003 • Response

puzzle_id:: 3-1e0a9b12
description:: example_3
timestamp:: 24.329.071439
call_count:: 3
model:: models/gemini-exp-1114

OK, let’s analyze example 3 of puzzle 3-1e0a9b12.

Perception

The input grid is a 5x5 grid with several non-zero values: 1 (blue), 3 (green), 2 (red), and 6 (magenta). The value 3 (green) appears three times, and the value 1 (blue) appears twice. Most of the cells are white (0).

The output grid is also 5x5. The top two rows are 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.

As observed in the previous examples, the values from the input grid appear to be collected and moved to the bottom row of the output grid in a specific order: values from the last row come first, followed by values from preceding rows, skipping columns already occupied.

Code Execution

code_execution:

import numpy as np

input_grid = np.array([[0, 0, 0, 1, 0], [0, 3, 0, 0, 0], [0, 3, 0, 1, 2], [6, 0, 0, 0, 0], [0, 3, 0, 0, 0]])
output_grid = np.array([[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 3, 0, 0, 0], [0, 3, 0, 1, 0], [6, 3, 0, 1, 2]])

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: [1 3 3 1 2 6 3]
Non-zero values in output: [3 3 3 1 1 6 2]
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: 1, 3, 3, 1, 2, 6, 3 (reading top-to-bottom, left-to-right). In the output grid, the non-zero values are: 3, 3, 3, 1, 1, 6, 2.

Following the pattern identified in the previous examples:

Start with the last row of the input: 0, 3, 0, 0, 0. We have 3 in column 1.
Move to the second-to-last row: 6, 0, 0, 0, 0. We have 6 in column 0.
Move to the third row: 0, 3, 0, 1, 2. We have 3 in column 1 (occupied), 1 in column 3, and 2 in column 4.
Move to the second row: 0, 3, 0, 0, 0. We have 3 in column 1 (occupied), so we skip it.
Move to the first row: 0, 0, 0, 1, 0. We have 1 in column 3 (occupied), so we skip it.

The order in the output is 3, 6, 3, 1, 2, skipping duplicate columns as we move through the rows from bottom to top.

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: 5
  height: 5
  colors:
    0: 18  # white
    1: 2   # blue
    2: 1   # red
    3: 3   # green
    6: 1   # magenta
  objects:
    - single cells with values 1, 3, 2, 6
output:
  width: 5
  height: 5
  colors:
    0: 18  # white
    1: 2   # blue
    2: 1   # red
    3: 3   # green
    6: 1   # magenta
  objects:
    - single cells with values 3, 6, 3, 1, 2 in the last row
differences:
  cells_changed: 7
  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
44.669	160.343

usage
token type	call count	total used
Prompt	6252	12482
Response	1394	2937
Total	7646	15419
Cached	0	0