002 • Response

puzzle_id:: 3-1e0a9b12
description:: example_2
timestamp:: 24.357.081407
call_count:: 2
model:: gemini-2.0-flash-thinking-exp-1219

The user wants me to analyze the second example pair of the ARC task 3-1e0a9b12 and formulate a natural language program describing the transformation.

Plan:

Describe the input and output grids visually.
Use code to analyze the grids, focusing on color counts, changed pixels, and object properties.
Formulate a natural language program based on the analysis.
Capture the analysis and program in YAML blocks.

Example 2 Input Grid: The input grid is 6x6. It contains white, maroon, azure, yellow, and orange pixels. There’s a vertical stack of three yellow pixels on the left side. A maroon pixel is in the top right corner. Two azure pixels are present, one above the other. Two orange pixels are stacked vertically in the lower left quadrant.

Example 2 Output Grid: The output grid is also 6x6. The three yellow pixels remain in the same position. The two orange pixels remain in the same position. The azure pixels appear to have moved to the bottom row. The maroon pixel has also moved to the bottom row.

Hypothesis: It appears that all the non-yellow and non-orange single-pixel objects are moved to the last row, maintaining their relative column order.

Let’s use code to verify this.

observations

The input grid is a 6x6 grid. It features white (0), maroon (9), azure (8), yellow (4), and orange (7) pixels. There appears to be a vertical line of three yellow pixels on the left edge. An isolated maroon pixel is located in the top right corner. Two azure pixels form a vertical line in the upper middle section. Two orange pixels are stacked vertically in the lower left quadrant.

The output grid is also a 6x6 grid with the same color palette. The three yellow pixels on the left remain in their original positions. The two orange pixels also appear to be in the same positions as the input. The azure and maroon pixels seem to have moved to the bottom row.

import numpy as np
from collections import Counter

input_grid = np.array([[0, 0, 0, 0, 0, 9],
                       [0, 0, 0, 8, 0, 0],
                       [0, 0, 0, 0, 0, 0],
                       [4, 0, 0, 0, 0, 0],
                       [4, 0, 7, 8, 0, 0],
                       [4, 0, 7, 0, 0, 0]])

output_grid = np.array([[0, 0, 0, 0, 0, 0],
                        [0, 0, 0, 0, 0, 0],
                        [0, 0, 0, 0, 0, 0],
                        [4, 0, 0, 0, 0, 0],
                        [4, 0, 7, 8, 0, 0],
                        [4, 0, 7, 8, 0, 9]])

input_colors = Counter(input_grid.flatten())
output_colors = Counter(output_grid.flatten())

print("Input Grid:")
print(input_grid)
print("\nOutput Grid:")
print(output_grid)

print("\nInput Color Counts:")
print(input_colors)
print("\nOutput Color Counts:")
print(output_colors)

input_width = input_grid.shape[1]
input_height = input_grid.shape[0]
output_width = output_grid.shape[1]
output_height = output_grid.shape[0]

print(f"\nInput Grid Dimensions: {input_width}x{input_height}")
print(f"Output Grid Dimensions: {output_width}x{output_height}")

changed_pixels = []
for y in range(input_height):
    for x in range(input_width):
        if input_grid[y, x] != output_grid[y, x]:
            changed_pixels.append(((y, x), input_grid[y, x], output_grid[y, x]))

print("\nChanged Pixels ( (row, col), old_color, new_color ):")
for pixel in changed_pixels:
    print(f"  {pixel}")

input:
  width: 6
  height: 6
  colors:
    0: 27
    9: 1
    8: 2
    4: 3
    7: 2
  objects:
    - size: 3, positions: [(3, 0), (4, 0), (5, 0)], color: yellow # Vertical line
    - size: 1, position: (0, 5), color: maroon
    - size: 1, position: (1, 3), color: azure
    - size: 1, position: (4, 3), color: azure
    - size: 1, position: (4, 2), color: orange
    - size: 1, position: (5, 2), color: orange

output:
  width: 6
  height: 6
  colors:
    0: 27
    9: 1
    8: 2
    4: 3
    7: 2
  objects:
    - size: 3, positions: [(3, 0), (4, 0), (5, 0)], color: yellow # Vertical line
    - size: 1, position: (5, 5), color: maroon
    - size: 1, position: (5, 3), color: azure
    - size: 1, position: (4, 3), color: azure
    - size: 1, position: (4, 2), color: orange
    - size: 1, position: (5, 2), color: orange

differences:
  cells_changed: 4
  colors_changed:
    - maroon: moved from (0, 5) to (5, 5)
    - azure: moved from (1, 3) to (5, 3)
    - white: changed to white at (0, 5), (1, 3)
    - white: changed from white at (5, 5), (5, 3)
  transformation:
    - Non-white pixels that are not part of the contiguous yellow or orange blocks appear to have moved to the bottom row.
    - The order of these moved pixels in the bottom row corresponds to their column position in the input.

Natural Language Program:

Context: The input is a 6x6 grid containing pixels of white, maroon, azure, yellow, and orange. There is a vertical line of three yellow pixels on the left edge and a vertical line of two orange pixels in the lower left. Other non-white pixels appear as single, disconnected objects.

Process:

Initialize an empty output grid of the same dimensions as the input grid, filled with white pixels.
Identify the contiguous blocks of yellow and orange pixels in the input grid. Copy these blocks directly to the same positions in the output grid.
Identify all remaining non-white, single-pixel objects in the input grid, along with their colors and column positions.
Place these remaining non-white pixels in the last row of the output grid, maintaining their relative order based on their original column position in the input. The leftmost of these pixels in the input (smallest column index) should be placed in the leftmost available empty (white) cell in the last row of the output, and so on.
Any remaining cells in the output grid will remain white.

time
response time	total elapsed
14.39	24.417

usage
token type	call count	total used
Prompt	4138	6305
Response	1768	3022
Total	5906	9327
Cached	0	0