003 • Response

puzzle_id:: 6-0520fde7
description:: example_3
timestamp:: 24.329.071439
call_count:: 3
model:: models/gemini-exp-1114

Observations of Example 3

In this example, the input grid continues the pattern of being a 3x7 rectangle with a central column of 5s (gray) and a mix of 1s (blue) and 0s (white). The output grid is again a 3x3 square with two 2s (red) and the rest 0s (white).

The key difference seems to be the placement of the 2s (red) in the output grid, which appears to be influenced by the arrangement of 1s (blue) adjacent to the central 5s (gray) column in the input grid. In this example, the 2s (red) are in the first column, second row, and the third column, third row of the output grid, suggesting a specific pattern of detecting 1s (blue) adjacent to the 5s (gray) in the input grid.

It appears the hypothesis from Example 2 might be correct: the 2s (red) appear in the output based on whether there is a 1 (blue) adjacent to the 5s (gray) in the input. However, the exact rule needs further refinement.

input:
  width: 7
  height: 3
  colors:
    - 0: 11
    - 1: 7
    - 5: 3
  objects:
    - central column of 5 (gray)
    - scattered 1 (blue)
    - background of 0 (white)

output:
  width: 3
  height: 3
  colors:
    - 0: 7
    - 2: 2
  objects:
    - two 2 (red) in specific locations
    - background of 0 (white)

differences:
  cells_changed: 19
  colors_changed: gray (5) to red (2), blue (1) to white (0)
transformation:
  - Reduce size from 3x7 to 3x3.
  - Analyze adjacent cells (horizontally) to the central 5s.
  - If a cell to the left of 5 is 1, the corresponding cell in the output is 2.
  - If a cell to the right of 5 is 1, the corresponding cell in the output is 2.
  - Fill remaining cells with 0 (white).

Code Execution

code_execution:

import numpy as np

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

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

# Get input grid properties
input_height, input_width = input_grid.shape
input_colors, input_color_counts = np.unique(input_grid, return_counts=True)
input_color_map = dict(zip(input_colors, input_color_counts))

# Get output grid properties
output_height, output_width = output_grid.shape
output_colors, output_color_counts = np.unique(output_grid, return_counts=True)
output_color_map = dict(zip(output_colors, output_color_counts))

print("Input Grid Properties:")
print("Width:", input_width)
print("Height:", input_height)
print("Color Map:", input_color_map)
print("\nOutput Grid Properties:")
print("Width:", output_width)
print("Height:", output_height)
print("Color Map:", output_color_map)

print("\nChanges:")
print("Size change:", f"{input_height}x{input_width} to {output_height}x{output_width}")
print("Color changes:")
for color in input_colors:
    if color not in output_colors:
        print(f"  {color} removed")
for color in output_colors:
    if color not in input_colors:
        print(f"  {color} added")

code_execution_result: 1

Input Grid Properties:
Width: 7
Height: 3
Color Map: {np.int64(0): np.int64(11), np.int64(1): np.int64(7), np.int64(5): np.int64(3)}

Output Grid Properties:
Width: 3
Height: 3
Color Map: {np.int64(0): np.int64(7), np.int64(2): np.int64(2)}

Changes:
Size change: 3x7 to 3x3
Color changes:
  1 removed
  5 removed
  2 added

Analysis of Code Execution Results

The code execution confirms the observations about the size and color changes. The input grid has dimensions 3x7, and the output grid has dimensions 3x3. The colors in the input grid are 0 (white), 1 (blue), and 5 (gray), while the colors in the output grid are 0 (white) and 2 (red).

The changes are:

Size reduction from 3x7 to 3x3.
Color 1 (blue) is removed.
Color 5 (gray) is removed.
Color 2 (red) is added.

Natural Language Program

The transformation still involves reducing the grid size to 3x3. Based on the observations and the results from the previous examples, the refined hypothesis is that if a cell immediately to the left of the central 5s (gray) column in the input grid is 1 (blue), the corresponding cell in the output grid becomes 2 (red).

Transform the input grid by reducing its size to a 3x3 grid. Analyze the cells immediately to the left of the central column of 5s (gray). If a cell to the left of 5 (gray) is 1 (blue), change the corresponding cell in the 3x3 output grid to 2 (red). Fill all other cells in the 3x3 grid with 0 (white).

time
response time	total elapsed
48.156	137.491

usage
token type	call count	total used
Prompt	6063	12261
Response	1471	3100
Total	7534	15361
Cached	0	0