004 • Response

puzzle_id:

4-0d3d703e

description:

example_4

timestamp:

24.357.081407

call_count:

4

model:

gemini-2.0-flash-thinking-exp-1219

The user wants me to analyze the fourth example pair, building upon the previous three examples, and to formally document my findings and the natural language program.

Plan:

1. Describe the input and output grids visually.

2. Use code to analyze the grids, verifying the column-wise transformation and identifying specific color mappings.

3. Document the findings in YAML format, specifically focusing on the color changes.

4. Update the natural language program to incorporate the information from the fourth example, ensuring it accurately reflects the observed transformation rule.

Example 4 Analysis:

The input grid is a 3x3 grid. The columns are maroon (9), yellow (4), and red (2).

The output grid is also a 3x3 grid. The columns are azure (8), green (3), and magenta (6).

This example should solidify the column-wise color transformation rule. Let’s confirm the color mappings.

example_4

input

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

output

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

observations

The input grid is a 3x3 grid with three distinct vertical columns of color. The leftmost column is maroon, the middle column is yellow, and the rightmost column is red.

The output grid is also a 3x3 grid with three distinct vertical columns of color. The leftmost column is azure, the middle column is green, and the rightmost column is magenta.

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]])

input_colors = {}
for row in input_grid:
    for pixel in row:
        color = int(pixel)
        input_colors[color] = input_colors.get(color, 0) + 1

output_colors = {}
for row in output_grid:
    for pixel in row:
        color = int(pixel)
        output_colors[color] = output_colors.get(color, 0) + 1

changed_pixels = []
for r in range(input_grid.shape[0]):
    for c in range(input_grid.shape[1]):
        if input_grid[r, c] != output_grid[r, c]:
            changed_pixels.append(((r, c), int(input_grid[r, c]), int(output_grid[r, c])))

print("Input grid shape:", input_grid.shape)
print("Output grid shape:", output_grid.shape)
print("Input color counts:", input_colors)
print("Output color counts:", output_colors)
print("Changed pixels (coordinates, old_color, new_color):", changed_pixels)

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

differences:
  cells_changed: 9
  colors_changed:
    maroon to azure in the first column
    yellow to green in the second column
    red to magenta in the third column
  transformation:
    - Each column's color is transformed into a new color.
    - The transformation is consistent across all rows within a column.
    - The transformation is a mapping of input column color to output column color.

Natural Language Program:

The task involves transforming a 3x3 input grid into a 3x3 output grid. The input grid is characterized by having three distinct vertical columns, each filled with a uniform color.

To generate the output grid:

1. Initialization: Create a new 3x3 grid that will serve as the output.

2. Identify Input Columns: Examine the input grid and identify the color of each of the three vertical columns. The leftmost column will have one consistent color, the middle column another, and the rightmost column a third.

3. Establish Color Mapping: Determine the transformation rule for each column’s color based on the provided examples. This rule maps each input color to a specific output color. Based on the four examples, the complete color mapping is as follows:

   • Green (3) transforms to Yellow (4).

   • Blue (1) transforms to Gray (5).

   • Red (2) transforms to Magenta (6).

   • Azure (8) transforms to Maroon (9).

   • Gray (5) transforms to Blue (1).

   • Magenta (6) transforms to Red (2).

   • Maroon (9) transforms to Azure (8).

   • Yellow (4) transforms to Green (3).

4. Apply Transformation: Iterate through each column of the input grid.

   • For the first column, note its color. Using the color mapping, find the corresponding output color. Fill every cell in the first column of the output grid with this transformed color.

   • Repeat this process for the second column of the input grid, mapping its color and filling the second column of the output grid.

   • Repeat this process for the third column of the input grid, mapping its color and filling the third column of the output grid.

For instance, if the first column of the input is maroon, the first column of the output will be azure. If the second column of the input is yellow, the second column of the output will be green. If the third column of the input is red, the third column of the output will be magenta.

time

response time	total elapsed
10.838	39.99

usage

token type	call count	total used
Prompt	7632	19196
Response	1348	5052
Total	8980	24248
Cached	0	0

See also

• 004 • History

• 004 • Response