003 • History

puzzle_id:

1-3aa6fb7a

description:

example_summary

timestamp:

24.329.064813

call_count:

3

Begin puzzle: 1-3aa6fb7a

example_1

input

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

output

[[0 0 0 0 0 0 0]
 [0 8 1 0 0 0 0]
 [0 8 8 0 0 0 0]
 [0 0 0 0 8 8 0]
 [0 0 0 0 1 8 0]
 [0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0]]

images

../../../../_images/000-example_1_input.png ../../../../_images/000-example_1_output.png

observations

The input grid shows a cluster of azure (8) pixels. The output grid is identical except one azure pixel has changed to blue (1). The blue pixel is adjacent to, and below, a cluster of azure pixels.

code_execution:

import numpy as np

input_grid = np.array([[0, 0, 0, 0, 0, 0, 0],
                      [0, 8, 0, 0, 0, 0, 0],
                      [0, 8, 8, 0, 0, 0, 0],
                      [0, 0, 0, 0, 8, 8, 0],
                      [0, 0, 0, 0, 0, 8, 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, 8, 1, 0, 0, 0, 0],
                       [0, 8, 8, 0, 0, 0, 0],
                       [0, 0, 0, 0, 8, 8, 0],
                       [0, 0, 0, 0, 1, 8, 0],
                       [0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0]])

diff = np.where(input_grid != output_grid)
print(f"Differences found at coordinates: {diff}")
print(f"Input grid shape: {input_grid.shape}")
print(f"Number of azure pixels in input: {np.count_nonzero(input_grid == 8)}")
print(f"Number of blue pixels in output: {np.count_nonzero(output_grid == 1)}")

code_execution_result: 1

Differences found at coordinates: (array([1, 4]), array([2, 4]))
Input grid shape: (7, 7)
Number of azure pixels in input: 6
Number of blue pixels in output: 2

input:
  width: 7
  height: 7
  colors:
    - 0: 43
    - 8: 6
  objects:
    - size: 6, position: scattered, color: azure

output:
  width: 7
  height: 7
  colors:
    - 0: 43
    - 8: 4
    - 1: 2
  objects:
    - size: 4, position: scattered, color: azure
    - size: 2, position: scattered, color: blue

differences:
  cells_changed: 2
  colors_changed: Two azure pixels changed to blue.  The blue pixels are adjacent to the remaining cluster of azure pixels.
transformation:
  - A subset of azure pixels change to blue.  Specifically, azure pixels adjacent to other azure pixels are transformed.  The transformation might depend on the location and size of the cluster.

Based on the analysis, a possible natural language program for the transformation is: “Identify clusters of azure pixels. Change one azure pixel in each cluster to blue, selecting a pixel adjacent to other azure pixels within the cluster. If there’s only one azure pixel, leave it unchanged.” This needs further validation with more examples.

example_2

input

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

output

[[0 0 0 0 8 8 0]
 [0 0 0 0 1 8 0]
 [0 0 8 1 0 0 0]
 [0 0 8 8 0 0 0]
 [0 0 0 0 0 0 0]
 [0 0 0 1 8 0 0]
 [0 0 0 8 8 0 0]]

images

../../../../_images/001-example_2_input.png ../../../../_images/001-example_2_output.png

observations

The input grid for example 2 shows several clusters of azure (8) pixels. The output grid is almost identical, but several azure pixels have been replaced with blue (1) pixels. Each blue pixel appears adjacent to, and below or to the left of, a remaining azure pixel within the same cluster.

code_execution:

import numpy as np

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

output_grid = np.array([[0, 0, 0, 0, 8, 8, 0],
                       [0, 0, 0, 0, 1, 8, 0],
                       [0, 0, 8, 1, 0, 0, 0],
                       [0, 0, 8, 8, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 1, 8, 0, 0],
                       [0, 0, 0, 8, 8, 0, 0]])

diff = np.where(input_grid != output_grid)
print(f"Differences found at coordinates: {diff}")
print(f"Input grid shape: {input_grid.shape}")
print(f"Number of azure pixels in input: {np.count_nonzero(input_grid == 8)}}")
print(f"Number of blue pixels in output: {np.count_nonzero(output_grid == 1)}")

code_execution_result:

Differences found at coordinates: (array([1, 2, 5]), array([4, 3, 3]))
Input grid shape: (7, 7)
Number of azure pixels in input: 10
Number of blue pixels in output: 3

input:
  width: 7
  height: 7
  colors:
    - 0: 40
    - 8: 10
  objects:
    - size: 10, position: scattered, color: azure

output:
  width: 7
  height: 7
  colors:
    - 0: 40
    - 8: 7
    - 1: 3
  objects:
    - size: 7, position: scattered, color: azure
    - size: 3, position: scattered, color: blue

differences:
  cells_changed: 3
  colors_changed: Three azure pixels changed to blue. Each blue pixel is below or to the left of a cluster of azure pixels.
transformation:
  -  Similar to example 1, a subset of azure pixels changes to blue.  The transformation seems to target azure pixels that are adjacent to other azure pixels, but the selection is more complex and might be based on the overall cluster's shape.

Based on the two examples, the transformation appears to select a subset of azure pixels within each cluster to change to blue. The selection criteria seem to favor pixels adjacent to other azure pixels, and potentially also considers positional relationships within the cluster (below or to the left). More examples would help refine the natural language program and clarify any ambiguities in the selection process.

examples summary

INSTRUCTIONS:

  • summarize your observations to explain the transformation of the input to output

  • use code_execution to investigate properties, patterns and differences in the grids

See also