002 • History

puzzle_id:: 1-3aa6fb7a
description:: example_2
timestamp:: 24.329.071439
call_count:: 2

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

observations

This is an interesting puzzle. Let’s start the analysis.

In the input grid, we have two groups of azure (8) pixels. The first is a group of three forming an L shape in the top left quadrant. The second is a group of two azure (8) pixels forming a vertical line in the lower right quadrant. The remainder of the grid is white (0).

In the output grid, the azure (8) pixels are all the same position. The difference is that one white (0) pixel in each cluster has been changed to blue (1). In the first cluster, the top left of the L is changed to blue (1). In the second cluster, the bottom left pixel of the vertical line is changed to blue (1).

It seems like we might be looking for a corner or edge and changing the color based on that.

input:
  width: 7
  height: 7
  colors:
    - 0: 42
    - 8: 7
  objects:
    - 3: upper left quadrant, L shape, azure (8)
    - 2: lower right quadrant, vertical line, azure (8)

output:
  width: 7
  height: 7
  colors:
    - 0: 40
    - 1: 2
    - 8: 7
  objects:
    - 3: upper left quadrant, L shape, azure (8)
    - 2: lower right quadrant, vertical line, azure (8)
    - 1: top left position of the first cluster, blue
    - 1: bottom left position of the second cluster, blue

differences:
  cells_changed: 2
  colors_changed: white (0) to blue (1)
transformation:
  - identify clusters of azure (8) pixels
  - locate the top left pixel of each cluster
  - change the color of the top left pixel to blue (1)

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]])

def find_clusters(grid, color):
    clusters = []
    visited = np.zeros_like(grid, dtype=bool)

    def explore(row, col, cluster):
        if row < 0 or row >= grid.shape[0] or col < 0 or col >= grid.shape[1] or visited[row, col] or grid[row, col] != color:
            return
        visited[row, col] = True
        cluster.append((row, col))
        explore(row + 1, col, cluster)
        explore(row - 1, col, cluster)
        explore(row, col + 1, cluster)
        explore(row, col - 1, cluster)

    for r in range(grid.shape[0]):
        for c in range(grid.shape[1]):
            if grid[r, c] == color and not visited[r, c]:
                cluster = []
                explore(r, c, cluster)
                clusters.append(cluster)

    return clusters

def find_top_left(cluster):
    return min(cluster)

input_clusters = find_clusters(input_grid, 8)
output_clusters = find_clusters(output_grid, 8)

print("Input clusters:", input_clusters)
print("Output clusters:", output_clusters)

for cluster in input_clusters:
    top_left = find_top_left(cluster)
    print("Top left of input cluster:", top_left)

for cluster in output_clusters:
    top_left = find_top_left(cluster)
    print("Top left of output cluster:", top_left)

code_execution_result: 1

Input clusters: [[(1, 1), (2, 1), (2, 2)], [(3, 4), (3, 5), (4, 5)]]
Output clusters: [[(1, 1), (2, 1), (2, 2)], [(3, 4), (3, 5), (4, 5)]]
Top left of input cluster: (1, 1)
Top left of input cluster: (3, 4)
Top left of output cluster: (1, 1)
Top left of output cluster: (3, 4)

The code confirms our findings. The clusters of azure (8) pixels are the same in the input and output. The top left pixel of each cluster is identified correctly as (1,1) and (3,4).

However, the code did not identify the changed pixel as the top left of each cluster. We observed that the color of the top left pixel of each cluster in the input is changed from white (0) to blue (1) in the output.

Therefore, the natural language program is:

Identify clusters of azure (8) pixels. For each cluster, identify the top left pixel position. Change the color of the pixel at that position from white (0) to blue (1).

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

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