001 • Response

puzzle_id:: 2-0ca9ddb6
description:: example_1
timestamp:: 24.357.081407
call_count:: 1
model:: gemini-2.0-flash-thinking-exp-1219

The user wants me to analyze an input-output pair of grids from an ARC task and derive a natural language program that describes the transformation from input to output.

I need to:

Describe the input and output grids.
Use code to analyze the grids, focusing on color counts, changed pixels, and object properties.
Formulate a hypothesis about the transformation rule.
Express the transformation rule as a natural language program.

Example 1 Analysis:

Input grid: 9x9, mostly white (0) with a single red (2) pixel and a single blue (1) pixel. Output grid: 9x9, the red pixel remains, the blue pixel remains, and new yellow (4) and orange (7) pixels have appeared around them.

Let’s analyze the changes:

The red pixel at (3, 2) remains at (3, 2).
The blue pixel at (6, 6) remains at (6, 6).
Yellow pixels appear at (2, 1), (2, 3), (4, 1), (4, 3). These are adjacent (horizontally and vertically) to the red pixel.
Orange pixels appear at (5, 6), (6, 5), (6, 7), (7, 6). These are adjacent (horizontally and vertically) to the blue pixel.

It seems like the transformation involves identifying non-white pixels and adding adjacent pixels of specific colors based on the original color.

Okay, I will analyze the provided input and output grids for example_1.

The input grid is a 9x9 grid that is mostly white. There is a single red pixel and a single blue pixel. The red pixel is located in the fourth row, third column (using 0-based indexing, so at coordinates (3, 2)). The blue pixel is located in the seventh row, seventh column (at coordinates (6, 6)).

The output grid is also a 9x9 grid. The red and blue pixels remain in their original positions. New pixels of yellow and orange have appeared around the red and blue pixels respectively. Around the red pixel, yellow pixels have appeared in the cells directly adjacent (horizontally and vertically). Around the blue pixel, orange pixels have appeared in the cells directly adjacent (horizontally and vertically).

import numpy as np

input_grid = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 2, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 1, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 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],
                        [0, 4, 0, 4, 0, 0, 0, 0, 0],
                        [0, 0, 2, 0, 0, 0, 0, 0, 0],
                        [0, 4, 0, 4, 0, 0, 0, 0, 0],
                        [0, 0, 0, 0, 0, 0, 7, 0, 0],
                        [0, 0, 0, 0, 0, 7, 1, 7, 0],
                        [0, 0, 0, 0, 0, 0, 7, 0, 0],
                        [0, 0, 0, 0, 0, 0, 0, 0, 0]])

input_colors, input_counts = np.unique(input_grid, return_counts=True)
output_colors, output_counts = np.unique(output_grid, return_counts=True)

print("Input grid dimensions:", input_grid.shape)
print("Output grid dimensions:", output_grid.shape)
print("Input color counts:", dict(zip(input_colors, input_counts)))
print("Output color counts:", dict(zip(output_colors, output_counts)))

changed_pixels = np.where(input_grid != output_grid)
print("Indices of changed pixels:", list(zip(changed_pixels[0], changed_pixels[1])))

input:
  width: 9
  height: 9
  colors:
    0: 79
    1: 1
    2: 1
  objects:
    - color: red
      position: (3, 2)
    - color: blue
      position: (6, 6)

differences:
  cells_changed: 8
  colors_changed:
    - white to yellow around red
    - white to orange around blue
  transformation:
    - for each non-white pixel in the input, add adjacent pixels of a specific color in the output.
    - the color to add depends on the color of the original pixel.

Natural Language Program:

The input grid is a 9x9 grid. Identify all non-white pixels in the input grid.

For each red pixel found in the input grid:

Locate the position of the red pixel.
In the output grid, fill the cells directly adjacent (up, down, left, right) to the original red pixel with yellow. The original red pixel remains red in the output.

For each blue pixel found in the input grid:

Locate the position of the blue pixel.
In the output grid, fill the cells directly adjacent (up, down, left, right) to the original blue pixel with orange. The original blue pixel remains blue in the output.

Initialize the output grid as a copy of the input grid. Iterate through each cell in the input grid. If a cell is red, change its adjacent white cells in the output grid to yellow. If a cell is blue, change its adjacent white cells in the output grid to orange. The color palette consists of white, blue, red, yellow, and orange.

Okay, proceed to the next example.

time
response time	total elapsed
12.76	12.865

usage
token type	call count	total used
Prompt	2444	2444
Response	1598	1598
Total	4042	4042
Cached	0	0