006 • History

puzzle_id:

4-0d3d703e

description:

test input

timestamp:

24.329.071439

call_count:

6

Begin puzzle: 4-0d3d703e

example_1

input

[[3 1 2]
 [3 1 2]
 [3 1 2]]

output

[[4 5 6]
 [4 5 6]
 [4 5 6]]

images

../../../../_images/000-example_1_input9.png ../../../../_images/000-example_1_output9.png

observations

This is a very straightforward transformation. The input grid has three columns with each column containing a different color. The output grid is the same size and the cell colors are changed. There appears to be a one-to-one mapping between input colors and output colors, 3->4, 1->5, 2->6.

input:
  width: 3
  height: 3
  colors:
    - 3: 3
    - 1: 3
    - 2: 3
  objects:
    - three columns of color
output:
  width: 3
  height: 3
  colors:
    - 4: 3
    - 5: 3
    - 6: 3
  objects:
    - three columns of color
differences:
  cells_changed: 9
  colors_changed: all colors changed to a new color
transformation:
  color value mapping 3->4, 1->5, 2->6

code_execution:

import numpy as np
input_grid = np.array([[3, 1, 2], [3, 1, 2], [3, 1, 2]])
output_grid = np.array([[4, 5, 6], [4, 5, 6], [4, 5, 6]])

def find_color_mapping(in_grid, out_grid):
    color_map = {}
    for i in range(in_grid.shape[0]):
        for j in range(in_grid.shape[1]):
            color_map[in_grid[i, j]] = out_grid[i, j]
    return color_map

color_map = find_color_mapping(input_grid, output_grid)
print(color_map)

code_execution_result: 1

{np.int64(3): np.int64(4), np.int64(1): np.int64(5), np.int64(2): np.int64(6)}

The code confirms the color mapping speculation.

The natural language program for this transformation is to map the color values in the input grid to the specified color values in the output grid according to the mapping 3->4, 1->5, 2->6.

example_2

input

[[2 3 8]
 [2 3 8]
 [2 3 8]]

output

[[6 4 9]
 [6 4 9]
 [6 4 9]]

images

../../../../_images/001-example_2_input9.png ../../../../_images/001-example_2_output9.png

observations

This example is very similar to example 1, with each column containing a different color. The output grid has the same dimensions as the input and also shows columns of a single color.

input:
  width: 3
  height: 3
  colors:
    - 2: 3
    - 3: 3
    - 8: 3
  objects:
    - three columns of color
output:
  width: 3
  height: 3
  colors:
    - 6: 3
    - 4: 3
    - 9: 3
  objects:
    - three columns of color
differences:
  cells_changed: 9
  colors_changed: all colors changed to a new color
transformation:
  color value mapping 2->6, 3->4, 8->9

code_execution:

import numpy as np
input_grid = np.array([[2, 3, 8], [2, 3, 8], [2, 3, 8]])
output_grid = np.array([[6, 4, 9], [6, 4, 9], [6, 4, 9]])

def find_color_mapping(in_grid, out_grid):
    color_map = {}
    for i in range(in_grid.shape[0]):
        for j in range(in_grid.shape[1]):
            color_map[in_grid[i, j]] = out_grid[i, j]
    return color_map

color_map = find_color_mapping(input_grid, output_grid)
print(color_map)

code_execution_result: 1

{np.int64(2): np.int64(6), np.int64(3): np.int64(4), np.int64(8): np.int64(9)}

The code confirms the color mapping speculation: 2->6, 3->4, 8->9.

The natural language program for this transformation is to map the color values in the input grid to the specified color values in the output grid according to the mapping 2->6, 3->4, 8->9.

example_3

input

[[5 8 6]
 [5 8 6]
 [5 8 6]]

output

[[1 9 2]
 [1 9 2]
 [1 9 2]]

images

../../../../_images/002-example_3_input7.png ../../../../_images/002-example_3_output7.png

observations

This example follows the same pattern as the previous two, with each column containing a single color. The output grid also has three columns with each column a different single color.

input:
  width: 3
  height: 3
  colors:
    - 5: 3
    - 8: 3
    - 6: 3
  objects:
    - three columns of color
output:
  width: 3
  height: 3
  colors:
    - 1: 3
    - 9: 3
    - 2: 3
  objects:
    - three columns of color
differences:
  cells_changed: 9
  colors_changed: all colors changed to a new color
transformation:
  color value mapping 5->1, 8->9, 6->2

code_execution:

import numpy as np
input_grid = np.array([[5, 8, 6], [5, 8, 6], [5, 8, 6]])
output_grid = np.array([[1, 9, 2], [1, 9, 2], [1, 9, 2]])

def find_color_mapping(in_grid, out_grid):
    color_map = {}
    for i in range(in_grid.shape[0]):
        for j in range(in_grid.shape[1]):
            color_map[in_grid[i, j]] = out_grid[i, j]
    return color_map

color_map = find_color_mapping(input_grid, output_grid)
print(color_map)

code_execution_result: 1

{np.int64(5): np.int64(1), np.int64(8): np.int64(9), np.int64(6): np.int64(2)}

The code confirms the color mapping speculation: 5->1, 8->9, 6->2.

The natural language program for this transformation is to map the color values in the input grid to the specified color values in the output grid according to the mapping 5->1, 8->9, 6->2.

example_4

input

[[9 4 2]
 [9 4 2]
 [9 4 2]]

output

[[8 3 6]
 [8 3 6]
 [8 3 6]]

images

../../../../_images/003-example_4_input1.png ../../../../_images/003-example_4_output1.png

observations

This example follows the same pattern as the previous three, with each column containing a single color. The output grid also has three columns with each column a different single color.

input:
  width: 3
  height: 3
  colors:
    - 9: 3
    - 4: 3
    - 2: 3
  objects:
    - three columns of color
output:
  width: 3
  height: 3
  colors:
    - 8: 3
    - 3: 3
    - 6: 3
  objects:
    - three columns of color
differences:
  cells_changed: 9
  colors_changed: all colors changed to a new color
transformation:
  color value mapping 9->8, 4->3, 2->6

code_execution:

import numpy as np
input_grid = np.array([[9, 4, 2], [9, 4, 2], [9, 4, 2]])
output_grid = np.array([[8, 3, 6], [8, 3, 6], [8, 3, 6]])

def find_color_mapping(in_grid, out_grid):
    color_map = {}
    for i in range(in_grid.shape[0]):
        for j in range(in_grid.shape[1]):
            color_map[in_grid[i, j]] = out_grid[i, j]
    return color_map

color_map = find_color_mapping(input_grid, output_grid)
print(color_map)

code_execution_result: 1

{np.int64(9): np.int64(8), np.int64(4): np.int64(3), np.int64(2): np.int64(6)}

The code confirms the color mapping speculation: 9->8, 4->3, 2->6.

The natural language program for this transformation is to map the color values in the input grid to the specified color values in the output grid according to the mapping 9->8, 4->3, 2->6.

examples summary

Ruminate Phase

All four examples present the same pattern. The input grids consist of three columns, each of a single color. The output grids are the same size as the input grids, also with three columns, and each column is a single color. The transformation in each example is the same: each color in the input grid is mapped to a specific color in the output grid. Each example provides a unique color mapping.

The transformation rule in all examples is a direct color mapping. The input colors are replaced with corresponding output colors according to a consistent mapping table, specific to each example.

Natural language program

For the test grid, identify the color values in each of the three columns of the input grid. Create an output grid of the same size as the input grid. Apply the color mapping based on the learned mappings in the examples: for each cell in the input grid, replace its color with the corresponding color defined in the mapping table for that example. The resulting output grid will have three columns, each filled with a single, mapped color.

To confirm the natural language program I will check for consistent mappings across all examples, then run the program in code_execution on the test input after it’s revealed.

Summary of color mappings

  • Example 1: 3->4, 1->5, 2->6

  • Example 2: 2->6, 3->4, 8->9

  • Example 3: 5->1, 8->9, 6->2

  • Example 4: 9->8, 4->3, 2->6

I note that there is some overlap in mappings. This further supports the consistency of the transformation program - colors map to the same output across examples:

  • 2 maps to 6 in examples 1, 2, and 4

  • 3 maps to 4 in examples 1 and 2

  • 8 maps to 9 in examples 2 and 3

This suggests a global mapping rule, though the provided examples do not fully define this rule. For the test puzzle, we should apply the specific mapping based on the test input’s color values, following the pattern observed in the examples.

code_execution:

import numpy as np

# Example mappings
example_mappings = [
    {3: 4, 1: 5, 2: 6},
    {2: 6, 3: 4, 8: 9},
    {5: 1, 8: 9, 6: 2},
    {9: 8, 4: 3, 2: 6}
]

# Check for consistent mappings
consistent_mappings = {}
for mapping in example_mappings:
    for in_val, out_val in mapping.items():
        if in_val in consistent_mappings:
            if consistent_mappings[in_val] != out_val:
                print(f"Inconsistency found for {in_val}: {consistent_mappings[in_val]} vs {out_val}")
        else:
            consistent_mappings[in_val] = out_val

print("Consistent mappings found (if no inconsistencies were reported above):")
print(consistent_mappings)

code_execution_result: 1

Consistent mappings found (if no inconsistencies were reported above):
{3: 4, 1: 5, 2: 6, 8: 9, 5: 1, 6: 2, 9: 8, 4: 3}

This confirms the mapping is consistent.

test

input

[[8 1 3]
 [8 1 3]
 [8 1 3]]

image

../../../../_images/005-test_input1.png

observations

INSTRUCTIONS:

  • generate report as per instructions

  • use code_execution to investigate properties

See also