004 • Response

puzzle_id:: 4-0d3d703e
description:: example_4
timestamp:: 24.356.195518
call_count:: 4
model:: gemini-2.0-flash-thinking-exp-1219

The user wants me to analyze the fourth 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:

Describe the input grid.
Describe the output grid.
Use code to analyze the input and output grids.
Formulate a natural language program for the transformation.

example_4

input

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

output

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

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 = [[9, 4, 2], [9, 4, 2], [9, 4, 2]]
output_grid = [[8, 3, 6], [8, 3, 6], [8, 3, 6]]

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

observations

The input grid is a 3x3 grid. The first column is maroon, the second column is yellow, and the third column is red.

The output grid is also a 3x3 grid. The first column is azure, the second column is green, and the third column is magenta.

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

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

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 = [[9, 4, 2], [9, 4, 2], [9, 4, 2]]
output_grid = [[8, 3, 6], [8, 3, 6], [8, 3, 6]]

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: {9: 8, 4: 3, 2: 6}
  transformation:
    - Each color in the input maps consistently to a new color in the output.
    - Maroon (9) maps to Azure (8).
    - Yellow (4) maps to Green (3).
    - Red (2) maps to Magenta (6).
    - The grid dimensions remain the same.

Natural language program:

The input grid is a 3x3 grid with three distinct colors arranged in columns: maroon in the first, yellow in the second, and red 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 maroon, change its color to azure. If the pixel is yellow, change its color to green. If the pixel is red, change its color to magenta. The positions of the colors remain the same; only the colors themselves are changed according to this mapping.

time
response time	total elapsed
14.03	44.937

usage
token type	call count	total used
Prompt	8100	20751
Response	1661	5400
Total	9761	26151
Cached	0	0