003 • Response

puzzle_id:: 2-0ca9ddb6
description:: example_3
timestamp:: 24.356.195518
call_count:: 3
model:: gemini-2.0-flash-thinking-exp-1219

The user has provided a new example pair. I need to analyze it and formulate a natural language program describing the transformation.

Input Grid Analysis:

The input grid is 9x9.
It contains white (0), red (2), magenta (6), and blue (1) pixels.
There is a single red pixel, a single magenta pixel, and a single blue pixel.

Output Grid Analysis:

The output grid is also 9x9.
It contains white (0), red (2), magenta (6), blue (1), yellow (4), and orange (7) pixels.
The red, magenta, and blue pixels remain in their original positions.
Yellow pixels appear around the red pixel.
Orange pixels appear around the blue pixel.
No new colors appear around the magenta pixel.

Transformation Hypothesis: The transformation seems to apply to red and blue pixels only. The surrounding white pixels change color based on the central pixel’s color.

Let’s analyze the example in detail.

The input grid has a single red pixel at (2, 2), a single magenta pixel at (5, 6), and a single blue pixel at (7, 3).

The output grid shows the original colored pixels unchanged. Around the red pixel at (2, 2), adjacent white pixels have become yellow. Around the blue pixel at (7, 3), adjacent white pixels have become orange. The area around the magenta pixel remains unchanged.

Review Example

example_1

input

[[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 6 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]]

output

[[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 0 0 0]
 [0 0 0 0 0 0 6 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]]

images

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, 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, 6, 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]])

output_grid = np.array([[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, 0, 0, 0],
                        [0, 0, 0, 0, 0, 0, 6, 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]])

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)

Observations:

The input grid is a 9x9 grid with a white background. There is a single red pixel at (2, 2), a single magenta pixel at (5, 6), and a single blue pixel at (7, 3).

The output grid is also a 9x9 grid. The red, magenta, and blue pixels remain in their original positions. The white pixels immediately surrounding the red pixel have changed to yellow. The white pixels immediately surrounding the blue pixel have changed to orange. The white pixels surrounding the magenta pixel remain white.

input:
  width: 9
  height: 9
  colors:
    0: 86
    2: 1
    6: 1
    1: 1
  objects:
    - color: red
      position: (2, 2)
    - color: magenta
      position: (5, 6)
    - color: blue
      position: (7, 3)

output:
  width: 9
  height: 9
  colors:
    0: 74
    2: 1
    6: 1
    1: 1
    4: 4
    7: 3
  objects:
    - color: red
      position: (2, 2)
    - color: magenta
      position: (5, 6)
    - color: blue
      position: (7, 3)
    - color: yellow
      positions: [(1, 1), (1, 3), (3, 1), (3, 3)]
    - color: orange
      positions: [(6, 3), (7, 2), (7, 4), (8, 3)]

differences:
  cells_changed: 7
  colors_changed: white to yellow around red, white to orange around blue
  transformation:
    - Identify single red pixel and change adjacent whites to yellow.
    - Identify single blue pixel and change adjacent whites to orange.
    - Magenta pixels do not cause adjacent white pixels to change.

Natural Language Program:

The input grid is a 9x9 grid with single red, magenta, 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 magenta pixel does not cause any changes to the surrounding white pixels.
The remaining pixels stay the same.

time
response time	total elapsed
16.13	68.542

usage
token type	call count	total used
Prompt	11599	20095
Response	1965	8850
Total	13564	28945
Cached	0	0