001 • Response

puzzle_id:: 2-0ca9ddb6
description:: example_1
timestamp:: 24.356.195518
call_count:: 1
model:: gemini-2.0-flash-thinking-exp-1219

The user wants me to analyze the first example pair of an ARC task. I need to describe the input and output grids, use code to extract relevant information, and then formulate a natural language program explaining the transformation.

Input Grid Analysis:

The input grid is 9x9.
It contains white (0), red (2), and blue (1) pixels.
There is a single red pixel and a single blue pixel.

Output Grid Analysis:

The output grid is also 9x9.
It contains white (0), red (2), blue (1), yellow (4), and orange (7) pixels.
The red and blue pixels remain in their original positions.
Yellow pixels appear around the red pixel.
Orange pixels appear around the blue pixel.

Transformation Hypothesis: It seems like the colors around the single colored pixels are changed based on the color of the central pixel.

Okay, let’s analyze the first example.

The input grid is a 9x9 grid with mostly white pixels. There is a single red pixel located at (3, 2) (row index, column index) and a single blue pixel located at (6, 6).

The output grid is also a 9x9 grid. The red pixel remains at (3, 2) and the blue pixel remains at (6, 6). Surrounding the red pixel, the adjacent white pixels (horizontally, vertically, and diagonally) have become yellow. Surrounding the blue pixel, the adjacent white pixels have become orange.

import numpy as np
from collections import Counter

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

print("Input Color Counts:", input_colors)
print("Output Color Counts:", output_colors)

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

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

output:
  width: 9
  height: 9
  colors:
    0: 69
    1: 1
    2: 1
    4: 4
    7: 3
  objects:
    - color: red
      position: (3, 2)
    - color: blue
      position: (6, 6)
    - color: yellow
      positions: [(2, 1), (2, 3), (4, 1), (4, 3)]
    - color: orange
      positions: [(5, 6), (6, 5), (6, 7), (7, 6)]

differences:
  cells_changed: 10
  colors_changed: white to yellow around red, white to orange around blue
  transformation:
    - Identify single red pixel.
    - Change adjacent white pixels to yellow.
    - Identify single blue pixel.
    - Change adjacent white pixels to orange.

Natural Language Program:

The input grid is a 9x9 grid containing single isolated red and blue pixels on a white background.

To create the output grid:

Start with the input grid.
Locate the single red pixel.
Change the color of the immediately adjacent white pixels (horizontally, vertically, and diagonally) to yellow.
Locate the single blue pixel.
Change the color of the immediately adjacent white pixels (horizontally, vertically, and diagonally) to orange.
The remaining pixels stay the same.

Review Example Phase

example_2

input

[[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 0 0 0 8 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 5 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 0 0 0]]

output

[[0 0 0 0 0 0 8 0 0]
 [0 0 0 0 0 8 8 8 0]
 [0 0 0 0 0 0 8 0 0]
 [0 0 5 0 0 0 0 0 0]
 [0 6 5 6 0 0 0 0 0]
 [0 0 5 0 0 0 0 0 0]
 [0 6 0 6 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]]

images

time
response time	total elapsed
14.678	14.772

usage
token type	call count	total used
Prompt	2895	2895
Response	1795	1795
Total	4690	4690
Cached	0	0