003 • History

puzzle_id:: 6-0520fde7
description:: example_3
timestamp:: 24.329.064813
call_count:: 3

Begin puzzle: 6-0520fde7

example_1

input

[[1 0 0 5 0 1 0]
 [0 1 0 5 1 1 1]
 [1 0 0 5 0 0 0]]

output

[[0 0 0]
 [0 2 0]
 [0 0 0]]

images

observations

The input grid is a 3x7 grid containing blue (1), white (0), and gray (5) pixels. The gray pixels form a vertical line in the center. The blue pixels are clustered around the gray line.

The output grid is a 3x3 grid. It contains only white (0) and red (2) pixels. A single red pixel is located in the center.

code_execution:

import numpy as np

input_grid = np.array([[1, 0, 0, 5, 0, 1, 0],
                      [0, 1, 0, 5, 1, 1, 1],
                      [1, 0, 0, 5, 0, 0, 0]])

output_grid = np.array([[0, 0, 0],
                       [0, 2, 0],
                       [0, 0, 0]])

print("Input Grid Shape:", input_grid.shape)
print("Output Grid Shape:", output_grid.shape)

print("\nInput Grid Color Counts:")
for color, count in np.nditer(np.unique(input_grid, return_counts=True)):
    print(f"{color}: {count}")

print("\nOutput Grid Color Counts:")
for color, count in np.nditer(np.unique(output_grid, return_counts=True)):
    print(f"{color}: {count}")

code_execution_result: 1

Input Grid Shape: (3, 7)
Output Grid Shape: (3, 3)

Input Grid Color Counts:
0: 11
1: 7
5: 3

Output Grid Color Counts:
0: 8
2: 1

input:
  width: 7
  height: 3
  colors:
    - 0: 11
    - 1: 7
    - 5: 3
  objects:
    - size: 3x1, position: center, color: gray
    - size: various, position: around central gray line, color: blue

output:
  width: 3
  height: 3
  colors:
    - 0: 8
    - 2: 1
  objects:
    - size: 1x1, position: center, color: red

differences:
  cells_changed: 9
  colors_changed: Gray and blue pixels are replaced by white and one red pixel in the center.
transformation:
  - The input grid is reduced in size.
  - The central gray column is replaced with a single red pixel in the center of the output grid.
  - All other pixels are replaced with white.

The transformation appears to involve a reduction in size, focusing on the central column of the input grid. The central gray column is transformed into a single red pixel in the center of the smaller output grid. All other pixels become white. A possible natural language program could be: “Reduce the grid size, replace the central column with a red pixel, and fill the rest with white”.

example_2

input

[[1 1 0 5 0 1 0]
 [0 0 1 5 1 1 1]
 [1 1 0 5 0 1 0]]

output

[[0 2 0]
 [0 0 2]
 [0 2 0]]

images

observations

Example 2 Analysis

The input grid is a 3x7 grid consisting of blue (1), white (0), and gray (5) pixels. The gray pixels again form a vertical central line, with blue pixels clustered around it, similar to Example 1.

The output grid is a 3x3 grid. It contains white (0) and red (2) pixels. Three red pixels are arranged in an L-shape pattern.

code_execution:

import numpy as np

input_grid = np.array([[1, 1, 0, 5, 0, 1, 0],
                      [0, 0, 1, 5, 1, 1, 1],
                      [1, 1, 0, 5, 0, 1, 0]])

output_grid = np.array([[0, 2, 0],
                       [0, 0, 2],
                       [0, 2, 0]])

print("Input Grid Shape:", input_grid.shape)
print("Output Grid Shape:", output_grid.shape)

print("\nInput Grid Color Counts:")
for color, count in np.nditer(np.unique(input_grid, return_counts=True)):
    print(f"{color}: {count}")

print("\nOutput Grid Color Counts:")
for color, count in np.nditer(np.unique(output_grid, return_counts=True)):
    print(f"{color}: {count}")

code_execution_result: 1

Input Grid Shape: (3, 7)
Output Grid Shape: (3, 3)

Input Grid Color Counts:
0: 8
1: 10
5: 3

Output Grid Color Counts:
0: 6
2: 3

input:
  width: 7
  height: 3
  colors:
    - 0: 8
    - 1: 10
    - 5: 3
  objects:
    - size: 3x1, position: center, color: gray
    - size: various, position: around central gray line, color: blue

output:
  width: 3
  height: 3
  colors:
    - 0: 6
    - 2: 3
  objects:
    - size: 3x1, position: L-shape around center, color: red

differences:
  cells_changed: 9
  colors_changed: Gray and blue pixels are replaced by white and red pixels forming an L shape.
transformation:
  - The input grid is reduced in size.
  - The gray column is replaced, and some nearby pixels are changed to red pixels forming an L shape.
  - The remaining pixels are set to white.

The transformation in this example is similar to the first, with grid size reduction. However, instead of a single central red pixel, we see three red pixels forming an “L” shape. The positions of the red pixels seem related to the positions of the blue and gray pixels in the input. A more refined natural language program might be: “Reduce the grid size; replace the central gray column and some adjacent pixels with red pixels forming an ‘L’ shape; fill the rest with white.”

example_3

input

[[0 0 1 5 0 0 0]
 [1 1 0 5 1 0 1]
 [0 1 1 5 1 0 1]]

output

[[0 0 0]
 [2 0 0]
 [0 0 2]]

images

observations

INSTRUCTIONS:

Review Examples Phase

pairs of input and output grids will be shown to you one at a time

you will examine and analyze the text and image for each example

you may use code execution with tools like numpy to examine patterns after examining the grids, document the attributes of each as such

use a yaml block for the details

input:
width: X
height: Y
colors:
  - N: (count)
objects:
  - size, position and color - desc

output:
width: X
height: Y
colors:
  - N: (count)
objects:
  - size, position and color - desc

differences:
cells_changed: N
colors_changed: desc
transformation:
  - speculate on transformation rules

your response for this phase should contain the following content parts

begin with a verbal description of your perception of the input and output grid
run a code_execution part to test your perceptions - since the code you use may not be carried forward on following prompts, be sure to have the code print you findings in the output remember that you have access to many python libraries for analyzing the grids and validating patterns
review your findings and try to determine what the natural language program is for the transformation