001 • Response

puzzle_id:: 3-1e0a9b12
description:: example_1
timestamp:: 24.329.071439
call_count:: 1
model:: models/gemini-exp-1114

OK. Let’s start with example 1 of puzzle 3-1e0a9b12.

Perception

The input grid is a 4x4 grid with four non-zero values: 4 (yellow), 9 (maroon), 6 (magenta), and 1 (blue). The yellow (4) appears twice. Most of the cells are white (0).

The output grid is also 4x4. All the non-zero values from the input grid are present in the output grid, but their positions have changed. Specifically, they have moved to the bottom row while maintaining their left-to-right order. The rest of the cells are white (0).

It appears that the non-zero values from the input grid are collected and moved to the bottom row of the output grid, maintaining their order.

Code Execution

code_execution:

import numpy as np

input_grid = np.array([[0, 4, 0, 9], [0, 0, 0, 0], [0, 4, 6, 0], [1, 0, 0, 0]])
output_grid = np.array([[0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 0, 0], [1, 4, 6, 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: [4 9 4 6 1]
Non-zero values in output: [4 1 4 6 9]
Are non-zero values the same and in the same order? False

Review of Findings

The code execution shows that my initial perception was incorrect. The non-zero values in the input and output are the same, but their order is different. Let me take a closer look.

In the input grid, the non-zero values are: 4, 9, 4, 6, 1 (reading top-to-bottom, left-to-right). In the output grid, the non-zero values are: 4, 4, 6, 1, 9.

It seems that the values in the output are rearranged. Specifically, the values from the last row (1, 0, 0, 0) come first, followed by the values from the third row that are not in the same column as the last row’s non-zero value, then the values from the first row that are not in the same columns as the non-zero values already placed.

I need to revise my understanding of the transformation.

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: 4
  height: 4
  colors:
    0: 12  # white
    1: 1   # blue
    4: 2   # yellow
    6: 1   # magenta
    9: 1   # maroon
  objects:
    - single cells with values 1, 4, 6, 9
output:
  width: 4
  height: 4
  colors:
    0: 12  # white
    1: 1   # blue
    4: 2   # yellow
    6: 1   # magenta
    9: 1   # maroon
  objects:
    - single cells with values 1, 4, 4, 6, 9 in the last row
differences:
  cells_changed: 5
  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
44.571	44.628

usage
token type	call count	total used
Prompt	2188	2188
Response	659	659
Total	2847	2847
Cached	0	0