006 • History

puzzle_id:

4-0d3d703e

description:

test input

timestamp:

24.329.064813

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_input3.png ../../../../_images/000-example_1_output3.png

observations

The input grid is a 3x3 grid with three colors: green (3), blue (1), and red (2), each color occupying a column. The output grid is also a 3x3 grid, but with yellow (4), gray (5), and magenta (6) occupying the same respective columns. The transformation appears to be a simple sequential replacement of colors, adding 1 to each color value.

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]])

print("Input Grid:\n", input_grid)
print("\nOutput Grid:\n", output_grid)

# Check if the transformation is a simple addition of 1 to each cell value.
transformed_grid = input_grid + 1
print("\nTransformed Grid (input + 1):\n", transformed_grid)

comparison = np.equal(transformed_grid, output_grid)
print("\nComparison (Transformed Grid == Output Grid):\n", comparison)
all_equal = np.all(comparison)
print(f"\nAre all values equal? {all_equal}")

code_execution_result: 1

Input Grid:
 [[3 1 2]
 [3 1 2]
 [3 1 2]]

Output Grid:
 [[4 5 6]
 [4 5 6]
 [4 5 6]]

Transformed Grid (input + 1):
 [[4 2 3]
 [4 2 3]
 [4 2 3]]

Comparison (Transformed Grid == Output Grid):
 [[ True False False]
 [ True False False]
 [ True False False]]

Are all values equal? False

input:
  width: 3
  height: 3
  colors:
    - 3: 3
    - 1: 3
    - 2: 3
  objects:
    - size: 3x1, position: (0,0), color: green
    - size: 3x1, position: (0,1), color: blue
    - size: 3x1, position: (0,2), color: red

output:
  width: 3
  height: 3
  colors:
    - 4: 3
    - 5: 3
    - 6: 3
  objects:
    - size: 3x1, position: (0,0), color: yellow
    - size: 3x1, position: (0,1), color: gray
    - size: 3x1, position: (0,2), color: magenta

differences:
  cells_changed: 9
  colors_changed: All colors are changed sequentially.  Green becomes yellow, blue becomes gray, and red becomes magenta.

transformation:
  - Add 1 to each color value.  This is not entirely accurate because the values are replaced with different colours, rather than simply incrementing the numbers in place. A more accurate description would be "replace each color with the next color in the sequence (green -> yellow, blue -> gray, red -> magenta)"

The code reveals that a simple addition of 1 to each cell isn’t the transformation rule. Instead, the transformation appears to be a sequential replacement of colors, where each color is replaced by the next color in a specific sequence (green -> yellow, blue -> gray, red -> magenta). This could be represented as a lookup table or a function mapping input colors to output colors. The code didn’t capture this because it treated the color values numerically rather than qualitatively. A more sophisticated analysis is needed to account for the color mapping in order to capture the relationship completely.

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_input3.png ../../../../_images/001-example_2_output3.png

observations

The input grid is a 3x3 grid containing three colors: red (2), green (3), and azure (8), each occupying a column. The output grid is also a 3x3 grid, but the colors have changed. Red (2) has become magenta (6), green (3) has become yellow (4), and azure (8) has become maroon (9). The transformation appears to be a non-sequential mapping of input colors to output colors, unlike the first example.

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]])

print("Input Grid:\n", input_grid)
print("\nOutput Grid:\n", output_grid)

#Attempting a color mapping
color_map = {2:6, 3:4, 8:9}
transformed_grid = np.zeros_like(input_grid)

for i in range(input_grid.shape[0]):
    for j in range(input_grid.shape[1]):
        transformed_grid[i,j] = color_map[input_grid[i,j]]

print("\nTransformed Grid (color mapping):\n", transformed_grid)

comparison = np.equal(transformed_grid, output_grid)
print("\nComparison (Transformed Grid == Output Grid):\n", comparison)
all_equal = np.all(comparison)
print(f"\nAre all values equal? {all_equal}")

code_execution_result: 1

Input Grid:
 [[2 3 8]
 [2 3 8]
 [2 3 8]]

Output Grid:
 [[6 4 9]
 [6 4 9]
 [6 4 9]]

Transformed Grid (color mapping):
 [[6 4 9]
 [6 4 9]
 [6 4 9]]

Comparison (Transformed Grid == Output Grid):
 [[ True  True  True]
 [ True  True  True]
 [ True  True  True]]

Are all values equal? True

input:
  width: 3
  height: 3
  colors:
    - 2: 3
    - 3: 3
    - 8: 3
  objects:
    - size: 3x1, position: (0,0), color: red
    - size: 3x1, position: (0,1), color: green
    - size: 3x1, position: (0,2), color: azure

output:
  width: 3
  height: 3
  colors:
    - 6: 3
    - 4: 3
    - 9: 3
  objects:
    - size: 3x1, position: (0,0), color: magenta
    - size: 3x1, position: (0,1), color: yellow
    - size: 3x1, position: (0,2), color: maroon

differences:
  cells_changed: 9
  colors_changed: All colors are changed. Red becomes magenta, green becomes yellow, and azure becomes maroon.

transformation:
  - A color mapping is applied.  Red (2) maps to magenta (6), green (3) maps to yellow (4), and azure (8) maps to maroon (9).  This is a non-sequential mapping.

The code confirms that a direct color mapping is the transformation rule. Each input color is replaced with a specific output color according to a predefined mapping. There is no arithmetic or sequential relationship between the input and output values.

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_input2.png ../../../../_images/002-example_3_output2.png

observations

The input grid is a 3x3 grid consisting of gray (5), azure (8), and magenta (6) each in a column. The output grid is also a 3x3 grid, but now contains blue (1), maroon (9), and red (2) in the same respective columns. The transformation again seems to be a color mapping, but a different one than in example 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]])

print("Input Grid:\n", input_grid)
print("\nOutput Grid:\n", output_grid)

#Attempting a color mapping
color_map = {5:1, 8:9, 6:2}
transformed_grid = np.zeros_like(input_grid)

for i in range(input_grid.shape[0]):
    for j in range(input_grid.shape[1]):
        transformed_grid[i,j] = color_map[input_grid[i,j]]

print("\nTransformed Grid (color mapping):\n", transformed_grid)

comparison = np.equal(transformed_grid, output_grid)
print("\nComparison (Transformed Grid == Output Grid):\n", comparison)
all_equal = np.all(comparison)
print(f"\nAre all values equal? {all_equal}")

code_execution_result: 1

Input Grid:
 [[5 8 6]
 [5 8 6]
 [5 8 6]]

Output Grid:
 [[1 9 2]
 [1 9 2]
 [1 9 2]]

Transformed Grid (color mapping):
 [[1 9 2]
 [1 9 2]
 [1 9 2]]

Comparison (Transformed Grid == Output Grid):
 [[ True  True  True]
 [ True  True  True]
 [ True  True  True]]

Are all values equal? True

input:
  width: 3
  height: 3
  colors:
    - 5: 3
    - 8: 3
    - 6: 3
  objects:
    - size: 3x1, position: (0,0), color: gray
    - size: 3x1, position: (0,1), color: azure
    - size: 3x1, position: (0,2), color: magenta

output:
  width: 3
  height: 3
  colors:
    - 1: 3
    - 9: 3
    - 2: 3
  objects:
    - size: 3x1, position: (0,0), color: blue
    - size: 3x1, position: (0,1), color: maroon
    - size: 3x1, position: (0,2), color: red

differences:
  cells_changed: 9
  colors_changed: All colors are changed. Gray becomes blue, azure becomes maroon, and magenta becomes red.

transformation:
  - A color mapping is applied. Gray (5) maps to blue (1), azure (8) maps to maroon (9), and magenta (6) maps to red (2).

The code confirms a color mapping is in operation; however, a different mapping than in example 2 is used for this example. There’s no consistent arithmetic or sequential pattern across the mappings. Each example appears to have a unique color mapping.

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_input.png ../../../../_images/003-example_4_output.png

observations

The input grid is a 3x3 grid with maroon (9), yellow (4), and red (2) each occupying a column. The output grid is also a 3x3 grid, but the colors have changed. Maroon (9) is now azure (8), yellow (4) is now green (3), and red (2) is now magenta (6). This again appears to be a color mapping, but different from the previous examples.

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]])

print("Input Grid:\n", input_grid)
print("\nOutput Grid:\n", output_grid)

#Attempting a color mapping
color_map = {9:8, 4:3, 2:6}
transformed_grid = np.zeros_like(input_grid)

for i in range(input_grid.shape[0]):
    for j in range(input_grid.shape[1]):
        transformed_grid[i,j] = color_map[input_grid[i,j]]

print("\nTransformed Grid (color mapping):\n", transformed_grid)

comparison = np.equal(transformed_grid, output_grid)
print("\nComparison (Transformed Grid == Output Grid):\n", comparison)
all_equal = np.all(comparison)
print(f"\nAre all values equal? {all_equal}")

code_execution_result: 1

Input Grid:
 [[9 4 2]
 [9 4 2]
 [9 4 2]]

Output Grid:
 [[8 3 6]
 [8 3 6]
 [8 3 6]]

Transformed Grid (color mapping):
 [[8 3 6]
 [8 3 6]
 [8 3 6]]

Comparison (Transformed Grid == Output Grid):
 [[ True  True  True]
 [ True  True  True]
 [ True  True  True]]

Are all values equal? True

input:
  width: 3
  height: 3
  colors:
    - 9: 3
    - 4: 3
    - 2: 3
  objects:
    - size: 3x1, position: (0,0), color: maroon
    - size: 3x1, position: (0,1), color: yellow
    - size: 3x1, position: (0,2), color: red

output:
  width: 3
  height: 3
  colors:
    - 8: 3
    - 3: 3
    - 6: 3
  objects:
    - size: 3x1, position: (0,0), color: azure
    - size: 3x1, position: (0,1), color: green
    - size: 3x1, position: (0,2), color: magenta

differences:
  cells_changed: 9
  colors_changed: All colors are changed. Maroon becomes azure, yellow becomes green, and red becomes magenta.

transformation:
  - A color mapping is applied. Maroon (9) maps to azure (8), yellow (4) maps to green (3), and red (2) maps to magenta (6).

The code confirms that a color mapping is the transformation rule. Each input color is replaced by a specific output color; however, the mapping is unique to this example, just as in previous examples. There’s no single, consistent mathematical or sequential rule across all four examples besides the application of a unique color mapping for each input grid.

examples summary

The transformation applied to each input grid involves a unique color mapping. There’s no consistent arithmetic operation or sequential pattern across the examples. Each input grid is transformed by a different mapping that replaces each color with a specific, new color. The mapping is not based on any discernible numerical relationship between the input and output color values.

code_execution:

import numpy as np

# Example mappings from the examples above
mappings = {
    1: {1: 5, 2: 6, 3: 4},  # Example 1
    2: {2: 6, 3: 4, 8: 9},  # Example 2
    3: {5: 1, 6: 2, 8: 9},  # Example 3
    4: {2: 6, 4: 3, 9: 8}   # Example 4
}

def apply_mapping(input_grid, mapping):
    transformed_grid = np.zeros_like(input_grid)
    for i in range(input_grid.shape[0]):
        for j in range(input_grid.shape[1]):
            transformed_grid[i, j] = mapping.get(input_grid[i, j], input_grid[i, j]) #Handle cases where a color isn't in the mapping
    return transformed_grid

# Test the function on the input grids from example 1-4
example_inputs = [
    np.array([[3, 1, 2], [3, 1, 2], [3, 1, 2]]),
    np.array([[2, 3, 8], [2, 3, 8], [2, 3, 8]]),
    np.array([[5, 8, 6], [5, 8, 6], [5, 8, 6]]),
    np.array([[9, 4, 2], [9, 4, 2], [9, 4, 2]])
]

example_outputs = [
    np.array([[4, 5, 6], [4, 5, 6], [4, 5, 6]]),
    np.array([[6, 4, 9], [6, 4, 9], [6, 4, 9]]),
    np.array([[1, 9, 2], [1, 9, 2], [1, 9, 2]]),
    np.array([[8, 3, 6], [8, 3, 6], [8, 3, 6]])
]

for i in range(len(example_inputs)):
    transformed = apply_mapping(example_inputs[i], mappings[i+1])
    comparison = np.equal(transformed, example_outputs[i])
    print(f"Example {i+1}: All values match output? {np.all(comparison)}")

code_execution_result:

Example 1: All values match output? True
Example 2: All values match output? True
Example 3: All values match output? True
Example 4: All values match output? True

The code confirms that each example can be solved with a unique color mapping. The absence of a generalizable numerical or sequential pattern across the mappings suggests that the puzzle requires memorizing or learning individual mappings rather than inferring a general rule. The challenge seems to be focused on pattern recognition of specific color associations.

test

input

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

image

../../../../_images/005-test_input.png

observations

INSTRUCTIONS:

  • generate report as per instructions

  • use code_execution to investigate properties

See also