004 • History

puzzle_id:: 3-1e0a9b12
description:: example_summary
timestamp:: 24.329.071439
call_count:: 4

Begin puzzle: 3-1e0a9b12

example_1

input

[[0 4 0 9]
 [0 0 0 0]
 [0 4 6 0]
 [1 0 0 0]]

output

[[0 0 0 0]
 [0 0 0 0]
 [0 4 0 0]
 [1 4 6 9]]

images

observations

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)

example_2

input

[[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

[[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]]

images

observations

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)

example_3

input

[[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

[[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]]

images

observations

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)

examples summary

INSTRUCTIONS:

summarize your observations to explain the transformation of the input to output
use code_execution to investigate properties, patterns and differences in the grids