005 • Response

puzzle_id:: 3-1e0a9b12
description:: test input
timestamp:: 24.357.081407
call_count:: 5
model:: gemini-2.0-flash-thinking-exp-1219

The user wants me to apply the derived natural language program to the test input grid to generate the output grid. The program states that non-white pixels should “fall down” to the bottom of their respective columns.

Plan:

Initialize an empty output grid of the same dimensions as the input grid.
Iterate through each column of the input grid.
For each column, identify the non-white pixels and their order.
Place these non-white pixels in the corresponding column of the output grid, starting from the bottom row.

Input Grid Analysis:

[[0 2 0 4 3]
 [5 0 0 0 0]
 [0 0 6 0 0]
 [5 2 0 4 0]
 [5 0 0 0 0]]

Column 0: Gray (5), Gray (5), Gray (5)
Column 1: Red (2), Red (2)
Column 2: Magenta (6)
Column 3: Yellow (4), Yellow (4)
Column 4: Green (3)

Output Grid Generation:

[[0 0 0 0 0]
 [0 0 0 0 0]
 [5 2 0 0 0]
 [5 2 6 4 3]
 [5 0 0 4 0]]

Let’s double check the placement.

Column 0: The three gray (5) pixels from the input should be in the bottom three cells of the output column 0.
Column 1: The two red (2) pixels from the input should be in the bottom two cells of the output column 1.
Column 2: The magenta (6) pixel should be in the bottom cell of output column 2.
Column 3: The two yellow (4) pixels should be in the bottom two cells of output column 3.
Column 4: The green (3) pixel should be in the bottom cell of output column 4.

Revised Output Grid:

[[0 0 0 0 0]
 [0 0 0 0 0]
 [5 2 0 0 0]
 [5 2 6 4 0]
 [5 0 0 4 3]]

There was an error in the manual placement in column 4.

Let’s use code to generate and verify.

import numpy as np

input_grid = np.array([[0, 2, 0, 4, 3],
                       [5, 0, 0, 0, 0],
                       [0, 0, 6, 0, 0],
                       [5, 2, 0, 4, 0],
                       [5, 0, 0, 0, 0]])

output_grid = np.zeros_like(input_grid)
height, width = input_grid.shape

for col in range(width):
    non_white_pixels = [input_grid[row, col] for row in range(height) if input_grid[row, col] != 0]
    num_non_white = len(non_white_pixels)
    for i in range(num_non_white):
        output_grid[height - num_non_white + i, col] = non_white_pixels[i]

print(output_grid.tolist())

time
response time	total elapsed
7.068	57.39

usage
token type	call count	total used
Prompt	9717	30787
Response	821	7118
Total	10538	37905
Cached	0	0