002 • Response

puzzle_id:: 3-1e0a9b12
description:: example_2
timestamp:: 24.329.071439
call_count:: 2
model:: models/gemini-exp-1114

OK. Let’s analyze example 2 of puzzle 3-1e0a9b12.

Perception

The input grid is a 6x6 grid with several non-zero values: 9 (maroon), 8 (azure), 4 (yellow), and 7 (orange). The yellow (4) and orange (7) appear multiple times. Most of the cells are white (0).

The output grid is also 6x6. The upper part of the grid (rows 1 to 3) is completely white (0). The non-zero values from the input grid are present in the output grid, but their positions have changed. Some values remain in their original positions, while others have moved to the bottom row.

Specifically, it looks like the values from the bottom row in the input are moved to the bottom row of the output in a specific order. The non-zero values in the last row come first, followed by non-zero values from preceding rows, in a bottom-to-top fashion, skipping already-occupied columns.

Code Execution

code_execution:

import numpy as np

input_grid = np.array([[0, 0, 0, 0, 0, 9], [0, 0, 0, 8, 0, 0], [0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0], [4, 0, 7, 8, 0, 0], [4, 0, 7, 0, 0, 0]])
output_grid = np.array([[0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0], [4, 0, 7, 8, 0, 0], [4, 0, 7, 8, 0, 9]])

input_non_zeros = input_grid[input_grid != 0]
output_non_zeros = output_grid[output_grid != 0]

print("Non-zero values in input:", input_non_zeros)
print("Non-zero values in output:", output_non_zeros)
print("Are non-zero values the same and in the same order?", np.array_equal(input_non_zeros, output_non_zeros))

code_execution_result: 1

Non-zero values in input: [9 8 4 4 7 8 4 7]
Non-zero values in output: [4 4 7 8 4 7 8 9]
Are non-zero values the same and in the same order? False

Review of Findings

The code execution confirms that the non-zero values in the input and output are the same, but their order is different. Let’s analyze the specific rearrangement:

In the input grid, the non-zero values are: 9, 8, 4, 4, 7, 8, 4, 7 (reading top-to-bottom, left-to-right). In the output grid, the non-zero values are: 4, 4, 7, 8, 4, 7, 8, 9.

Following the pattern identified in the first example, let’s examine the order in the output:

Start with the last row of the input: 4, 0, 7, 0, 0, 0. This gives us 4 and 7 in columns 0 and 2, respectively.
Move to the second-to-last row: 4, 0, 7, 8, 0, 0. We have 4, 7, and 8. 4 is in column 0 (already occupied), 7 is in column 2 (already occupied), so we take 8.
Move to the fourth row: 4, 0, 0, 0, 0, 0. We have 4 in column 0 (already occupied).
Move to the third row: All zeros.
Move to the second row: 0, 0, 0, 8, 0, 0. We have 8 in column 3.
Move to the first row: 0, 0, 0, 0, 0, 9. We have 9 in column 5.

The order in the output is 4, 7, 8, 4, 7, 8, 9. This matches my observation from the previous example.

Natural Language Program

Identify Non-Zero Cells: Find all non-zero cells in the input grid.
Rearrange Non-Zero Cells: Rearrange the non-zero cells according to the following logic:
- Start with the non-zero value(s) from the last row, placed in the last row of the output grid, left-to-right.
- Place the non-zero values from the preceding rows, in order from bottom-to-top, skipping columns already occupied.
Place in Output Grid: Place the rearranged non-zero values in the bottom row of the output grid, maintaining their order.
Fill with Zeros: Fill the rest of the output grid with zeros (white).

Let’s express this transformation in a YAML format:

input:
  width: 6
  height: 6
  colors:
    0: 28  # white
    4: 3   # yellow
    7: 2   # orange
    8: 2   # azure
    9: 1   # maroon
  objects:
    - single cells with values 4, 7, 8, 9
output:
  width: 6
  height: 6
  colors:
    0: 28  # white
    4: 3   # yellow
    7: 2   # orange
    8: 2   # azure
    9: 1   # maroon
  objects:
    - single cells with values 4, 4, 7, 8, 4, 7, 8, 9 in the last row
differences:
  cells_changed: 8
  colors_changed: no new colors, positions changed
transformation:
  - gather all non-zero cells
  - rearrange non-zero cells starting from the last row, then preceding rows, skipping occupied columns
  - place rearranged cells in the last row of the output grid, left-to-right
  - fill remaining cells with 0 (white)

time
response time	total elapsed
70.861	115.591

usage
token type	call count	total used
Prompt	4042	6230
Response	884	1543
Total	4926	7773
Cached	0	0