003 • Response

puzzle_id:

4-0d3d703e

description:

example_3

timestamp:

24.356.195518

call_count:

3

model:

gemini-2.0-flash-thinking-exp-1219

The user wants me to analyze the third example of the ARC task and formulate a natural language program for the transformation. I need to describe the input and output grids, use code to analyze them, and then describe the transformation.

Plan:

1. Describe the input grid.

2. Describe the output grid.

3. Use code to analyze the input and output grids.

4. Formulate a natural language program for the transformation.

example_3

input

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

output

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

images

import matplotlib.pyplot as plt
import numpy as np

def show_grid(grid, title):
    cmap = plt.cm.colors.ListedColormap([(0.93, 0.93, 0.93), (0.12, 0.58, 1.00), (0.86, 0.20, 0.16), (0.31, 0.80, 0.19), (0.90, 0.78, 0.00), (0.33, 0.33, 0.33), (0.90, 0.23, 0.64), (0.90, 0.47, 0.08), (0.53, 0.85, 0.94), (0.57, 0.07, 0.19)])
    bounds = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
    norm = plt.cm.colors.BoundaryNorm(bounds, cmap.N)

    data = np.array(grid)
    fig, ax = plt.subplots()
    ax.imshow(data, cmap=cmap, norm=norm)

    ax.grid(which='major', axis='both', linestyle='-', color='k', linewidth=2)
    ax.set_xticks(np.arange(-.5, len(grid[0])-.5, 1))
    ax.set_yticks(np.arange(-.5, len(grid)-.5, 1))
    ax.set_xticklabels([])
    ax.set_yticklabels([])
    ax.set_title(title)
    for i in range(data.shape[0]):
        for j in range(data.shape[1]):
            ax.text(j, i, str(data[i, j]), ha="center", va="center", color="black")
    plt.show()

input_grid = [[5, 8, 6], [5, 8, 6], [5, 8, 6]]
output_grid = [[1, 9, 2], [1, 9, 2], [1, 9, 2]]

show_grid(input_grid, "Input Grid")
show_grid(output_grid, "Output Grid")

observations

The input grid is a 3x3 grid. The first column is gray, the second column is azure, and the third column is magenta.

The output grid is also a 3x3 grid. The first column is blue, the second column is maroon, and the third column is red.

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

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

def analyze_grid(grid):
    height = len(grid)
    width = len(grid[0])
    colors = {}
    for row in grid:
        for cell in row:
            colors[cell] = colors.get(cell, 0) + 1
    return {"width": width, "height": height, "colors": colors}

input_grid = [[5, 8, 6], [5, 8, 6], [5, 8, 6]]
output_grid = [[1, 9, 2], [1, 9, 2], [1, 9, 2]]

input_analysis = analyze_grid(input_grid)
output_analysis = analyze_grid(output_grid)

print("Input analysis:", input_analysis)
print("Output analysis:", output_analysis)

differences = {}
if input_analysis['width'] != output_analysis['width'] or input_analysis['height'] != output_analysis['height']:
    differences['size_change'] = 'yes'
else:
    differences['size_change'] = 'no'

changed_cells = 0
color_changes = {}
for r in range(input_analysis['height']):
    for c in range(input_analysis['width']):
        if input_grid[r][c] != output_grid[r][c]:
            changed_cells += 1
            old_color = input_grid[r][c]
            new_color = output_grid[r][c]
            if old_color not in color_changes:
                color_changes[old_color] = new_color

differences['cells_changed'] = changed_cells
differences['color_changes'] = color_changes

print("Differences:", differences)

differences:
  cells_changed: 9
  colors_changed: {5: 1, 8: 9, 6: 2}
  transformation:
    - Each color in the input maps consistently to a new color in the output.
    - Gray (5) maps to Blue (1).
    - Azure (8) maps to Maroon (9).
    - Magenta (6) maps to Red (2).
    - The grid dimensions remain the same.

Natural language program:

The input grid is a 3x3 grid with three distinct colors arranged in columns: gray in the first, azure in the second, and magenta in the third. The output grid has the same dimensions. To generate the output grid, iterate through each pixel in the input grid. If the pixel is gray, change its color to blue. If the pixel is azure, change its color to maroon. If the pixel is magenta, change its color to red. The positions of the colors remain the same; only the colors themselves are changed according to this mapping.

time

response time	total elapsed
13.147	30.78

usage

token type	call count	total used
Prompt	5847	12651
Response	1661	3739
Total	7508	16390
Cached	0	0

See also

• 003 • History

• 003 • Response