component placement as every position becomes a larger square footprint."

We have training example 1: Input grid 3x3? Let's examine.

Example 1 Input:
```
. A .
. M M
W A .
```
So 3 rows, 3 columns. Colors: '.' black, 'A' azure, 'M' magenta, 'W' maroon.

Output grid:
```
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .
```
So output grid is 9x9. Each input cell becomes a 3x3 block? Let's check: Input grid 3x3, output 9x9. So scaling factor is 3. That matches "side equals the number of unique part types on the board." Let's count unique part types: In input, we have '.' (black), 'A', 'M', 'W'. That's 4 unique types. But scaling factor is 3, not 4. Wait maybe they exclude '.'? Let's check: Unique part types maybe only colored components? But '.' is empty pad. The description: "Each component and each empty pad scales into a square region whose side equals the number of unique part types on the board." So includes empty pad. So number of unique part types is 4. But scaling factor is 3. So maybe they count only colored components? Let's count colored components: 'A', 'M', 'W' => 3 unique types. That matches scaling factor 3. So '.' is not counted as a part type? But the description says "each component and each empty pad scales into a square region". But maybe they treat '.' as empty pad but not counted as part type? But they say "unique part types on the board" maybe refers to colored components only. Let's examine training example 1: Input has 3 colored types: A, M, W. So scaling factor 3. Output 9x9. Each input cell becomes 3x3 block. Let's verify mapping: Input cell (0,0) '.' becomes output block of 3x3 '.'? Let's check output: top-left 3x3 block: rows 0-2, cols 0-2: all '.'? Output shows first 3 rows: first 3 columns are '.'? Let's check output: first row: ". . . A A A . . ." So first 3 columns are '.'? Yes. So '.' maps to 3x3 '.' block. Good.

Input cell (0,1) 'A' maps to 3x3 block of 'A'? Let's check output: top-left 3x3 block of 'A' should be at rows 0-2, cols 3-5. Output: first row: ". . . A A A . . ." So columns 3-5 are 'A'. Good. So mapping holds.

Input cell (0,2) '.' maps to 3x3 '.' block at rows 0-2, cols 6-8. Output: first row: ". . . A A A . . ." So columns 6-8 are '.'? Yes.

Input cell (1,0) '.' maps to 3x3 '.' block at rows 3-5, cols 0-2. Output: row 3: ". . . M M M M M M" Wait row 3: ". . . M M M M M M". So columns 0-2 are '.'? Yes. Good.

Input cell (1,1) 'M' maps to 3x3 'M' block at rows 3-5, cols 3-5. Output: row 3: ". . . M M M M M M" columns 3-5 are 'M'

... [9406 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A small celestial map with colored divine domains and primordial void. What to do: Each god's domain and each stretch of void expands into a square territory proportional to the number of distinct deities in the pantheon. Grid details: The cosmic map scales uniformly, each original position becoming a block, preserving the divine arrangement."

We have training example 1: Input grid 3x3? Let's parse.

Example 1 Input:
```
. A .
. M M
W A .
```
So 3 rows, 3 columns. '.' is black? Actually '.' is black. Colors: B=blue, R=red, G=green, Y=yellow, X=grey, M=magenta, O=orange, A=azure, W=maroon. '.' is black.

So input grid:
Row1: . A .
Row2: . M M
Row3: W A .

Output grid:
```
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .
```
So output grid is 9x9? Let's count: Each row has 9 columns. Yes 9x9. So each input cell expanded into a 3x3 block? Let's check: Input 3x3, output 9x9. So scaling factor 3. Each input cell becomes a 3x3 block. But the pattern is not uniform: For example, input cell (1,1) is '.' (black). In output, the top-left 3x3 block is all '.'? Let's check: Output row1: . . . A A A . . . So first 3 columns are '.'? Yes. Row2: . . . A A A . . . So first 3 columns '.' again. Row3: . . . A A A . . . So first 3 columns '.' again. So top-left 3x3 block is all '.'.

Input cell (1,2) is 'A' (azure). In output, the block at rows 1-3, columns 4-6 is 'A A A' repeated. So that block is all 'A'. Good.

Input cell (1,3) is '.' again. In output, block at rows 1-3, columns 7-9 is '.' all. Good.

Input cell (2,1) is '.' again. Output block rows 4-6, columns 1-3 is '.'? Let's check row4: . . . M M M M M M. Wait row4: . . . M M M M M M. So first 3 columns '.'? Yes. Row5: . . . M M M M M M. Row6: . . . M M M M M M. So block rows 4-6, columns 1-3 is '.' all. Good.

Input cell (2,2) is 'M' (magenta). Output block rows 4-6, columns 4-6 is 'M M M'? Let's check row4: . . . M M M M M M. So columns 4-6 are M M M. Row5: same. Row6: same. So block is all 'M'.

Input cell (2,3) is 'M' again. Output block rows 4-6, columns 7-9 is 'M M M'? Let's check row4: . . . M M M M M M. So columns 7-9 are M M M. Row5: same. Row6: same. So block is all 'M'.

Input cell (3,1) is 'W' (maroon). Output block rows 7-9, columns 1-3 is 'W W W'? Let's check row7: W W W A A A . . . So columns 1-3 are W W W. Row8: same. Row9: same. Good.

Input cell (3,2) is 'A' again. Output block rows 7-9, columns 4-6 is 'A A A'? Row7: W W W A A A . . . So columns 4-6 are A A A. Row8: same. Row9: same. Good.

Input cell (3,3) is '.' again. Output block rows 7-9, columns 7-9 is '.'? Row7: W W W A A A . . . So columns 7-9 are . . . Good.

So the transformation is: Each input cell expands into a block of size N x N, where N is the number of distinct colors (deities) in the input? Wait the description: "

... [5040 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A small geological cross-section with colored mineral deposits and barren rock. What to do: Each mineral deposit and each barren zone grows into a square crystal whose dimensions match the number of distinct minerals in the sample. Grid details: The cross-section scales uniformly, preserving the original stratigraphy as every position expands into a square block."

We have training example 1: Input grid 3x3? Let's parse.

Example 1 Input:
```
. A .
. M M
W A .
```
So 3 rows, 3 columns. '.' is black? Actually '.' is black. Colors: B=blue, R=red, G=green, Y=yellow, X=grey, M=magenta, O=orange, A=azure, W=maroon. '.' is black.

So input grid:

Row1: . A .
Row2: . M M
Row3: W A .

Output grid:
```
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .
```
So output grid is 9x9? Let's count: Each row has 9 characters. Yes 9x9.

So transformation: Each cell in input expands into a square block of size equal to number of distinct minerals in the sample. Distinct minerals: In input, we have colors: '.' (black), 'A', 'M', 'W'. That's 4 distinct colors. So each cell expands into a 4x4 block? Wait output block size: For each input cell, we see a 3x3 block? Let's examine.

Input cell (1,1) is '.' (black). In output, the top-left 3x3 block? Let's check output row1: ". . . A A A . . ." So first 3 columns are '.'? Actually row1: . . . A A A . . . So first 3 columns are '.'? Yes. Row2: . . . A A A . . . So first 3 columns are '.' again. Row3: . . . A A A . . . So first 3 columns are '.' again. So the top-left 3x3 block is all '.'.

So each input cell expands into a 3x3 block. But we expected 4x4? Let's check other cells.

Input cell (1,2) is 'A'. In output, the block at columns 4-6, rows 1-3: A A A repeated. So 3x3 block of 'A'.

Input cell (1,3) is '.' again. In output, columns 7-9, rows 1-3: . . . So 3x3 block of '.'.

Input cell (2,1) is '.' again. In output, rows 4-6, columns 1-3: . . .? Let's check row4: . . . M M M M M M. Wait row4: . . . M M M M M M. So first 3 columns are '.'? Actually row4: . . . M M M M M M. So first 3 columns are '.'? Yes. Row5: . . . M M M M M M. Row6: . . . M M M M M M. So rows 4-6, columns 1-3 are '.'.

Input cell (2,2) is 'M'. In output, rows 4-6, columns 4-6: M M M. So 3x3 block of 'M'.

Input cell (2,3) is 'M'. In output, rows 4-6, columns 7-9: M M M. So 3x3 block of 'M'.

Input cell (3,1) is 'W'. In output, rows 7-9, columns 1-3: W W W. So 3x3 block of 'W'.

Input cell (3,2) is 'A'. In output, rows 7-9, columns 4-6: A A A. So 3x3 block of 'A'.

Input cell (3,3) is '.' again. In output, rows 7-9, columns 7-9: . . . So 3x3 block of '.'.

Thus each input cell expands into a 3x3 block. So the scaling factor is 3. But the description says "Each mineral deposit and each barren zone grows into a square crystal whose dimensions match 

... [10801 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A sparse arrangement of ingredients resting on a neutral surface, some spaces left bare. What to do: Each ingredient puffs up into a generous portion proportional to how many distinct flavors share the recipe, while bare spaces become equally generous servings of nothing. Grid details: The cutting board grows to accommodate every inflated ingredient, each occupying a square region, preserving the original mise en place layout."

We have training example 1: Input grid 3x3? Let's parse.

Input:
. A .
. M M
W A .

So grid 3 rows, 3 columns. Represented as:

Row1: . A .
Row2: . M M
Row3: W A .

Output grid: Let's parse the output lines:

. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .

So output grid is 9x9? Let's count columns: The first line: ". . . A A A . . ." That's 9 columns. So output grid is 9x9. So each input cell expands to a 3x3 block? Let's check: Input 3x3, output 9x9. So each input cell expands to 3x3 block. But the output shows that each cell is expanded to a 3x3 block of the same color? Let's examine.

Input cell (1,1) is '.' (black). Output block at top-left 3x3: first 3 rows, first 3 columns: all '.'? Let's check: first line: ". . . A A A . . ." first 3 columns are '.' '.' '.' yes. second line: ". . . A A A . . ." first 3 columns '.' '.' '.' yes. third line: ". . . A A A . . ." first 3 columns '.' '.' '.' yes. So that block is all '.'.

Input cell (1,2) is 'A'. Output block at top-left 3x3? Actually the block for (1,2) would be columns 4-6, rows 1-3. Let's check: first line columns 4-6: "A A A" yes. second line: "A A A" yes. third line: "A A A" yes. So block is all 'A'.

Input cell (1,3) is '.' again. Output block at columns 7-9, rows 1-3: all '.'? Let's check: first line columns 7-9: ". . ." yes. second line: ". . ." yes. third line: ". . ." yes.

Input cell (2,1) is '.' again. Output block at rows 4-6, columns 1-3: all '.'? Let's check: row4: ". . . M M M M M M" first 3 columns '.' '.' '.' yes. row5: same. row6: same. So block is all '.'.

Input cell (2,2) is 'M'. Output block at rows 4-6, columns 4-6: "M M M" each row? Let's check: row4 columns 4-6: "M M M" yes. row5: "M M M" yes. row6: "M M M" yes.

Input cell (2,3) is 'M'. Output block at rows 4-6, columns 7-9: "M M M" each row? Let's check: row4 columns 7-9: "M M M" yes. row5: "M M M" yes. row6: "M M M" yes.

Input cell (3,1) is 'W'. Output block at rows 7-9, columns 1-3: "W W W" each row? Let's check: row7: "W W W A A A . . ." first 3 columns "W W W" yes. row8: same. row9: same.

Input cell (3,2) is 'A'. Output block at rows 7-9, columns 4-6: "A A A" each row? Let's check: row7 columns 4-6: "A A A" yes. row8: same. row9: same.

Input cell (3,3) is '.' again. Output block at rows 7-9, columns 7-9: all '.'? Let's check: row7 columns 7-9: ". . ." yes. row8: same. row9: s

... [10050 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: Athletes and empty patches scattered across a small playing field. What to do: Each player stakes out a square territory whose size reflects the total number of teams competing; unoccupied zones grow by the same proportion. Grid details: The field expands uniformly, each original position becoming a block, maintaining the spatial formation of the original lineup."

We have training example 1: Input grid 3x3? Let's examine.

Example 1 Input:
```
. A .
. M M
W A .
```
So 3 rows, 3 columns. Output grid is 9x9? Let's check. Output:

```
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .
```

That's 9 rows, 9 columns. So the transformation expands each cell into a 3x3 block? Let's check: Input cell (0,0) is '.' (black). In output, the top-left 3x3 block is all '.'? Let's see: Output rows 0-2, columns 0-2: all '.'? Yes, first 3 rows, first 3 columns: all '.'.

Input cell (0,1) is 'A' (azure). In output, the block at rows 0-2, columns 3-5: all 'A'? Yes, rows 0-2, columns 3-5: all 'A'.

Input cell (0,2) is '.' again. Output block rows 0-2, columns 6-8: all '.'? Yes.

Input cell (1,0) is '.' again. Output block rows 3-5, columns 0-2: all '.'? Wait, output rows 3-5, columns 0-2: all '.'? Let's check: row 3: ". . . M M M M M M" -> columns 0-2 are '.'? Yes. Row 4: same. Row 5: same. So yes.

Input cell (1,1) is 'M' (magenta). Output block rows 3-5, columns 3-5: all 'M'? Let's check: row 3: ". . . M M M M M M" -> columns 3-5 are 'M'? Yes. Row 4: same. Row 5: same.

Input cell (1,2) is 'M' again. Output block rows 3-5, columns 6-8: all 'M'? Let's check: row 3: columns 6-8 are 'M'? Yes. Row 4: same. Row 5: same.

Input cell (2,0) is 'W' (maroon). Output block rows 6-8, columns 0-2: all 'W'? Let's check: row 6: "W W W A A A . . ." -> columns 0-2 are 'W'? Yes. Row 7: same. Row 8: same.

Input cell (2,1) is 'A'. Output block rows 6-8, columns 3-5: all 'A'? Yes. Row 6: columns 3-5 are 'A'? Yes. Row 7: same. Row 8: same.

Input cell (2,2) is '.' again. Output block rows 6-8, columns 6-8: all '.'? Yes.

So the transformation is: each cell expands into a 3x3 block of the same color. So the scaling factor is 3. But the description says "Each player stakes out a square territory whose size reflects the total number of teams competing; unoccupied zones grow by the same proportion. Grid details: The field expands uniformly, each original position becoming a block, maintaining the spatial formation of the original lineup." That matches: each cell becomes a block of size equal to the number of teams? But we need to deduce the scaling factor from the input. In example 1, the input is 3x3, output is 9x9, scaling factor 3. That might be the number of distinct colors? Let's count distinct colors in input: '.' (black), 'A', 'M', 'W'. That's 4 distinct colors. But s

... [10600 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A small forecast map with colored weather systems and calm patches. What to do: Each system — and each calm zone — inflates its area based on how many distinct fronts are present, as if mutual atmospheric pressure forces them all to swell equally. Grid details: The map scales uniformly outward, each original cell becoming a square region, preserving the original meteorological layout."

We have training example 1: Input grid 3x3? Let's parse.

Example 1 Input:
```
. A .
. M M
W A .
```
So 3 rows, 3 columns. Output grid is 9x9? Let's examine output:

```
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .
```

So output is 9x9. Each input cell becomes a 3x3 block? Let's check: Input cell (0,0) is '.' (black). In output, top-left 3x3 block is all '.'? Let's see: first 3 rows, first 3 columns: all '.'? Output shows first 3 rows: first 3 columns are '.'? Let's check: Row1: ". . . A A A . . ." -> first 3 columns '.' '.' '.' yes. Row2: same. Row3: same. So yes, input cell '.' maps to 3x3 block of '.'.

Input cell (0,1) is 'A'. In output, the block at rows 0-2, columns 3-5 is 'A'? Let's check: Row1 columns 4-6? Wait indexing: columns 0-8. For block (0,1) we expect columns 3-5. Row1: ". . . A A A . . ." -> columns 3-5 are 'A A A'. Row2 same. Row3 same. So yes, 'A' maps to 3x3 block of 'A'.

Input cell (0,2) is '.' again -> block rows 0-2, columns 6-8 all '.'? Row1 columns 6-8: ". . ." yes.

Input cell (1,0) is '.' -> block rows 3-5, columns 0-2 all '.'? Let's check row4: ". . . M M M M M M" -> columns 0-2 are '.' '.' '.' yes. Row5 same. Row6 same.

Input cell (1,1) is 'M' -> block rows 3-5, columns 3-5 should be 'M'? Row4 columns 3-5: "M M M" yes. Row5 same. Row6 same.

Input cell (1,2) is 'M' -> block rows 3-5, columns 6-8 should be 'M'? Row4 columns 6-8: "M M M" yes.

Input cell (2,0) is 'W' -> block rows 6-8, columns 0-2 should be 'W'? Row7 columns 0-2: "W W W" yes.

Input cell (2,1) is 'A' -> block rows 6-8, columns 3-5 should be 'A'? Row7 columns 3-5: "A A A" yes.

Input cell (2,2) is '.' -> block rows 6-8, columns 6-8 all '.'? Row7 columns 6-8: ". . ." yes.

So the transformation is simply scaling each cell to a 3x3 block of the same color. That is a simple scaling by factor 3. But the description says "Each system — and each calm zone — inflates its area based on how many distinct fronts are present, as if mutual atmospheric pressure forces them all to swell equally." That might refer to scaling factor equal to number of distinct colors? But in example, scaling factor is 3. Let's examine number of distinct colors in input: '.' (black), 'A', 'M', 'W' => 4 distinct colors. But scaling factor is 3, not 4. Maybe scaling factor equals number of distinct colors minus 1? 4-1=3. But that seems a

... [9975 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A small floorplan with colored rooms and vacant lots arranged in a grid. What to do: Every room and every vacancy scales up its footprint equally, determined by how many distinct tenants occupy the building — more tenants, grander rooms for all. Grid details: The blueprint grows proportionally, each original unit becoming a square block, maintaining the spatial relationships of the original design."

We have training example 1: Input grid 3x3? Let's parse.

Example 1 Input:
```
. A .
. M M
W A .
```
So 3 rows, 3 columns. Output grid is 9x9? Let's examine output:

```
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .
```

So output is 9x9. Each input cell becomes a 3x3 block? Let's check: Input cell (0,0) is '.' (black). In output, the top-left 3x3 block is all '.'? Let's see: first 3 rows, first 3 columns: all '.'? The output shows first 3 rows: first 3 columns are '.'? Let's check: first row: ". . . A A A . . ." So first 3 columns are '.'? Yes. Second row: ". . . A A A . . ." So first 3 columns '.'? Yes. Third row: ". . . A A A . . ." So first 3 columns '.'? Yes. So input cell (0,0) '.' maps to 3x3 block of '.'.

Input cell (0,1) is 'A'. In output, the block at rows 0-2, columns 3-5 should be 'A'? Let's check: first row columns 3-5: "A A A". Yes. Second row: "A A A". Third row: "A A A". So yes.

Input cell (0,2) '.' maps to block at rows 0-2, columns 6-8: all '.'? Let's check: first row columns 6-8: ". . .". Yes.

Input cell (1,0) '.' maps to block at rows 3-5, columns 0-2: all '.'? Let's check: row 3 columns 0-2: ". . .". Yes. Row 4: ". . .". Row 5: ". . .". So yes.

Input cell (1,1) 'M' maps to block at rows 3-5, columns 3-5: all 'M'? Let's check: row 3 columns 3-5: "M M M". Row 4: "M M M". Row 5: "M M M". Yes.

Input cell (1,2) 'M' maps to block at rows 3-5, columns 6-8: all 'M'? Let's check: row 3 columns 6-8: "M M M". Row 4: "M M M". Row 5: "M M M". Yes.

Input cell (2,0) 'W' maps to block at rows 6-8, columns 0-2: all 'W'? Let's check: row 6 columns 0-2: "W W W". Row 7: "W W W". Row 8: "W W W". Yes.

Input cell (2,1) 'A' maps to block at rows 6-8, columns 3-5: all 'A'? Let's check: row 6 columns 3-5: "A A A". Row 7: "A A A". Row 8: "A A A". Yes.

Input cell (2,2) '.' maps to block at rows 6-8, columns 6-8: all '.'? Let's check: row 6 columns 6-8: ". . .". Row 7: ". . .". Row 8: ". . .". Yes.

So the transformation is: each cell expands to a block of size N x N, where N is the number of distinct colors (including '.'?) in the input grid? Let's check: Input grid has colors: '.' (black), 'A', 'M', 'W'. That's 4 distinct colors. But the block size is 3, not 4. So maybe N is the number of distinct non-blank colors? Let's count: 'A', 'M', 'W' = 3. That matches block size 3. So the rule: For each cell, expand to a block of size equal 

... [10572 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the transformation rule. Let's analyze.

We have a grid transformation puzzle. Input grid is small (3x3). Output grid is larger (9x9 or 12x12). The transformation seems to involve expanding each cell into a 3x3 block? Let's examine Example 1.

Example 1 Input:
```
. A .
. M M
W A .
```
So 3x3 grid. Output is 9x9 grid. Let's examine output:

```
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .
```

We can see that each input cell is expanded into a 3x3 block. But the mapping of colors is not straightforward: For example, input cell (0,0) is '.' (black). In output, the top-left 3x3 block is all '.'? Let's check: The output top-left 3x3 block is:

Rows 0-2, columns 0-2: all '.'? Let's check: Row 0: ". . .", Row 1: ". . .", Row 2: ". . .". Yes, all '.'.

Input cell (0,1) is 'A' (azure). In output, the block at rows 0-2, columns 3-5: all 'A'? Let's check: Row 0: "A A A", Row 1: "A A A", Row 2: "A A A". Yes, all 'A'.

Input cell (0,2) is '.' again. Output block rows 0-2, columns 6-8: all '.'? Row 0: ". . .", Row 1: ". . .", Row 2: ". . .". Yes.

Input cell (1,0) is '.' again. Output block rows 3-5, columns 0-2: all '.'? Let's check: Row 3: ". . .", Row 4: ". . .", Row 5: ". . .". Yes.

Input cell (1,1) is 'M' (magenta). Output block rows 3-5, columns 3-5: all 'M'? Let's check: Row 3: "M M M", Row 4: "M M M", Row 5: "M M M". Yes.

Input cell (1,2) is 'M' again. Output block rows 3-5, columns 6-8: all 'M'? Row 3: "M M M", Row 4: "M M M", Row 5: "M M M". Yes.

Input cell (2,0) is 'W' (maroon). Output block rows 6-8, columns 0-2: all 'W'? Row 6: "W W W", Row 7: "W W W", Row 8: "W W W". Yes.

Input cell (2,1) is 'A'. Output block rows 6-8, columns 3-5: all 'A'? Row 6: "A A A", Row 7: "A A A", Row 8: "A A A". Yes.

Input cell (2,2) is '.' again. Output block rows 6-8, columns 6-8: all '.'? Row 6: ". . .", Row 7: ". . .", Row 8: ". . .". Yes.

So Example 1: Each input cell expands to a 3x3 block of the same color. So the transformation is simply scaling by factor 3, replicating each cell into a 3x3 block. But we need to confirm with other examples.

Example 2 Input:
```
B . Y
. Y .
. B .
```
Output:
```
B B . . Y Y
B B . . Y Y
. . Y Y . .
. . Y Y . .
. . B B . .
. . B B . .
```
Let's analyze. Input is 3x3. Output is 6x6. So scaling factor 2? Let's check: Input cell (0,0) is 'B'. Output block rows 0-1, columns 0-1: "B B" in row 0, "B B" in row 1. Yes.

Input cell (0,1) is '.' (black). Output block rows 0-1, columns 2-3: ". ." in row 0, ". ." in row 1. Yes.

Input cell (0,2) is 'Y'. Output block rows 0-1, columns 4-5: "Y Y" in row 0, "Y Y" in row 1. Yes.

Input cell (1,0) is '.' (black). Output block rows 2-3, columns 0-1: ". ." in row 2, ". ." in row 3. Yes.

Input cell (1,1) is 'Y'. Output block rows 2-3, columns 2-3: "Y Y" in row 2, "Y Y" in row 3. Yes.

In

... [8395 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the rule. Let's analyze.

We have a grid transformation puzzle. Input grid is small (3x3). Output grid is larger (9x9). The transformation seems to involve expanding each cell into a 3x3 block? Let's examine Example 1.

Example 1 Input:
```
. A .
. M M
W A .
```
So 3x3 grid. Output is 9x9 grid. Let's write the output grid from example 1:

```
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .
```

Let's analyze mapping. Input cell (0,0) is '.' (black). In output, the top-left 3x3 block is all '.'? Let's check: The first 3 rows, first 3 columns: all '.'? The output shows first 3 rows: first 3 columns are '.'? Let's check: Row 0: ". . . A A A . . ." So first 3 columns are '.' '.' '.' yes. Row 1: same. Row 2: same. So yes, the top-left 3x3 block is all '.'.

Input cell (0,1) is 'A'. In output, the block at rows 0-2, columns 3-5 is 'A'? Let's check: Row 0: columns 3-5: "A A A". Row 1: same. Row 2: same. So yes, 3x3 block of 'A'.

Input cell (0,2) is '.' again. Output block rows 0-2, columns 6-8: all '.'? Row 0: columns 6-8: ". . .". Row 1: same. Row 2: same. So yes.

Input cell (1,0) is '.' again. Output block rows 3-5, columns 0-2: all '.'? Let's check: Row 3: ". . . M M M M M M" Wait row 3: first 3 columns are '.' '.' '.'? Actually row 3: ". . . M M M M M M". So yes, first 3 columns '.' '.' '.'.

Input cell (1,1) is 'M'. Output block rows 3-5, columns 3-5: 'M'? Let's check: Row 3: columns 3-5: "M M M". Row 4: same. Row 5: same. So yes.

Input cell (1,2) is 'M'. Output block rows 3-5, columns 6-8: 'M'? Row 3: columns 6-8: "M M M". Row 4: same. Row 5: same. So yes.

Input cell (2,0) is 'W'. Output block rows 6-8, columns 0-2: 'W'? Row 6: "W W W A A A . . .". So first 3 columns are 'W W W'. Row 7: same. Row 8: same. So yes.

Input cell (2,1) is 'A'. Output block rows 6-8, columns 3-5: 'A'? Row 6: columns 3-5: "A A A". Row 7: same. Row 8: same. So yes.

Input cell (2,2) is '.' again. Output block rows 6-8, columns 6-8: '.'? Row 6: columns 6-8: ". . .". Row 7: same. Row 8: same. So yes.

Thus the transformation is: each input cell expands into a 3x3 block of the same color. So the output grid is 3 times larger in each dimension (3x3 input -> 9x9 output). Each cell is replaced by a 3x3 block of that cell's color.

But we need to confirm with Example 2 and 3.

Example 2 Input:
```
B . Y
. Y .
. B .
```
Output:
```
B B . . Y Y
B B . . Y Y
. . Y Y . .
. . Y Y . .
. . B B . .
. . B B . .
```
Let's analyze: Input 3x3 -> output 6x6? Wait output is 6x6. Let's check: The output grid has 6 rows, each row has 6 columns. So scaling factor is 2? Let's check mapping: Input cell (0,0) is 'B'. Output block rows 0-1, columns 0-1: 'B'? Row 0: "B B . . Y Y". So columns 0-1: "B B". Row 1: same. So yes.

Input cell (0,1) is '.' -> output block rows 0-1, columns 2-3:

... [9342 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A small plot with colored plantings and bare soil arranged in a grid. What to do: Each plant and each bare patch claims a square territory whose side equals the number of distinct species in the garden. Grid details: The garden expands uniformly from its original layout, every plot position becoming a larger square block."

We have training example 1: Input grid 3x3? Let's parse.

Example 1 Input:
```
. A .
. M M
W A .
```
So 3 rows, 3 columns. Colors: '.' black, 'A' azure, 'M' magenta, 'W' maroon.

Output grid:
```
. . . A A A . . .
. . . A A A . . .
. . . A A A . . .
. . . M M M M M M
. . . M M M M M M
. . . M M M M M M
W W W A A A . . .
W W W A A A . . .
W W W A A A . . .
```
So output grid is 9x9? Let's count: each row has 9 characters. Yes 9x9. So the transformation expands each cell into a 3x3 block? Wait 3x3 input -> 9x9 output. So each cell becomes a 3x3 block. But the pattern is not uniform: For example, input cell (0,0) is '.' (black). In output, the top-left 3x3 block is all '.'? Let's check: Output rows 0-2, columns 0-2: all '.'? The output shows first 3 rows: ". . . A A A . . ." So first 3 columns are '.'? Actually row 0: ". . . A A A . . ." So columns 0-2 are '.'; columns 3-5 are 'A'; columns 6-8 are '.'.

So the first 3x3 block (rows 0-2, cols 0-2) is all '.'? Yes. That matches input cell (0,0) '.'.

Input cell (0,1) is 'A'. In output, the block rows 0-2, cols 3-5 is 'A' repeated. So that block is all 'A'. Good.

Input cell (0,2) is '.' again. Output block rows 0-2, cols 6-8 is '.'.

Input cell (1,0) is '.'? Wait row 1 of input: ". M M". So cell (1,0) '.'; block rows 3-5, cols 0-2 is '.'? Let's check output rows 3-5: ". . . M M M M M M" Wait row 3: ". . . M M M M M M". So columns 0-2 are '.'? Yes. So block rows 3-5, cols 0-2 is '.'.

Input cell (1,1) is 'M'. Output block rows 3-5, cols 3-5 is 'M'? Let's check row 3: ". . . M M M M M M". So columns 3-5 are 'M'. Good.

Input cell (1,2) is 'M'. Output block rows 3-5, cols 6-8 is 'M'? Row 3: columns 6-8 are 'M'. Yes.

Input cell (2,0) is 'W'. Output block rows 6-8, cols 0-2 is 'W'? Row 6: "W W W A A A . . .". So columns 0-2 are 'W'. Good.

Input cell (2,1) is 'A'. Output block rows 6-8, cols 3-5 is 'A'? Row 6: columns 3-5 are 'A'. Yes.

Input cell (2,2) is '.'? Wait row 2 of input: "W A .". So cell (2,2) '.'; output block rows 6-8, cols 6-8 is '.'? Row 6: columns 6-8 are '.'.

So transformation is: each input cell expands to a block of size equal to number of distinct species in the garden? Wait the description: "Each plant and each bare patch claims a square territory whose side equals the number of distinct species in the garden." So the side length of each block equals the number of distinct species in the garden. In example 1, distinct species: '.' (black), 'A', 'M', 'W' => 4 distinct? Wait '.' counts as a species? The description says "Each plant and each bare patch claims a squ

... [9642 chars truncated]

We need to parse the puzzle. The description: "grid transformation puzzle" with metaphorical description. We have training examples. We need to deduce rule. Let's analyze.

We have a 3-lane grid: top, middle, bottom rows. The center lane is always full of yellow marchers. The outer lanes alternate presence and absence in opposite lockstep. So top lane has pattern Y . Y . Y ...? bottom lane has . Y . Y . Y ...? They are offset by one cell. The grid length can vary.

The transformation: "drumbeat sounds every three steps along the center lane, and each marcher standing on that beat swaps their yellow uniform for a magenta one." So at positions in center lane that are multiples of 3 steps? Starting from first cell? "every three steps along the center lane" likely means positions 0,3,6,9,...? But we need to confirm with examples.

Also "outer lanes hear a slower rhythm — a cymbal crash every six steps. But the two outer lanes are offset from each other: whichever lane has a marcher standing at the start of the route hears the crash on the downbeat, while the lane that begins with a gap hears it on the off-beat, halfway between crashes. Wherever a crash lands on an occupied position, that marcher also turns magenta. Empty gaps stay empty — you can't dye what isn't there."

So for outer lanes: there is a crash every 6 steps. But the lanes are offset: the lane that starts with a marcher at the start of the route hears the crash on the downbeat (i.e., at positions 0,6,12,...). The lane that starts with a gap hears it on the off-beat, halfway between crashes (i.e., at positions 3,9,15,...). So basically for outer lanes, the positions that get magenta are those that are multiples of 6 for the lane that starts with a marcher, and those that are multiples of 6 plus 3 for the lane that starts with a gap.

But we need to confirm with training examples.

Let's analyze Example 1.

Input grid:

Row1: Y . Y . Y . Y . Y . Y . Y
Row2: Y Y Y Y Y Y Y Y Y Y Y Y Y
Row3: . Y . Y . Y . Y . Y . Y .

Let's write indices 0-based across columns.

Row1: positions: 0:Y,1:.,2:Y,3:.,4:Y,5:.,6:Y,7:.,8:Y,9:.,10:Y,11:.,12:Y
Row2: all Y across 13 columns.
Row3: 0:.,1:Y,2:.,3:Y,4:.,5:Y,6:.,7:Y,8:.,9:Y,10:.,11:Y,12:.

So top lane starts with Y at position 0. Bottom lane starts with . at position 0. So top lane offset 0, bottom lane offset 1 relative to Y pattern.

Now output grid:

Row1: M . Y . Y . M . Y . Y . M
Row2: M Y Y M Y Y M Y Y M Y Y M
Row3: . Y . M . Y . Y . M . Y .

Let's analyze each row.

Row1: positions: 0:M,1:.,2:Y,3:.,4:Y,5:.,6:M,7:.,8:Y,9:.,10:Y,11:.,12:M

So Y at positions 0,2,4,6,8,10,12 originally. After transformation, Y at 0 changed to M, 2 remains Y, 4 remains Y, 6 changed to M, 8 remains Y, 10 remains Y, 12 changed to M. So positions 0,6,12 changed to M. These are multiples of 6? 0,6,12 yes. So for top lane, positions multiples of 6 changed to M. That matches the rule: top lane starts with Y at position 0, so it hears crash on downbeat at positions 0

... [9819 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the rule. Let's parse the problem carefully.

We have a metaphorical description: "Three horizontal bands of golden stars: a continuous central band and two outer bands with alternating stars and voids in opposite phase. What to do: Magenta flares erupt periodically in the central band. The outer bands flare at double the interval, only on stars positioned at the resonant points. Grid details: Three rows. Center row solid golden. Outer rows alternate golden/dark oppositely. Magenta replaces golden at regular intervals — twice as dense in the center."

We have color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

So Y=yellow is golden stars. '.' is black (void). M=magenta is the flare. The puzzle: we have 3 rows. The center row is all Y. Outer rows alternate Y and . in opposite phase. So row1: Y . Y . Y . ... row3: . Y . Y . Y ... etc. The transformation: Magenta flares erupt periodically in the central band. The outer bands flare at double the interval, only on stars positioned at the resonant points.

So we need to map input to output. Let's examine training examples.

Example 1:

Input:
Row1: Y . Y . Y . Y . Y . Y . Y
Row2: Y Y Y Y Y Y Y Y Y Y Y Y Y
Row3: . Y . Y . Y . Y . Y . Y .

Output:
Row1: M . Y . Y . M . Y . Y . M
Row2: M Y Y M Y Y M Y Y M Y Y M
Row3: . Y . M . Y . Y . M . Y .

Let's analyze.

Input row1: Y . Y . Y . Y . Y . Y . Y (length 13). Output row1: M . Y . Y . M . Y . Y . M. So positions: 1,7,13 changed to M. Others remain Y or . unchanged. So pattern: every 6th? Let's index positions 1-13. Input row1: Y at odd positions 1,3,5,7,9,11,13. Output row1: M at positions 1,7,13. So M at positions 1,7,13. That's positions 1, 7, 13. That's 6 apart. So M at positions 1, 7, 13. So pattern: M at positions 1 + 6k. So M at positions 1,7,13. So basically every 6th Y becomes M. So the interval is 6. So the rule: In outer rows, Y's become M at positions that are multiples of 6? But we need to check row3.

Row3 input: . Y . Y . Y . Y . Y . Y . (positions 1-13). Output row3: . Y . M . Y . Y . M . Y . So M at positions 4 and 10? Wait let's index: positions: 1 '.'; 2 'Y'; 3 '.'; 4 'Y'; 5 '.'; 6 'Y'; 7 '.'; 8 'Y'; 9 '.'; 10 'Y'; 11 '.'; 12 'Y'; 13 '.'. Output: . Y . M . Y . Y . M . Y . So M at positions 4 and 10. So positions 4 and 10. That's also 6 apart. So M at positions 4,10. So pattern: In outer rows, Y's become M at positions 4,10, etc. So offset 4 relative to row1's offset 1. So row1 offset 1, row3 offset 4. So pattern: Outer rows alternate offset by 3? Wait difference between 1 and 4 is 3. But row1 offset 1, row3 offset 4. So maybe the offset is 1 for row1, 4 for row3. That matches the description: outer rows alternate golden/dark oppositely. So row1 has Y at odd positions, row3 has Y at even positions. So the M positions are at positions 1,7,13 for row1; 4,10 for row3. So basically M at positions that are 1

... [8989 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the rule. Let's parse the problem carefully.

We have a metaphorical description: "What you see: Three horizontal lines of golden buoys: a solid center channel marker flanked by two alternating lines with buoys and gaps in opposite arrangement. What to do: A periodic lighthouse beam turns some golden buoys magenta. The center line is swept most often; flanking lines are caught at half the frequency, only where buoys sit at the right positions. Grid details: Three rows. Center row all golden. Outer rows alternate golden/empty in antiphase. Magenta replaces golden at regular spacings."

We have color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

So the grid uses '.' for black, Y for yellow, M for magenta. The input grid uses Y and '.' only. The output grid uses Y, M, and '.'.

We need to deduce transformation rule: For each cell, maybe some cells become M (magenta) based on some pattern.

Let's analyze training examples.

Example 1:

Input:
Row1: Y . Y . Y . Y . Y . Y . Y
Row2: Y Y Y Y Y Y Y Y Y Y Y Y Y
Row3: . Y . Y . Y . Y . Y . Y .

Output:
Row1: M . Y . Y . M . Y . Y . M
Row2: M Y Y M Y Y M Y Y M Y Y M
Row3: . Y . M . Y . Y . M . Y .

Let's write them as arrays.

Input1 Row1: Y . Y . Y . Y . Y . Y . Y
Indices: 0 1 2 3 4 5 6 7 8 9 10 11 12
Input1 Row2: Y Y Y Y Y Y Y Y Y Y Y Y Y
Indices: 0-12
Input1 Row3: . Y . Y . Y . Y . Y . Y .

Output1 Row1: M . Y . Y . M . Y . Y . M
Output1 Row2: M Y Y M Y Y M Y Y M Y Y M
Output1 Row3: . Y . M . Y . Y . M . Y .

Let's analyze pattern.

Observations: In output, some Y cells become M. Which ones? Let's mark positions.

Row1: Input Y at positions 0,2,4,6,8,10,12. Output M at positions 0,6,12. So Y at 0,6,12 become M. Y at 2,4,8,10 remain Y.

Row2: Input Y at all positions 0-12. Output M at positions 0,3,6,9,12. So Y at 0,3,6,9,12 become M. Y at 1,2,4,5,7,8,10,11 remain Y.

Row3: Input Y at positions 1,3,5,7,9,11. Output M at positions 3,9. So Y at 3,9 become M. Y at 1,5,7,11 remain Y.

So pattern: M appears at positions that are multiples of 3? Let's check: positions 0,3,6,9,12 are multiples of 3. Yes. In Row1, Y at positions 0,6,12 are multiples of 3. In Row3, Y at positions 3,9 are multiples of 3. So rule: For each row, Y cells at positions that are multiples of 3 become M. But Row1 has Y at positions 0,2,4,6,8,10,12. Among them, multiples of 3: 0,6,12. Row3 Y at 1,3,5,7,9,11. Multiples of 3: 3,9. So yes.

But we need to confirm with Example 2.

Example 2 Input:
Row1: . Y . Y . Y . Y . Y .
Indices: 0-10? Let's count: . Y . Y . Y . Y . Y . => 11 cells? Actually pattern: . Y . Y . Y . Y . Y . => 11 cells. Let's index 0-10.

Row2: Y Y Y Y Y Y Y Y Y Y Y => 11 cells.

Row3: Y . Y . Y . Y . Y . Y => 11 cells.

Output:
Row1: . Y . M . Y . Y . M .
Row2: M Y Y M Y Y M Y Y M Y
Row3: M . Y . Y . M . Y . Y

Let's analyze.

Row1 Input Y at positions 1,3,5,7,9. Output M at positio

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We need to solve a grid transformation puzzle. We have a metaphorical description: "Three golden threads on a cosmic loom: a solid center thread and two flanking threads that alternate woven/unwoven in opposite pattern. Magenta ichor marks the threads at regular intervals. The center thread is marked most densely; the outer threads receive marks at half the rate, only where thread is present at the right interval."

We have training examples. Let's parse them.

Example 1:

Input:
```
Y . Y . Y . Y . Y . Y . Y
Y Y Y Y Y Y Y Y Y Y Y Y Y
. Y . Y . Y . Y . Y . Y .
```
Output:
```
M . Y . Y . M . Y . Y . M
M Y Y M Y Y M Y Y M Y Y M
. Y . M . Y . Y . M . Y .
```

We need to understand the transformation rule.

We have a 3-row grid. Input uses Y and . (yellow and black). Output uses M (magenta) and Y and . . So transformation: some Y cells become M. The pattern: In the input, the middle row is all Y. The top and bottom rows alternate Y and . starting with Y at first column. So top row: Y . Y . Y . Y . Y . Y . Y (13 columns). Bottom row: . Y . Y . Y . Y . Y . Y . (13 columns). So top row has Y at even columns (0-indexed?), bottom row has Y at odd columns.

Output: Let's examine each row.

Row 0 output: M . Y . Y . M . Y . Y . M
Row 1 output: M Y Y M Y Y M Y Y M Y Y M
Row 2 output: . Y . M . Y . Y . M . Y .

We need to see pattern: In output, some Y cells changed to M. Which ones? Let's compare row by row.

Row 0 input: Y . Y . Y . Y . Y . Y . Y
Output: M . Y . Y . M . Y . Y . M

Positions: 0: Y -> M. 1: . stays . 2: Y stays Y 3: . stays . 4: Y stays Y 5: . stays . 6: Y -> M 7: . stays . 8: Y stays Y 9: . stays . 10: Y stays Y 11: . stays . 12: Y -> M

So in row 0, Y at positions 0,6,12 changed to M. That's every 6 columns? Let's check: positions 0,6,12 difference 6. So pattern: every 6 columns starting at 0. So maybe the rule: In the center row, all Y become M? Wait row 1 output: M Y Y M Y Y M Y Y M Y Y M. Input row 1: Y Y Y Y Y Y Y Y Y Y Y Y Y. Output: M Y Y M Y Y M Y Y M Y Y M. So positions 0,3,6,9,12 changed to M. That's every 3 columns starting at 0. So center row: every 3rd cell becomes M. Row 2 output: . Y . M . Y . Y . M . Y . . Wait row 2 input: . Y . Y . Y . Y . Y . Y . . Wait input row 2: . Y . Y . Y . Y . Y . Y . (13 columns). Output: . Y . M . Y . Y . M . Y . . Wait output row 2: . Y . M . Y . Y . M . Y . . Wait there are 13 columns? Let's count: . Y . M . Y . Y . M . Y . . That's 14? Let's check carefully. The output row 2 in example: ". Y . M . Y . Y . M . Y ." Actually the example shows: ". Y . M . Y . Y . M . Y ." That's 13 columns: positions 0: .; 1: Y; 2: .; 3: M; 4: .; 5: Y; 6: .; 7: Y; 8: .; 9: M; 10: .; 11: Y; 12: . . Wait there is an extra dot at the end? Let's count: 0 ., 1 Y, 2 ., 3 M, 4 ., 5 Y, 6 ., 7 Y, 8 ., 9 M, 10 ., 11 Y, 12 . That's 13 columns. Good.

So row 2: Y at positions 1,5,7,11 changed to M at positions 3,9? Wait Y at positions 1,5,7,11. Output: Y at 1 remains Y; Y at 5 remains Y; Y at 7 remains Y; Y at 11 re

... [8778 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. Let's parse them carefully.

We have a grid transformation puzzle. The input grid is 3 rows. The output grid is also 3 rows. The grid uses characters: '.' for black, Y for yellow, M for magenta, etc. The transformation seems to replace some Y's with M's according to some rule. Let's analyze the training examples.

Example 1:

Input:
Row1: Y . Y . Y . Y . Y . Y . Y
Row2: Y Y Y Y Y Y Y Y Y Y Y Y Y
Row3: . Y . Y . Y . Y . Y . Y .

Output:
Row1: M . Y . Y . M . Y . Y . M
Row2: M Y Y M Y Y M Y Y M Y Y M
Row3: . Y . M . Y . Y . M . Y .

Let's write them in a grid with coordinates. Let's index columns from 0 to maybe 12? Let's count: Row1 has 13 entries: Y . Y . Y . Y . Y . Y . Y. That's 13 columns. Row2 has 13 Y's. Row3 has 13 entries: . Y . Y . Y . Y . Y . Y . That's 13 columns. So grid is 3x13.

Output Row1: M . Y . Y . M . Y . Y . M. That's 13 entries. Row2: M Y Y M Y Y M Y Y M Y Y M. Row3: . Y . M . Y . Y . M . Y . That's 13 entries.

So transformation: Some Y's replaced by M's. Let's mark positions.

Let's index columns 0-12.

Input Row1: col0 Y, col1 ., col2 Y, col3 ., col4 Y, col5 ., col6 Y, col7 ., col8 Y, col9 ., col10 Y, col11 ., col12 Y.

Output Row1: col0 M, col1 ., col2 Y, col3 ., col4 Y, col5 ., col6 M, col7 ., col8 Y, col9 ., col10 Y, col11 ., col12 M.

So Y at col0 replaced by M. Y at col2 remains Y. Y at col4 remains Y. Y at col6 replaced by M. Y at col8 remains Y. Y at col10 remains Y. Y at col12 replaced by M.

So pattern: Y at even columns 0,2,4,6,8,10,12. In output, Y at columns 0,6,12 replaced by M. Y at columns 2,4,8,10 remain Y. So maybe every third Y? Let's check: positions 0,6,12 are multiples of 6? 0,6,12. Yes. So maybe replace Y at columns that are multiples of 6? But 6 is 6, 12 is 12. 0 is 0. So yes, multiples of 6. But we need to check other rows.

Row2 Input: all Y's. Output Row2: M Y Y M Y Y M Y Y M Y Y M. So positions 0,3,6,9,12 replaced by M. So Y at columns 0,3,6,9,12 replaced by M. So pattern: every third column? 0,3,6,9,12. Yes. So for row2, replace Y at columns that are multiples of 3? Actually 0,3,6,9,12 are multiples of 3. So yes.

Row3 Input: . Y . Y . Y . Y . Y . Y . (positions 1,3,5,7,9,11). Output Row3: . Y . M . Y . Y . M . Y . So Y at columns 3 and 9 replaced by M. So Y at columns 3 and 9 replaced. So pattern: Y at columns 3 and 9 replaced. Those are multiples of 3? 3,6,9,12. But 6 is not present because there is no Y at 6. So Y at columns 3 and 9 replaced. So again multiples of 3. So for row3, Y at columns 3 and 9 replaced. So pattern: Y at columns that are multiples of 3? But row1 had Y at columns 0,2,4,6,8,10,12. Among those, multiples of 3 are 0,6,12. So yes, row1 replaced Y at columns 0,6,12. So rule: For each row, replace Y at columns that are multiples of 3? But row1 had Y at columns 0,2,4,6,8,10,12. Among those, multiples of 3: 0,6,12. So replaced. Row2 had Y at all columns 0-12. Multiples of 3: 0,3,6,9,12 replaced. Row3 had Y

... [8898 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "Three lanes of golden runners: a full center lane and two flanking lanes with staggered positions, offset from one another. What to do: A periodic strobe paints certain runners magenta. The center lane catches it most often. The outer lanes catch it at half the frequency, only where runners happen to stand at the right beat. Grid details: Three horizontal rows. Center is solid golden. Outer rows alternate golden and empty in opposite patterns. Magenta replaces some golden cells at regular intervals."

We have training examples. Example 1:

Input:
```
Y . Y . Y . Y . Y . Y . Y
Y Y Y Y Y Y Y Y Y Y Y Y Y
. Y . Y . Y . Y . Y . Y .
```
Output:
```
M . Y . Y . M . Y . Y . M
M Y Y M Y Y M Y Y M Y Y M
. Y . M . Y . Y . M . Y .
```

Test Input:
```
. Y . Y . Y . Y . Y . Y . Y . Y .
Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y
Y . Y . Y . Y . Y . Y . Y . Y . Y
```

We need to produce output grid.

We need to deduce transformation rule.

Let's analyze training example.

Input grid: 3 rows, each row length? Let's count: first row: "Y . Y . Y . Y . Y . Y . Y" that's 13 cells? Let's count: Y(1) space? Actually they separate by spaces. So row: Y . Y . Y . Y . Y . Y . Y. That's 13 cells: Y, ., Y, ., Y, ., Y, ., Y, ., Y, ., Y. So 13 cells.

Second row: Y Y Y Y Y Y Y Y Y Y Y Y Y: 13 Y's.

Third row: . Y . Y . Y . Y . Y . Y . : 13 cells: ., Y, ., Y, ., Y, ., Y, ., Y, ., Y, .? Wait there are 13 cells: ., Y, ., Y, ., Y, ., Y, ., Y, ., Y, .? Actually the pattern: . Y . Y . Y . Y . Y . Y . That's 13 cells: ., Y, ., Y, ., Y, ., Y, ., Y, ., Y, .? Wait we need to count: 1: ., 2: Y, 3: ., 4: Y, 5: ., 6: Y, 7: ., 8: Y, 9: ., 10: Y, 11: ., 12: Y, 13: .? But the pattern shows 13 cells: ., Y, ., Y, ., Y, ., Y, ., Y, ., Y, .? Actually there are 13 cells: ., Y, ., Y, ., Y, ., Y, ., Y, ., Y, .? Wait we need to check: The third row string: ". Y . Y . Y . Y . Y . Y ." That's 13 cells: ., Y, ., Y, ., Y, ., Y, ., Y, ., Y, .? Wait there are 13 cells: 1 ., 2 Y, 3 ., 4 Y, 5 ., 6 Y, 7 ., 8 Y, 9 ., 10 Y, 11 ., 12 Y, 13 .? Actually the pattern ends with a dot. So yes 13 cells.

So grid is 3x13.

Output grid: first row: "M . Y . Y . M . Y . Y . M" That's 13 cells: M, ., Y, ., Y, ., M, ., Y, ., Y, ., M. Wait there are 13 cells: M, ., Y, ., Y, ., M, ., Y, ., Y, ., M? Actually we need to count: 1 M, 2 ., 3 Y, 4 ., 5 Y, 6 ., 7 M, 8 ., 9 Y, 10 ., 11 Y, 12 ., 13 M. Yes.

Second row: "M Y Y M Y Y M Y Y M Y Y M" That's 13 cells: M, Y, Y, M, Y, Y, M, Y, Y, M, Y, Y, M.

Third row: ". Y . M . Y . Y . M . Y ." That's 13 cells: ., Y, ., M, ., Y, ., Y, ., M, ., Y, .? Wait we need to count: 1 ., 2 Y, 3 ., 4 M, 5 ., 6 Y, 7 ., 8 Y, 9 ., 10 M, 11 ., 12 Y, 13 .? Actually the pattern ends with a dot. So yes.

So transformation: In input, we have Y's in all cells except some '.' cells. In output, some Y's replaced by M (magenta). The pattern: In row 1, Y's at positions 1,3,5,7,9,11,13. In output, Y's at positions 3,5,9,11? Wait let's check

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We need to solve a grid transformation puzzle. We have a metaphorical description: "Three rows of golden stage lights: a fully lit center row and two outer rows that alternate on/off in opposite patterns. Magenta gels replace golden lights at periodic intervals. The center row changes most often; the outer rows change at half the rate, only on lamps that are lit at the right cue points."

We have training example 1: Input grid and output grid. We need to deduce transformation rule.

Let's parse the training example.

Input grid:

Row1: "Y . Y . Y . Y . Y . Y . Y" (13 cells? Let's count: Y, ., Y, ., Y, ., Y, ., Y, ., Y, ., Y => 13 cells)
Row2: "Y Y Y Y Y Y Y Y Y Y Y Y Y" (13 Y's)
Row3: ". Y . Y . Y . Y . Y . Y ." (13 cells)

Output grid:

Row1: "M . Y . Y . M . Y . Y . M"
Row2: "M Y Y M Y Y M Y Y M Y Y M"
Row3: ". Y . M . Y . Y . M . Y ."

Let's check lengths: Row1 output: M, ., Y, ., Y, ., M, ., Y, ., Y, ., M => 13 cells. Row2: M, Y, Y, M, Y, Y, M, Y, Y, M, Y, Y, M => 13 cells. Row3: ., Y, ., M, ., Y, ., Y, ., M, ., Y, . => 13 cells.

So transformation: Input had Y's and . (black). Output replaced some Y's with M (magenta). The pattern: In row1, Y's at positions 1,3,5,7,9,11,13. Output: M at positions 1,7,13; Y at positions 3,5,9,11. So pattern: M at positions 1,7,13. Row3: Y's at positions 2,4,6,8,10,12. Output: M at positions 4,10. So pattern: M at positions 4,10. Row2: all Y's at positions 1-13. Output: M at positions 1,4,7,10,13. So pattern: M at positions 1,4,7,10,13.

So we need to deduce rule: maybe periodic intervals: every 6 cells? Let's examine positions: For row2, M at 1,4,7,10,13: difference 3 each time. So M at positions 1 + 3k for k=0..4. For row1, M at 1,7,13: difference 6 then 6. So M at positions 1 + 6k for k=0..2. For row3, M at 4,10: difference 6. So M at positions 4 + 6k for k=0..1.

So pattern: For each row, M at positions that are congruent to some offset modulo 6. Row2 offset 1 mod 3? Wait 1 mod 3? Actually 1,4,7,10,13 difference 3. So offset 1 mod 3. Row1 offset 1 mod 6? Actually 1,7,13 difference 6. So offset 1 mod 6. Row3 offset 4 mod 6? 4,10 difference 6. So offset 4 mod 6.

But maybe the rule: For each row, M at positions that are multiples of 3? Let's check: Row2: positions 1,4,7,10,13: these are 1 mod 3? 1 mod 3: 1,4,7,10,13 indeed. Row1: positions 1,7,13: these are 1 mod 6? But also 1 mod 3? 1 mod 3: 1,4,7,10,13. Row1 positions 1,7,13: 1 mod 3? 1 mod 3: 1,4,7,10,13. Row1 has 1,7,13 which are 1 mod 3 but missing 4,10. So maybe rule: For row1, M at positions that are 1 mod 6? But 1 mod 6: 1,7,13. Yes. Row3: M at 4,10: 4 mod 6. So maybe rule: For each row, M at positions that are 1 mod 6 for center row? Wait center row is row2. Outer rows are row1 and row3. The description: "Three rows of golden stage lights: a fully lit center row and two outer rows that alternate on/off in opposite patterns." So row2 is fully lit (all Y). Row1 and row3 alternate on/off in opposite patterns: row1 has Y at odd positions, ro

... [8722 chars truncated]

We need to solve a grid transformation puzzle. We have training examples. We need to deduce the rule. Let's analyze.

We have a grid of 3 rows. Input and output grids are 3 rows each. The grid cells are either '.' (black) or a color letter: Y, M, etc. The transformation seems to replace some Y cells with M (magenta). The rule: "Magenta dahlias replace golden marigolds at periodic intervals. The center row is replanted most frequently; border rows receive dahlias at half the rate, only where flowers coincide with the longer cycle." So basically we have a pattern of Y cells in the input. The output has some Y cells replaced by M. The pattern: In the center row, all Y cells become M? Let's check.

Example 1:

Input:
Row1: Y . Y . Y . Y . Y . Y . Y
Row2: Y Y Y Y Y Y Y Y Y Y Y Y Y
Row3: . Y . Y . Y . Y . Y . Y .

Output:
Row1: M . Y . Y . M . Y . Y . M
Row2: M Y Y M Y Y M Y Y M Y Y M
Row3: . Y . M . Y . Y . M . Y .

Let's analyze each row.

Row1 input: Y . Y . Y . Y . Y . Y . Y
Indices: 0 1 2 3 4 5 6 7 8 9 10 11 12
Positions with Y: 0,2,4,6,8,10,12. Output row1: M . Y . Y . M . Y . Y . M
Positions: 0 M, 2 Y, 4 Y, 6 M, 8 Y, 10 Y, 12 M. So Y at positions 0,6,12 replaced by M. Y at positions 2,4,8,10 remain Y. So pattern: every 6 cells? Let's check: positions 0,6,12 difference 6. So maybe every 6 cells? But we need to check other rows.

Row2 input: all Y. Output row2: M Y Y M Y Y M Y Y M Y Y M
Indices 0-12. Output: M at 0,3,6,9,12. Y at 1,2,4,5,7,8,10,11. So M at positions 0,3,6,9,12. That's every 3 cells? Actually difference 3. So pattern: every 3 cells. Row3 input: . Y . Y . Y . Y . Y . Y . (positions 1,3,5,7,9,11). Output row3: . Y . M . Y . Y . M . Y . So M at positions 3,9. So pattern: every 6 cells? Actually difference 6. So row3: M at 3,9. So pattern: every 6 cells. Row1: M at 0,6,12. Row3: M at 3,9. Row2: M at 0,3,6,9,12. So row2 has M at every 3 cells. Row1 and Row3 have M at every 6 cells but offset: row1 at 0,6,12; row3 at 3,9. So row1 offset 0, row3 offset 3. So pattern: center row has M at every 3 cells; border rows have M at every 6 cells but offset by 3 relative to each other? Actually row1 offset 0, row3 offset 3. So they alternate.

Now Example 2:

Input:
Row1: . Y . Y . Y . Y . Y .
Row2: Y Y Y Y Y Y Y Y Y Y Y
Row3: Y . Y . Y . Y . Y . Y

Output:
Row1: . Y . M . Y . Y . M .
Row2: M Y Y M Y Y M Y Y M Y
Row3: M . Y . Y . M . Y . Y

Let's analyze.

Row1 input: . Y . Y . Y . Y . Y . (positions 1,3,5,7,9). Output row1: . Y . M . Y . Y . M . (positions 3,9 replaced by M). So M at positions 3,9. So pattern: every 6 cells? Actually difference 6. So row1 M at 3,9. Row3 input: Y . Y . Y . Y . Y . Y (positions 0,2,4,6,8,10). Output row3: M . Y . Y . M . Y . Y. So M at positions 0,6. So pattern: every 6 cells offset by 0. Row2 input: all Y. Output row2: M Y Y M Y Y M Y Y M Y. M at positions 0,3,6,9. So pattern: every 3 cells. So again center row M at every 3 cells. Border rows M at every 6 cells but offset: row1 offset 3, row3 offset 0. So same as e

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We need to solve a grid transformation puzzle. The description: "What you 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. What to 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 details: 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."

We have training example 1:

Input:
```
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
```
Output:
```
B B B B
B M M B
B M M B
B B B B
```

So the input grid is 4x9? Let's parse: The input grid lines:

Line1: B B B B X . . . .  (9 columns)
Line2: B . . B X . M M .  (9 columns)
Line3: B . . B X . M M .  (9 columns)
Line4: B B B B X . . . .  (9 columns)

So 4 rows, 9 columns. The output grid is 4x4: B B B B / B M M B / B M M B / B B B B. So the output is the left side of the input? Actually the left side of the input is 4x4: columns 1-4. The right side of the input is columns 6-9? Wait, the input has a grey wall X at column 5. So the left side is columns 1-4, the right side is columns 6-9. The output is 4x4, which matches the left side. So the transformation seems to be: If the right side (key) matches the left side (lock) in some way, then the left side is replaced by the key's color in the keyhole positions. The keyhole positions are the '.' cells on the left side? Let's examine.

Left side (columns 1-4) of input:

Row1: B B B B
Row2: B . . B
Row3: B . . B
Row4: B B B B

So the left side is a blue square with a 2x2 hole in the middle (positions (2,2),(2,3),(3,2),(3,3) are '.'), representing keyholes. The right side (columns 6-9) of input:

Row1: . . . .
Row2: M M . .
Row3: M M . .
Row4: . . . .

So the right side is a 4x4 grid with a 2x2 block of M's in the top-left corner? Wait, row2 col6-9: M M . . ; row3 col6-9: M M . . ; row1 col6-9: . . . . ; row4 col6-9: . . . . . So the key is a 2x2 block of M's in the top-left corner of the right side. The key is a single color (M). The lock has a 2x2 hole. The key's shape matches the lock's shape? The key's shape is a 2x2 block of M's. The lock's shape is a 2x2 hole. So the key fits into the lock. The rule: If the key shape matches the lock shape exactly (i.e., the positions of non-'.' cells in the key correspond to the positions of '.' cells in the lock), then the lock's '.' cells are replaced by the key's color. The output shows the left side with the '.' replaced b

... [9778 chars truncated]

We need to solve a grid transformation puzzle. The description: "What you see: A blue tissue sample with empty receptor cavities sits beside a colored molecular cluster, separated by a grey membrane wall. What to do: If every colored molecule aligns precisely with every cavity in the tissue, the molecules bind and fill the receptors. If even one molecule has no matching cavity or one cavity has no molecule, the tissue rejects the cluster entirely. Grid details: The left 4x4 region is the tissue; black cells are receptor cavities. The right 4x4 region holds the molecular cluster. The grey column is the membrane. Output is the 4x4 tissue, either filled or unchanged."

We have training examples. Let's parse them.

Example 1 Input:
```
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
```
So it's a 4x4 left side (tissue) and 4x4 right side (molecule cluster). The grey column X is the membrane. The left side is all B except some '.' cells. The right side has '.' and 'M' cells. The output is:
```
B B B B
B M M B
B M M B
B B B B
```
So the output is the left side but with '.' replaced by M where there was M on the right side? Wait, let's analyze.

Left side (tissue) grid (4x4):
Row1: B B B B
Row2: B . . B
Row3: B . . B
Row4: B B B B

Right side (molecule cluster) grid (4x4):
Row1: . . . .
Row2: . M M .
Row3: . M M .
Row4: . . . .

So the right side has M in positions (row2,col2),(row2,col3),(row3,col2),(row3,col3). The left side has '.' in those same positions. The output shows B M M B in rows 2 and 3. So the '.' cells in tissue that correspond to M cells in cluster become M. So the rule: If the cluster has a colored molecule in a position that matches a cavity ('.') in tissue, then the tissue cell becomes that color. But the description says: "If every colored molecule aligns precisely with every cavity in the tissue, the molecules bind and fill the receptors. If even one molecule has no matching cavity or one cavity has no molecule, the tissue rejects the cluster entirely." So we need to check if the cluster's colored cells exactly match the tissue's cavities. That is, the set of positions of '.' in tissue must equal the set of positions of colored cells in cluster. If yes, then fill the tissue with those colors. If not, output unchanged tissue.

In Example 1, the tissue cavities are exactly the positions of M in cluster. So the cluster matches exactly. So we fill tissue with M at those positions. The output shows B M M B in rows 2 and 3. So that matches.

Example 2 Input:
```
B B B B X R R . .
B . . B X R R . .
B . . B X . . . .
B B B B X . . . .
```
Let's parse left side tissue (4x4):
Row1: B B B B
Row2: B . . B
Row3: B . . B
Row4: B B B B

Right side cluster (4x4):
Row1: R R . .
Row2: R R . .
Row3: . . . .
Row4: . . . .

So cluster has R in positions (row1,col1),(row1,col2),(row2,col1),(row2,col2). Tissue has '.' in positions (row2,col2),(row2,col3),(row3,col2),(row3,col3). Wait, tissue '.' positions: row2 col2, row2 col3, row

... [10980 chars truncated]

We need to solve a grid transformation puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid.

Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

## Metaphorical Description

What you see: A blue celestial body with exposed bright patches sits beside a colored shadow pattern, divided by a grey orbital plane.
What to do: If the shadow fills every exposed patch exactly, the color of the shadow replaces the brightness. If alignment is off, the celestial body appears as it was before the transit.
Grid details: Left 4x4 is the body. Right 4x4 is the shadow. Grey column is the orbital divider. Output is 4x4.

Before predicting the output, perform a Conceptual Digestion:
1. Identify the CAST: What roles do different grid elements play?
2. Identify the AFFORDANCES: What can each element do or have done to it?
3. Identify the TRANSFORMATION RULE: What is the precise rule that maps input to output?

Then apply the rule to the test input to predict the output grid.

## Training Examples

Example 1:
Input:
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
Output:
B B B B
B M M B
B M M B
B B B B

Test Input:
B B B B X R . . .
. B B . X R R R R
. B B . X R . . .
. . . . X . . . .

Think step by step. After your reasoning, you MUST write out the complete predicted output grid using these single-character color codes:
Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

At the very end of your response, write the complete output grid inside a clearly labeled block like this:
ANSWER:
... etc"

We need to produce the output grid for the test input. We have one training example. We need to deduce the transformation rule.

Let's parse the training example.

Input grid: 4x4 left side (body) and 4x4 right side (shadow). There is a grey column X dividing them. So the input is 4x4 left, 1 column X, 4x4 right. So total width 9 columns? Actually 4+1+4=9. Height 4 rows.

Input example 1:

Row1: B B B B X . . . .
Row2: B . . B X . M M .
Row3: B . . B X . M M .
Row4: B B B B X . . . .

So left side (body) is 4x4:

Row1: B B B B
Row2: B . . B
Row3: B . . B
Row4: B B B B

Right side (shadow) is 4x4:

Row1: . . . .
Row2: . M M .
Row3: . M M .
Row4: . . . .

Output grid: 4x4:

Row1: B B B B
Row2: B M M B
Row3: B M M B
Row4: B B B B

So transformation: The body is a blue square with a central 2x2 area of '.' (black). The shadow has a 2x2 area of 'M' (magenta) in the same central location. The output replaced the '.' in the body with 'M' from the shadow. The rest of the body remains unchanged. So rule: For each cell in the body that is '.' (black), if the corresponding cell in the shadow is a color (not '.'), then replace the '.' with that color. If the shadow cell is '.' (black), keep the body cell as is. But the description says: "If the shadow fills every

... [12139 chars truncated]

We need to solve a puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid.

Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

## Metaphorical Description

What you see: A blue circuit board with empty sockets sits beside colored components on a grey anti-static mat.
What to do: If every component aligns with a socket and every socket gets a component, the board powers up and the components appear in place. Mismatch means the board stays in its original unpowered state.
Grid details: Left 4x4 is the board. Right 4x4 is the component tray. Grey column is the divider. Output is 4x4.

Before predicting the output, perform a Conceptual Digestion:
1. Identify the CAST: What roles do different grid elements play?
2. Identify the AFFORDANCES: What can each element do or have done to it?
3. Identify the TRANSFORMATION RULE: What is the precise rule that maps input to output?

Then apply the rule to the test input to predict the output grid.

## Training Examples

Example 1:
Input:
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
Output:
B B B B
B M M B
B M M B
B B B B

Example 2:
Input:
B B B B X R R . .
B . . B X R R . .
B . ... etc

We need to analyze the transformation.

We have a 4x4 board on left side, 4x4 component tray on right side, separated by a grey column X. The board is blue (B) and has empty sockets (represented by . maybe). The component tray has colored components (R, M, O, etc). The rule: If every component aligns with a socket and every socket gets a component, the board powers up and the components appear in place. Mismatch means the board stays in its original unpowered state.

So we need to interpret: The board is left 4x4. The component tray is right 4x4. The grey column X is a divider. The output is 4x4. The output likely is the board after powering up: the components from the tray are placed onto the board where there are sockets. But only if the alignment is perfect: each component must align with a socket and each socket must get a component. If not, the board stays unchanged (original board). So the output is either the board with components inserted or the board unchanged.

But we need to examine the training examples to confirm.

Example 1:

Input:
```
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
```
Let's parse: left 4x4 board:

Row1: B B B B
Row2: B . . B
Row3: B . . B
Row4: B B B B

Right 4x4 component tray:

Row1: . . . .
Row2: . M M .
Row3: . M M .
Row4: . . . .

So board has sockets at positions (2,2), (2,3), (3,2), (3,3) (assuming 1-indexed). The component tray has components at same positions: (2,2) M, (2,3) M, (3,2) M, (3,3) M. So each socket gets a component, and each component aligns with a socket. So board powers up: output board should have components placed in those sockets. The output given:

```
B B 

... [10646 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A blue enchanted mask with carved rune-slots faces a set of colored counter-sigils across a grey altar stone. What to do: If every counter-sigil corresponds to a rune-slot and every slot is matched, the sigils fill the mask and transform it. Imperfect alignment leaves the mask cursed and unchanged. Grid details: Left 4x4 is the mask. Right 4x4 is the sigil array. Grey column is the altar. Output is 4x4."

We have training example 1. Input grid: 4x4 left mask, 4x4 right sigil array, grey column between them. The input grid is 4x4 left, then X column, then 4x4 right. The output is 4x4. We need to deduce transformation rule.

Let's parse training example 1.

Input:

```
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
```

So left 4x4 mask:

Row1: B B B B
Row2: B . . B
Row3: B . . B
Row4: B B B B

Right 4x4 sigil array:

Row1: . . . .
Row2: M M . .
Row3: M M . .
Row4: . . . .

Grey column X between them.

Output:

```
B B B B
B M M B
B M M B
B B B B
```

So output mask is same as left mask but with some cells changed: the '.' cells in the mask (positions (2,2),(2,3),(3,2),(3,3)) are replaced by M from the sigil array. The sigil array had M in those positions. So transformation: fill the mask's empty cells with corresponding sigil colors if they match? But we need to check rule: "If every counter-sigil corresponds to a rune-slot and every slot is matched, the sigils fill the mask and transform it. Imperfect alignment leaves the mask cursed and unchanged." So maybe the rule: For each empty cell in mask ('.'), if the corresponding cell in sigil array has a color (not '.'), then fill mask cell with that color. But also maybe need to check that all empty cells are filled? In example, all empty cells were filled. But what if some empty cells remain '.'? Then maybe output unchanged? But we only have one training example.

Let's analyze the test input.

Test Input:

```
B B B B X R . . .
. B B . X R R R R
. B B . X R . . .
. . . . X . . . .
```

So left mask:

Row1: B B B B
Row2: . B B .
Row3: . B B .
Row4: . . . .

Right sigil array:

Row1: R . . .
Row2: R R R R
Row3: R . . .
Row4: . . . .

We need to produce output 4x4.

We need to deduce rule precisely. Let's analyze the metaphor: "blue enchanted mask with carved rune-slots faces a set of colored counter-sigils across a grey altar stone." So left mask is blue (B) with carved rune slots ('.' maybe). Right sigil array is colored counter-sigils (R, M, etc). Grey column is altar. "If every counter-sigil corresponds to a rune-slot and every slot is matched, the sigils fill the mask and transform it. Imperfect alignment leaves the mask cursed and unchanged." So maybe the rule: For each slot in mask ('.'), there must be a corresponding sigil in the same relative position in the sigil array. If all slots are matched (i.e., all '.' in mask have a non-'.' in sigil array), then fill them. If any 

... [11893 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A blue dance formation with open positions faces colored dancers waiting across a grey stage divide. What to do: If every dancer finds an open position and every position has a dancer, partners join and color fills the formation. If not, the original formation holds. Grid details: Left 4x4 is the formation. Right 4x4 is the waiting dancers. Grey column is the divide. Output is 4x4."

We have training example 1: Input grid 8x4? Wait: Input: 
```
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
```
So it's 4 rows, 8 columns. The left 4 columns are formation, right 4 columns are waiting dancers. The grey column is the divide: X column? Actually the X column is the grey column dividing left and right. In the input, we see X at column 5? Wait: The input shows "B B B B X . . . ." So columns: 1-4: B B B B; column 5: X; columns 6-8: . . . .? Wait there are 8 columns: B B B B X . . . . That's 9 tokens? Let's count: B(1) B(2) B(3) B(4) X(5) .(6) .(7) .(8) .(9). Actually there are 9 tokens. But the grid is 4x9? But the description says left 4x4 is formation, right 4x4 is waiting dancers, grey column is divide. So total width 4+1+4=9 columns. Yes, 9 columns. So the grid is 4 rows x 9 columns. The left 4 columns (1-4) are formation, column 5 is X dividing, columns 6-9 are waiting dancers.

In the example, the left formation is all B's in first row, B's in last row, and B's in first column? Wait: Let's parse the input:

Row1: B B B B X . . . .
Row2: B . . B X . M M .
Row3: B . . B X . M M .
Row4: B B B B X . . . .

So left 4 columns: 
Row1: B B B B
Row2: B . . B
Row3: B . . B
Row4: B B B B

So left formation is a blue border: a 4x4 square of B's with interior empty (.). So it's a blue ring.

Right 4 columns: columns 6-9: 
Row1: . . . .
Row2: . M M .
Row3: . M M .
Row4: . . . .

So right side has a 2x2 block of M's in the middle (rows 2-3, columns 7-8). So the waiting dancers are M's.

The output is:
```
B B B B
B M M B
B M M B
B B B B
```
So the output is a 4x4 grid: the left formation but with the interior replaced by M's. So the M's from the right side moved into the interior of the left formation, filling the open positions. The rule: If every dancer finds an open position and every position has a dancer, partners join and color fills the formation. If not, the original formation holds.

So we need to interpret: The left formation is a shape of B's with open positions (.). The right side has some colored dancers (M's). The rule: If the number of dancers equals the number of open positions, and each open position can be matched with a dancer, then the formation is filled with the color of the dancers. But if not, the formation remains unchanged.

In example 1, the left formation had 4x4 border of B's, interior 2x2 open positions (4 open positions). The right side had exactly 4 M's. So the condition is satisfied: each open position gets a d

... [13003 chars truncated]

We need to solve a puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid.

Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

## Metaphorical Description

What you see: A blue rock formation with hollow chambers sits beside a colored magma flow pattern, divided by a grey fault line.
What to do: If every magma channel maps to a chamber and every chamber has a channel, the lava fills the voids with color. Incomplete alignment means the rock stays cool and unchanged.
Grid details: Left 4x4 is the rock. Right 4x4 is the magma map. Grey column is the fault line. Output is 4x4.

Before predicting the output, perform a Conceptual Digestion:
1. Identify the CAST: What roles do different grid elements play?
2. Identify the AFFORDANCES: What can each element do or have done to it?
3. Identify the TRANSFORMATION RULE: What is the precise rule that maps input to output?

Then apply the rule to the test input to predict the output grid.

## Training Examples

Example 1:
Input:
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
Output:
B B B B
B M M B
B M M B
B B B B

Example 2:
Input:
B B B B X R R . .
B . . B X R R . .
B . ... etc.

We need to analyze the transformation rule.

We have a 4x4 left side (rock) and 4x4 right side (magma). The grey column X is the fault line dividing them. The output is 4x4. The rule: "If every magma channel maps to a chamber and every chamber has a channel, the lava fills the voids with color. Incomplete alignment means the rock stays cool and unchanged."

Interpretation: The left side is rock with blue cells B and maybe other colors? The right side is magma flow pattern with colors like M, R, O, etc. The grey column X is a separator. The output is a 4x4 grid that presumably is the rock after lava fills the voids with color. The rule: For each cell in the rock that is a chamber (maybe a hole or empty space?), if there is a corresponding magma channel (color) that maps to that chamber, then the chamber gets filled with that color. But if not all chambers have a magma channel or not all magma channels map to a chamber, then the rock stays unchanged (i.e., output equals input rock). But the examples show that sometimes the output is changed.

Let's analyze the examples carefully.

Example 1:

Input grid (4x4 left, 4x4 right):

Left side (rock):
Row1: B B B B
Row2: B . . B
Row3: B . . B
Row4: B B B B

Right side (magma):
Row1: . . . .
Row2: . M M .
Row3: . M M .
Row4: . . . .

Grey column X is between them.

So the rock has a rectangular cavity in the center: a 2x2 area of '.' (empty). The magma side has a 2x2 area of 'M' in the same positions (rows 2-3, columns 2-3). So the magma channels align with the cavity. The output is:

B B B B
B M M B
B M M B
B B B B

So the cavity cells are filled with M. So the rule: If the magma side has a color in a cell

... [11855 chars truncated]

We need to parse the puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid.

Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

## Metaphorical Description

What you see: A blue pastry mold with hollow spaces sits on one side of a grey countertop divider, and a colored batter shape sits on the other.
What to do: If the batter's shape is a perfect negative of the mold's hollows, pour it in and the color fills the gaps. If the shapes don't match perfectly, the mold remains unfilled.
Grid details: Left 4x4 is the mold (blue = walls, black = hollows). Right 4x4 is the batter (color = batter, black = air). Grey column divides them. Output is 4x4.

Before predicting the output, perform a Conceptual Digestion:
1. Identify the CAST: What roles do different grid elements play?
2. Identify the AFFORDANCES: What can each element do or have done to it?
3. Identify the TRANSFORMATION RULE: What is the precise rule that maps input to output?

Then apply the rule to the test input to predict the output grid.

## Training Examples

Example 1:
Input:
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
Output:
B B B B
B M M B
B M M B
B B B B

Test Input:
B B B B X R . . .
. B B . X R R R R
. B B . X R . . .
. . . . X . . . .

Think step by step. After your reasoning, you MUST write out the complete predicted output grid using these single-character color codes:
Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

At the very end of your response, write the complete output grid inside a clearly labeled block like this:
ANSWER:
... etc"

We need to produce the output grid for the test input.

We have a puzzle: left 4x4 is mold: blue walls, black hollows. Right 4x4 is batter: color cells (like red) and black cells (air). The rule: If the batter's shape is a perfect negative of the mold's hollows, pour it in and the color fills the gaps. If shapes don't match perfectly, the mold remains unfilled.

Interpretation: The mold is a shape of walls (blue) and hollows (black). The batter shape is a shape of color cells (like red) and air (black). The negative of the mold's hollows means that the shape of the color cells in the batter should exactly match the shape of the black cells in the mold, but inverted? Wait, "perfect negative of the mold's hollows" might mean that the shape of the batter's color cells is the complement of the mold's black cells. But the mold's black cells are hollows; the negative of that shape would be the shape of the black cells? Let's parse.

The metaphor: "If the batter's shape is a perfect negative of the mold's hollows, pour it in and the color fills the gaps." So the batter shape is a shape of color cells. The mold's hollows are black cells. The negative of the mold's hollows would be the shape of the black cells? Wait, neg

... [11440 chars truncated]

We need to parse the puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid.

Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

## Metaphorical Description

What you see: A blue musical score with silent rests is separated by a grey bar line from a colored sequence of notes.
What to do: If every colored note corresponds to a rest in the score and every rest has a note, the notes fill the silences. If the correspondence is imperfect, the original score plays as written.
Grid details: Left 4x4 is the score (blue = sustained tones, black = rests). Right 4x4 is the note pattern. Grey column separates them. Output is the 4x4 score.

Before predicting the output, perform a Conceptual Digestion:
1. Identify the CAST: What roles do different grid elements play?
2. Identify the AFFORDANCES: What can each element do or have done to it?
3. Identify the TRANSFORMATION RULE: What is the precise rule that maps input to output?

Then apply the rule to the test input to predict the output grid.

## Training Examples

Example 1:
Input:
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
Output:
B B B B
B M M B
B M M B
B B B B

Test Input:
B B B B X R . . .
. B B . X R R R R
. B B . X R . . .
. . . . X . . . .

Think step by step. After your reasoning, you MUST write out the complete predicted output grid using these single-character color codes:
Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

At the very end of your response, write the complete output grid inside a clearly labeled block like this:
ANSWER:
... etc"

We need to produce the output grid for the test input. Let's analyze the puzzle.

We have a 4x4 left side (score) and 4x4 right side (note pattern). The grey column X separates them. The left side is the "score" with blue B for sustained tones, black . for rests. The right side is a "note pattern" with colored notes (R, M, etc). The rule: "If every colored note corresponds to a rest in the score and every rest has a note, the notes fill the silences. If the correspondence is imperfect, the original score plays as written." So we need to fill the rests (.) in the left side with notes from the right side, but only if there's a perfect correspondence: each colored note corresponds to a rest in the score and every rest has a note. If not, we keep the original score unchanged.

But we need to interpret "corresponds" and "every rest has a note" precisely. Let's examine the training example.

Example 1 Input:

```
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
```

So left side (score) is 4x4:

Row1: B B B B
Row2: B . . B
Row3: B . . B
Row4: B B B B

Right side (note pattern) is 4x4:

Row1: . . . .
Row2: . M M .
Row3: . M M .
Row4: . . . .

So the right side has colored notes M in positions (row2, col2), (row

... [12815 chars truncated]

We need to solve a grid transformation puzzle. The description: "What you see: A blue defensive wall with openings faces a colored attacking squad across a grey midfield line. What to do: If attackers perfectly occupy every gap in the wall, they break through and appear in those positions. If any gap is left unfilled or any attacker has no gap, the wall stands unchanged. Grid details: Left 4x4 is the defensive wall. Right 4x4 is the attacking formation. Grey column is the midfield. Output is the 4x4 wall, breached or intact."

We have training example 1. Input grid: 4x4 left side (wall) and 4x4 right side (attackers). There's a grey column X between them. The input grid is 4 rows, each row has 9 cells: 4 left, 1 X, 4 right. The output grid is 4x4: the wall after transformation.

We need to deduce rule: If attackers perfectly occupy every gap in the wall, they break through and appear in those positions. If any gap is left unfilled or any attacker has no gap, the wall stands unchanged.

Interpretation: The wall is blue cells B. The wall has openings: cells that are not B? In the left 4x4, there are B cells and maybe other colors? In example 1, left side: row1: B B B B; row2: B . . B; row3: B . . B; row4: B B B B. So the wall is a blue border with two openings in the middle (two columns). The right side: row1: . . . .; row2: M M . .; row3: M M . .; row4: . . . .? Wait let's parse example 1 input:

Input:
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .

So each row has 9 cells: left 4, X, right 4. Let's index columns 1-4 left, 5 X, 6-9 right.

Row1: B B B B X . . . . => left: B B B B; right: . . . . (all black? Actually '.' is black). So row1 right side all black.

Row2: B . . B X . M M . => left: B . . B; right: . M M . (positions 6-9). So row2 right side: col6 '.', col7 'M', col8 'M', col9 '.'. So two magenta cells in middle.

Row3: B . . B X . M M . => same as row2.

Row4: B B B B X . . . . => left: B B B B; right: . . . . (all black).

So the right side has magenta cells in rows 2-3, columns 7-8. The left side has openings at columns 2-3 in rows 2-3. So the attackers (magenta) occupy exactly the openings in the wall. So rule: if attackers perfectly occupy every gap in the wall, they break through and appear in those positions. So the output should be the wall with magenta cells in the openings. Indeed output:

B B B B
B M M B
B M M B
B B B B

Yes, the output shows magenta cells in the openings. So rule: if the right side's colored cells exactly match the openings in the left side, then the left side's openings are replaced by those colors. If not, left side remains unchanged.

But we need to consider "If any gap is left unfilled or any attacker has no gap, the wall stands unchanged." So if the right side has some colored cells that don't match openings, or if some openings are not filled, then no change.

We need to apply to test input.

Test Input:
B B B B X R . . .
. B B . X R R R R
. B B . X R . . .
. . . .

... [9202 chars truncated]

We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A blue landscape with patches of dry earth sits beside a colored rain pattern, divided by a grey cloud bank. What to do: If the rain pattern is the exact complement of the dry patches, the rain soaks in and colors the earth. Otherwise the land remains unchanged, as if the storm passed over. Grid details: Left 4x4 is the terrain. Right 4x4 is the rainfall pattern. Grey column is the cloud bank. Output is 4x4 terrain."

We have training example 1: Input grid 8x4? Actually 4x8? Let's parse.

Example 1 Input:
```
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
```
So it's 4 rows, 8 columns. The left 4 columns are the terrain (blue landscape with patches of dry earth). The right 4 columns are rainfall pattern. The middle column is grey cloud bank? Wait, the description says "Grey column is the cloud bank." But in the input, we see "X" in column 5? Actually the input has 8 columns: columns 1-4 are terrain, column 5 is X? Wait, the input shows "B B B B X . . . ." So row 1: B B B B X . . . . That's 9 entries? Let's count: B, B, B, B, X, ., ., ., . That's 9 columns. But the description says 4x4 left, 4x4 right, grey column in between. That would be 4+1+4 = 9 columns. Yes, 9 columns. So the grid is 4 rows, 9 columns. The left 4 columns are terrain, column 5 is X (grey cloud bank), columns 6-9 are rainfall pattern. So the input is 4x9.

The output is 4x4 terrain. The output grid is:

```
B B B B
B M M B
B M M B
B B B B
```

So the transformation: The left 4x4 terrain is updated based on the rainfall pattern. The rainfall pattern is 4x4 (columns 6-9). The grey column is X. The rule: "If the rain pattern is the exact complement of the dry patches, the rain soaks in and colors the earth. Otherwise the land remains unchanged, as if the storm passed over."

We need to interpret "dry patches" and "rain pattern complement." The left terrain has some cells that are not B? In the example, left terrain: row1: B B B B; row2: B . . B; row3: B . . B; row4: B B B B. So the left terrain has B cells (blue) and . cells (black). The right rainfall pattern: row1: . . . .; row2: M M . .; row3: M M . .; row4: . . . .? Wait, let's parse the input again:

Row1: B B B B X . . . . (columns 1-4: B B B B; column5: X; columns6-9: . . . .)
Row2: B . . B X . M M . (columns1-4: B . . B; column5: X; columns6-9: . M M .)
Row3: B . . B X . M M . (same as row2)
Row4: B B B B X . . . . (columns1-4: B B B B; columns6-9: . . . .)

So rainfall pattern: row1: . . . .; row2: . M M .; row3: . M M .; row4: . . . . (4x4). The left terrain: row1: B B B B; row2: B . . B; row3: B . . B; row4: B B B B.

The output: row1: B B B B; row2: B M M B; row3: B M M B; row4: B B B B.

So the output changed the . cells in the left terrain to M where the rainfall pattern had M? Actually the rainfall pattern had M in positions (row2, col7-8) and (row3, col7-8). The left terrain had . at positions 

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We need to solve a puzzle. The description: "You are solving a grid transformation puzzle. You are given a metaphorical description of the transformation, training examples, and a test input grid.

Color key: .=black B=blue R=red G=green Y=yellow X=grey M=magenta O=orange A=azure W=maroon

## Metaphorical Description

What you see: A blue fortress with structural weak points faces a colored siege formation across a grey no-man's-land.
What to do: If every siege weapon aligns with a weak point and every weak point faces a weapon, the walls fall and the color fills the breaches. Misalignment means the fortress stands.
Grid details: Left 4x4 is the fortress. Right 4x4 is the siege. Grey column is the buffer zone. Output is the 4x4 fortress.

Before predicting the output, perform a Conceptual Digestion:
1. Identify the CAST: What roles do different grid elements play?
2. Identify the AFFORDANCES: What can each element do or have done to it?
3. Identify the TRANSFORMATION RULE: What is the precise rule that maps input to output?

Then apply the rule to the test input to predict the output grid.

## Training Examples

Example 1:
Input:
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
Output:
B B B B
B M M B
B M M B
B B B B

Example 2:
Input:
B B B B X R R . .
B . . B X R R . .
B . ... etc.

We need to analyze the transformation rule.

We have a 4x4 fortress on the left side of the grid, a 4x4 siege on the right side, separated by a grey column X. The fortress is blue (B) with structural weak points indicated by '.'? The siege is colored (R, M, O, etc). The rule: "If every siege weapon aligns with a weak point and every weak point faces a weapon, the walls fall and the color fills the breaches. Misalignment means the fortress stands."

Interpretation: The fortress is a 4x4 grid of cells. The siege is a 4x4 grid of cells on the right side. The grey column X is a buffer zone. The fortress cells are either B (blue) or '.' (weak point). The siege cells are colored (R, M, O, etc) or '.' (empty). The rule: For each column (or maybe each row?) we check alignment: If a siege cell (colored) aligns with a weak point ('.') in the fortress, and every weak point faces a siege weapon, then the fortress walls fall and the color fills the breaches. That means the fortress cells that were weak points ('.') become the color of the siege weapon that aligns with them. The fortress cells that were originally B remain B? Or maybe they become the color of the siege weapon if the fortress falls? Let's examine training examples.

Example 1:

Input grid:

Row1: B B B B X . . . .
Row2: B . . B X . M M .
Row3: B . . B X . M M .
Row4: B B B B X . . . .

So left 4x4 fortress:

Row1: B B B B
Row2: B . . B
Row3: B . . B
Row4: B B B B

Right 4x4 siege:

Row1: . . . .
Row2: . M M .
Row3: . M M .
Row4: . . . .

So siege cells: only rows 2-3, columns 2-3 have M. Others are '.'.

Now output:

B B B B
B M M B
B M M B
B B B B

So fortress remains same except the weak p

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We need to parse the puzzle. We have a grid transformation puzzle. The description: "What you see: A blue stage arrangement with empty marks sits beside colored understudies waiting in the wings, separated by a grey curtain. What to do: If every empty mark has a corresponding understudy and every understudy has an empty mark, the understudies take their positions. Otherwise the original arrangement holds. Grid details: Left 4x4 is the stage. Right 4x4 is the wing. Grey column is the curtain. Output is 4x4."

We have training example 1: Input grid 8x4? Wait: The input grid is 4x8? Let's examine.

Example 1 Input:

```
B B B B X . . . .
B . . B X . M M .
B . . B X . M M .
B B B B X . . . .
```

This appears to be 4 rows, each row has 8 columns: 4 left side (stage) + 1 grey column (curtain) + 4 right side (wing). So 4x8 grid. The left 4 columns are stage, right 4 columns wing, middle column is grey curtain (X). Output is 4x4 grid: presumably the stage after transformation.

The rule: "If every empty mark has a corresponding understudy and every understudy has an empty mark, the understudies take their positions. Otherwise the original arrangement holds."

Interpretation: The stage has some empty marks ('.') and some blue marks (B). The wing has some colored understudies (M, etc). The rule: If each empty mark on the stage has a corresponding understudy in the wing, and each understudy has an empty mark, then the understudies take their positions. That means the empty marks on the stage are replaced by the corresponding understudy colors from the wing. The wing empties? Or maybe the wing empties become empty? The output is 4x4 grid: presumably the stage after transformation. The wing is not output. So we only output the stage after transformation.

Thus the rule: For each empty cell '.' on the stage, we need to find a matching understudy in the wing. But what does "corresponding" mean? Possibly the same color? Or maybe each empty mark corresponds to a specific understudy color that matches the color of the empty mark? But empty marks are '.'; they don't have color. So maybe each empty mark corresponds to a specific understudy color that is present in the wing. But there may be multiple empty marks and multiple understudies. The rule says: "If every empty mark has a corresponding understudy and every understudy has an empty mark, the understudies take their positions." So we need a one-to-one mapping between empty marks and understudies. That means the number of empty marks on the stage equals the number of understudies in the wing. And each empty mark is replaced by the color of the corresponding understudy. But we need to decide which understudy goes to which empty mark. Possibly the mapping is by column? Or by row? Or by some pattern? Let's analyze the example.

Example 1 Input:

Row1: B B B B X . . . .
Row2: B . . B X . M M .
Row3: B . . B X . M M .
Row4: B B B B X . . . .

So stage (left 4 columns) is:

Row1: B B B B
Row2: B . . B
Row3: B . . B
Ro

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We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A blue garden bed with patches of tilled soil sits beside colored seeds on a grey potting bench. What to do: If every seed aligns with tilled soil and every plot receives a seed, the garden blooms in color. If the match is imperfect, the bed stays as it was. Grid details: Left 4x4 is the garden bed. Right 4x4 is the seed tray. Grey column is the bench. Output is 4x4."

We have training examples. Let's parse them.

We have a 4x4 left side (garden bed) and a 4x4 right side (seed tray). The middle column is grey X. The input grid is 4x8? Actually 4 rows, 8 columns: left 4 columns, then X column, then right 4 columns. The output is 4x4.

We need to figure out transformation rule.

Let's analyze Example 1.

Example 1 Input:

Row1: B B B B X . . . .
Row2: B . . B X . M M .
Row3: B . . B X . M M .
Row4: B B B B X . . . .

So left 4x4 (garden bed) is:

Row1: B B B B
Row2: B . . B
Row3: B . . B
Row4: B B B B

Right 4x4 (seed tray) is:

Row1: . . . .
Row2: . M M .
Row3: . M M .
Row4: . . . .

So the seed tray has M in positions (row2, col2-3) and (row3, col2-3). The left side has B in all cells except the interior 2x2 (rows2-3, cols2-3) which are '.' (black). So the left side has a 2x2 interior of black cells. The right side has M in that same 2x2 area. So the seeds align with the tilled soil? Wait, the left side interior is black (maybe tilled soil). The right side has seeds M. So seeds align with tilled soil. The rule: If every seed aligns with tilled soil and every plot receives a seed, the garden blooms in color. If the match is imperfect, the bed stays as it was.

So we need to check if the seeds align with the tilled soil and every plot receives a seed. That means: For each cell in the left side that is '.' (tilled soil), there must be a seed in the corresponding cell in the right side. And for each cell in the right side that has a seed, the corresponding left side cell must be '.' (tilled soil). And also every plot receives a seed: meaning all '.' cells in left side must have a seed in right side? Or maybe all cells in left side must be covered by seeds? Let's parse.

In Example 1, left side has 4x4 = 16 cells. The interior 2x2 = 4 cells are '.'; the rest 12 cells are B. Right side has M in the same 2x2 cells, and '.' elsewhere. So the seeds align with tilled soil: yes. And every plot receives a seed: meaning all '.' cells in left side have a seed. Yes. So the transformation: The output is the garden bed with seeds replaced? Let's see output:

Output:
B B B B
B M M B
B M M B
B B B B

So the output is the left side but with the interior '.' replaced by M (the seed color). So basically, if the seeds align with tilled soil and every plot receives a seed, then the garden bed is updated: the '.' cells become the seed color. The rest remains B. So the output is left side with '.' replaced by seed color.

Now Example 2.

Input:

Row1: B B B B X R R . .
Row2: 

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We need to solve a grid transformation puzzle. The description: "What you see: A still lake at night (the black expanse) reflects scattered stars (grey cells). Some stars hang in pairs across the water's center line — each one gazing at its twin on the opposite shore. Other stars shine alone, with no reflection to answer them. What to do: When a star finds its twin reflected perfectly across the lake's center, both ignite with blue fire — recognized, validated, made luminous by their symmetry. Stars that peer into the water and see only darkness remain dim and grey, forever unreflected."

So we have a 10x10 grid. The input grid has '.' for black, 'X' for grey stars. The output grid has '.' for black, 'X' for grey stars that remain unpaired, and 'B' for blue stars that are paired. The transformation: For each grey cell (X) in the input, check if there is another grey cell at the symmetric position across the center line. The center line is the vertical line between columns 4 and 5? Wait, the grid is 10 columns. The center line is between columns 4 and 5? Actually, the center line is the vertical line that splits the grid into left and right halves. For a 10x10 grid, the center line is between columns 4 and 5? Let's index columns 0-9. The center line is between columns 4 and 5 (i.e., between the 5th and 6th columns). So the reflection across the center line would map column c to column 9 - c? Wait, if we reflect across the center line, the mapping is: column 0 <-> column 9, column 1 <-> column 8, column 2 <-> column 7, column 3 <-> column 6, column 4 <-> column 5. So yes, mapping c to 9 - c. Similarly, for rows? The description says "across the water's center line" - maybe it's vertical reflection only. The examples show that only horizontal reflection across the vertical center line is considered. Let's confirm with examples.

Example 1: Input grid 10x10. Let's analyze a few positions. Input row 1: ". . . . . X . . . ." (row index 0). There's an X at column 5? Wait, row 0: ". . . . . X . . . ." So X at column 5 (0-index). The output row 0: ". . . . . X . . . ." unchanged. So X at column 5 remains X. But if we reflect across center line, column 5 maps to column 4? Wait, mapping c to 9 - c: 5 -> 4. So the symmetric position of (0,5) is (0,4). In input, at (0,4) there is '.' (black). So no pair. So X remains X. Good.

Now check row 1: Input row 1: ". X . . . . . . X X". So X at col 1, col 8, col 9. Output row 1: ". B . . . . . . B X". So X at col 1 becomes B. X at col 8 becomes B. X at col 9 remains X. Let's check: For X at col 1, symmetric col is 8. There is X at col 8. So pair. So both become B. For X at col 8, symmetric col is 1, also X. So B. For X at col 9, symmetric col is 0. Input at (1,0) is '.' so no pair. So remains X. Good.

Row 2: Input: ". . . X X X X . . ." (col 3,4,5,6). Output: ". . . B B B B . . ." So all X become B. Let's check: For X at col 3, symmetric col 6. Input at (2,6) is X. So pai

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We need to parse the puzzle. The description: "Two kingdoms sit on opposite sides of a golden bridge. The northern kingdom flies blue banners from some of its towers, while the southern kingdom lights red fires atop others. The darkness between them marks empty watchtowers where no one stands guard. What to do: The golden bridge opens and the two kingdoms merge their defenses. Any watchtower that had a blue banner flying OR a red fire burning sends a soldier to the unified army, marked in green. Only towers that were dark and abandoned in BOTH kingdoms remain empty in the new realm. Grid details: The world is a tall fortress split by a golden bridge spanning the full width. Above and below the bridge lie matching castle walls. The united army's banner—green against the darkness—flies only where at least one kingdom once kept watch."

So we have a grid transformation puzzle. The input grid has some colors: B, R, Y, ., etc. The output grid has G's and .s. The rule: For each cell, if either the cell in the northern part (above the bridge) or the southern part (below the bridge) had a B or R (blue or red), then output G. If both were empty (.), then output . (empty). But we need to confirm with training example.

Let's analyze Example 1.

Input grid: Provided as 10 rows? Let's parse.

Example 1 Input:
```
B B . .
B . B .
B B . B
B B B B
Y Y Y Y
R R . R
. . R .
. R . .
R . R .
```
Output:
```
G G . G
G . G .
G G . G
G G G G
```

Wait: The output grid is 4 rows? Actually output shows 4 rows of 4 columns each. But input grid is 10 rows of 4 columns each. So the transformation reduces the grid size? Let's examine.

Input grid: 10 rows, 4 columns. Output grid: 4 rows, 4 columns. So maybe the transformation merges the top 5 rows (northern kingdom) and bottom 5 rows (southern kingdom) into a single 4x4 grid? But 5+5=10 rows. But output has 4 rows. So maybe the golden bridge splits the grid into two halves: top half (rows 1-5) and bottom half (rows 6-10). Then we combine them by some rule: For each column, we combine the two halves? But output has 4 columns, same as input. So maybe we combine each column pair? Wait.

Let's analyze the input grid more carefully. The input grid has 10 rows, 4 columns. The first 5 rows (rows 1-5) are the northern kingdom? Actually the description says "Two kingdoms sit on opposite sides of a golden bridge." So the grid is split by a golden bridge spanning the full width. The golden bridge is maybe a row of Y's? In the input, row 5 is "Y Y Y Y". That might represent the golden bridge. So the top part (rows 1-4) is the northern kingdom, the bottom part (rows 6-10) is the southern kingdom. The golden bridge row (row 5) is Y Y Y Y. So the grid is 10 rows: 4 rows above the bridge, 1 row of Y's (bridge), 5 rows below the bridge. But the output grid is 4 rows. So maybe we ignore the bridge row and combine the two halves into a single grid of 4 rows? But we have 4 rows above the bridge and 5 rows below. So maybe we combine 

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We need to solve a grid transformation puzzle. We have a metaphorical description: "two-chambered petri dish divided by a golden membrane. The upper culture shows cold-pigment colonies; the lower shows warm-pigment colonies. Empty sites are sterile. Fuse the two cultures through the membrane. Any site where at least one chamber harbored a living colony blooms into a hybrid organism of a novel hue. Sterile sites remain barren. Grid details: Output is a single 4×4 dish. Hybrid colonies appear where either parent culture was active. Empty where both were sterile."

We have training examples. Example 1: Input: a 8x? Wait, the input grid appears to be 8 rows? Let's parse.

Example 1 Input:
```
B B . .
B . B .
B B . B
B B B B
Y Y Y Y
R R . R
. . R .
. R . .
R . R .
```
Wait, that's 9 rows? Let's count: 1: B B . . ; 2: B . B . ; 3: B B . B ; 4: B B B B ; 5: Y Y Y Y ; 6: R R . R ; 7: . . R . ; 8: . R . . ; 9: R . R . . Wait, the last row has 5 entries? Actually "R . R ." is 4 entries. Let's re-evaluate: The input lines:

1. B B . .
2. B . B .
3. B B . B
4. B B B B
5. Y Y Y Y
6. R R . R
7. . . R .
8. . R . .
9. R . R .

But the last line "R . R ." has 4 entries. So we have 9 rows of 4 columns each. So the input is 9x4 grid. The output is 4x4 grid:

Output:
```
G G . G
G . G .
G G . G
G G G G
```

So the transformation: The input is 9x4 grid. The output is 4x4 grid. The description says: "Output is a single 4×4 dish. Hybrid colonies appear where either parent culture was active. Empty where both were sterile." So we need to combine two cultures: upper culture (cold-pigment colonies) and lower culture (warm-pigment colonies). The input grid is 9x4. The first 4 rows maybe represent the upper culture? Wait, the input has 9 rows. The description says "two-chambered petri dish divided by a golden membrane." So maybe the input grid is 9 rows: the top 4 rows are the upper culture, the bottom 4 rows are the lower culture, and the middle row is the membrane? But we have 9 rows: 4 + 1 + 4 = 9. Yes, that fits: 4 rows of upper culture, 1 row of membrane (maybe golden?), 4 rows of lower culture. But the input lines: 1-4: B B . . ; B . B . ; B B . B ; B B B B. That's 4 rows. Then row 5: Y Y Y Y. That might be the membrane? But Y Y Y Y is all Y's. But the description says "golden membrane" maybe Y stands for yellow? Yes Y=yellow. So the membrane row is Y Y Y Y. Then rows 6-9: R R . R ; . . R . ; . R . . ; R . R . . Wait, row 9 has 5 entries? Let's check again: The input lines after Y Y Y Y: "R R . R" (4 entries), ". . R ." (4 entries), ". R . ." (4 entries), "R . R ." (4 entries). So 4 rows of lower culture. So the input is 4 rows upper, 1 row membrane, 4 rows lower. So the output is 4x4 grid. The rule: "Any site where at least one chamber harbored a living colony blooms into a hybrid organism of a novel hue. Sterile sites remain barren." So we need to combine the upper and lower cultures: For each column and row index, we need to check if either the upper or l

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We need to solve a grid transformation puzzle. We have a metaphorical description: "What you see: A starfield bisected by a golden band. Above: patches of cool nebular gas. Below: patches of hot nebular gas. The rest is void. What to do: Collapse both nebulae through the band. Any region containing gas from either nebula ignites into a newborn star. Void remains only where both sides were empty."

We have a 4x4 star chart with newborn stars where either nebula contributed matter.

We have training examples. Example 1: Input grid is 10x? Wait, let's parse.

Example 1 Input:
```
B B . .
B . B .
B B . B
B B B B
Y Y Y Y
R R . R
. . R .
. R . .
R . R .
```
Output:
```
G G . G
G . G .
G G . G
G G G G
```

So input grid is 10 rows? Let's count: lines: 1: B B . . ; 2: B . B . ; 3: B B . B ; 4: B B B B ; 5: Y Y Y Y ; 6: R R . R ; 7: . . R . ; 8: . R . . ; 9: R . R . . Wait line 9: "R . R ." ; 10: ??? Actually the input shows 9 lines? Let's recount: Provided input lines:

1. B B . .
2. B . B .
3. B B . B
4. B B B B
5. Y Y Y Y
6. R R . R
7. . . R .
8. . R . .
9. R . R .

That's 9 lines. But output is 4x4 grid. So maybe the input is 9x4? Wait each line has 4 columns. So input is 9 rows x 4 columns. Output is 4 rows x 4 columns. So transformation reduces rows from 9 to 4. The description: "A 4×4 star chart with newborn stars where either nebula contributed matter." So output is 4x4. Input is 9x4. So we need to map 9x4 to 4x4. The transformation rule: "Collapse both nebulae through the band. Any region containing gas from either nebula ignites into a newborn star. Void remains only where both sides were empty." So we have a band dividing the grid horizontally? The input has 9 rows. The band might be at row 5? Because we have 4 rows above (rows 1-4) and 4 rows below (rows 6-9). Row 5 is the band? Let's check: Row 5 is "Y Y Y Y". That might be the golden band. So the band is row 5. The rows above (1-4) are "cool nebular gas" (blue?). The rows below (6-9) are "hot nebular gas" (red?). The rest is void. The input uses B for blue, R for red, Y for golden band, . for void. So the rule: For each column, we collapse the two nebulae through the band: we look at each column, we consider the cells above the band (rows 1-4) and below the band (rows 6-9). For each column, if either side has a gas cell (B or R) in that column, then the output cell is a star (green). If both sides are empty (.), then output is empty. The output grid is 4x4. But we need to map 9 rows to 4 rows. How to map? The output grid is 4x4. The input has 4 rows above band and 4 rows below band. So maybe we collapse each column into a single cell? But output is 4x4, not 4x1. Wait, we need to produce 4x4 grid. So maybe we collapse each column into a 4x4 grid by mapping each of the 4 rows above to 4 rows in output? Let's analyze.

Input: 9 rows x 4 columns. Output: 4 rows x 4 columns. So we collapsed 9 rows into 4 rows. The band row (row 5) is removed. The 4 rows above and 4 rows below are collapsed i

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