002 • History

puzzle_id:: 2-0ca9ddb6
description:: example_2
timestamp:: 24.329.071439
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 appears to be a 9x9 grid with a sparse population of colored cells. There is a single red cell (color 2) and a single blue cell (color 1). The output grid is the same size but introduces new yellow cells (color 4) and orange cells (color 7). The original red and blue cells remain in place.

The new yellow cells appear in a specific pattern around the red cell. There are four yellow cells, two cells away in each cardinal direction from the red cell. The orange cells form a cross shape around the blue cell, one cell away in the cardinal directions and two diagonal cells adjacent to the blue.

Analysis

I will use Python to analyze the grid to confirm and detail the observations made.

code_execution:

import numpy as np

# Define the input and output grids
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]
])

# Find the positions of the non-zero cells in the input grid
input_positions = np.argwhere(input_grid != 0)
print("Non-zero positions in input grid:", input_positions)

# Find the positions of the new cells in the output grid
new_cells_positions = np.argwhere((output_grid != 0) & (input_grid == 0))
print("New cells in output grid:", new_cells_positions)
print("Colors of new cells:", output_grid[tuple(new_cells_positions.T)])

code_execution_result: 1

Non-zero positions in input grid: [[3 2]
 [6 6]]
New cells in output grid: [[2 1]
 [2 3]
 [4 1]
 [4 3]
 [5 6]
 [6 5]
 [6 7]
 [7 6]]
Colors of new cells: [4 4 4 4 7 7 7 7]

Observations

The code confirms the positions of the original non-zero cells. The new yellow cells (color 4) are located at positions (2,1), (2,3), (4,1), (4,3) and the orange cells (color 7) are at (5,6), (6,5), (6,7), (7,6).

Input

input:
  width: 9
  height: 9
  colors:
    - 0: 79
    - 1: 1
    - 2: 1
  objects:
    - 1x1, position (3,2), color red - single red cell
    - 1x1, position (6,6), color blue - single blue cell

Output

output:
  width: 9
  height: 9
  colors:
    - 0: 71
    - 1: 1
    - 2: 1
    - 4: 4
    - 7: 4
  objects:
    - 1x1, position (3,2), color red - original red cell
    - 1x1, position (6,6), color blue - original blue cell
    - 1x1, position (2,1), (2,3), (4,1), (4,3), color yellow - new yellow cells
    - 1x1, position (5,6), (6,5), (6,7), (7,6), color orange - new orange cells

Differences

differences:
  cells_changed: 8
  colors_changed: added colors 4 and 7 (yellow and orange)
  transformation:
    - new yellow cells appear in cross shape around red cell with distance 2
    - new orange cells appear in cross shape around blue cell with distance 1

Transformation

The transformation involves placing new cells of specific colors at fixed distances around the original colored cells. Yellow cells appear two cells away from the red cell in the cardinal directions. Orange cells appear one cell away from the blue cell in the cardinal directions. This is a pattern of expansion from the original colored cells, with different distances and colors for each.

Therefore, the natural language program for this transformation is:

For each red cell, place yellow cells two cells away in the north, south, east, and west directions. For each blue cell, place orange cells one cell away in the north, south, east, and west directions.

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