002 • History

puzzle_id:: 2-0ca9ddb6
description:: example_2
timestamp:: 24.329.064813
call_count:: 2

Begin puzzle: 2-0ca9ddb6

example_1

input

[[0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 2 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 1 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]]

output

[[0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 4 0 4 0 0 0 0 0]
 [0 0 2 0 0 0 0 0 0]
 [0 4 0 4 0 0 0 0 0]
 [0 0 0 0 0 0 7 0 0]
 [0 0 0 0 0 7 1 7 0]
 [0 0 0 0 0 0 7 0 0]
 [0 0 0 0 0 0 0 0 0]]

images

observations

The input grid is a 9x9 grid containing mostly white pixels (0). There is a single red (2) pixel at (3,2) and a single blue (1) pixel at (7,6).

The output grid expands on the input. The red pixel remains unchanged. The blue pixel is surrounded by orange (7) pixels, forming a 3x3 square with the blue pixel in the center. Additionally, yellow (4) pixels appear in a cross pattern around the red pixel.

code_execution:

import numpy as np

input_grid = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
                     [0, 0, 0, 0, 0, 0, 0, 0, 0],
                     [0, 0, 0, 0, 0, 0, 0, 0, 0],
                     [0, 0, 2, 0, 0, 0, 0, 0, 0],
                     [0, 0, 0, 0, 0, 0, 0, 0, 0],
                     [0, 0, 0, 0, 0, 0, 0, 0, 0],
                     [0, 0, 0, 0, 0, 0, 1, 0, 0],
                     [0, 0, 0, 0, 0, 0, 0, 0, 0],
                     [0, 0, 0, 0, 0, 0, 0, 0, 0]])

output_grid = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0],
                       [0, 4, 0, 4, 0, 0, 0, 0, 0],
                       [0, 0, 2, 0, 0, 0, 0, 0, 0],
                       [0, 4, 0, 4, 0, 0, 0, 0, 0],
                       [0, 0, 0, 0, 0, 0, 7, 0, 0],
                       [0, 0, 0, 0, 0, 7, 1, 7, 0],
                       [0, 0, 0, 0, 0, 0, 7, 0, 0],
                       [0, 0, 0, 0, 0, 0, 0, 0, 0]])

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

red_indices = np.where(input_grid == 2)
blue_indices = np.where(input_grid == 1)

print("\nRed Pixel Coordinates:", red_indices)
print("Blue Pixel Coordinates:", blue_indices)

code_execution_result: 1

Input Grid:
 [[0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 2 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 1 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]]

Output Grid:
 [[0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 4 0 4 0 0 0 0 0]
 [0 0 2 0 0 0 0 0 0]
 [0 4 0 4 0 0 0 0 0]
 [0 0 0 0 0 0 7 0 0]
 [0 0 0 0 0 7 1 7 0]
 [0 0 0 0 0 0 7 0 0]
 [0 0 0 0 0 0 0 0 0]]

Red Pixel Coordinates: (array([3]), array([2]))
Blue Pixel Coordinates: (array([6]), array([6]))

input:
  width: 9
  height: 9
  colors:
    - 0: 71
    - 1: 1
    - 2: 1
  objects:
    - size: 1x1, position: (3,2), color: red
    - size: 1x1, position: (6,6), color: blue

output:
  width: 9
  height: 9
  colors:
    - 0: 64
    - 2: 1
    - 4: 4
    - 7: 4
  objects:
    - size: 1x1, position: (3,2), color: red
    - size: 3x3, position: (6,5), color: blue surrounded by orange
    - size: 1x1, position: (2,1), color: yellow
    - size: 1x1, position: (2,3), color: yellow
    - size: 1x1, position: (4,1), color: yellow
    - size: 1x1, position: (4,3), color: yellow

differences:
  cells_changed: 13
  colors_changed: added yellow and orange colors around the blue pixel and added yellow pixels in a cross pattern around the red pixel.
transformation:
  - A cross pattern of yellow pixels appears around the red pixel.
  - The blue pixel is surrounded by an orange 3x3 square.

The transformation seems to involve the addition of new colored pixels around the existing red and blue pixels, forming distinct patterns. The red pixel gets a yellow cross, and the blue gets a 3x3 orange square. There’s no obvious mathematical relationship or positional rule beyond proximity to the original pixels.

example_2

input

[[0 0 0 8 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 2 0 0]
 [0 0 1 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 1 0 0]
 [0 2 0 0 0 0 0 0 0]
 [0 0 0 0 0 0 0 0 0]]

output

[[0 0 0 8 0 0 0 0 0]
 [0 0 0 0 0 4 0 4 0]
 [0 0 7 0 0 0 2 0 0]
 [0 7 1 7 0 4 0 4 0]
 [0 0 7 0 0 0 0 0 0]
 [0 0 0 0 0 0 7 0 0]
 [4 0 4 0 0 7 1 7 0]
 [0 2 0 0 0 0 7 0 0]
 [4 0 4 0 0 0 0 0 0]]

images

observations

INSTRUCTIONS:

Review Examples Phase

pairs of input and output grids will be shown to you one at a time

you will examine and analyze the text and image for each example

you may use code execution with tools like numpy to examine patterns after examining the grids, document the attributes of each as such

use a yaml block for the details

input:
width: X
height: Y
colors:
  - N: (count)
objects:
  - size, position and color - desc

output:
width: X
height: Y
colors:
  - N: (count)
objects:
  - size, position and color - desc

differences:
cells_changed: N
colors_changed: desc
transformation:
  - speculate on transformation rules

your response for this phase should contain the following content parts

begin with a verbal description of your perception of the input and output grid
run a code_execution part to test your perceptions - since the code you use may not be carried forward on following prompts, be sure to have the code print you findings in the output remember that you have access to many python libraries for analyzing the grids and validating patterns
review your findings and try to determine what the natural language program is for the transformation