001 • Response

puzzle_id:: 2-0ca9ddb6
description:: example_1
timestamp:: 24.329.071439
call_count:: 1
model:: models/gemini-exp-1114

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.

time
response time	total elapsed
68.039	68.121

usage
token type	call count	total used
Prompt	2465	2465
Response	570	570
Total	3035	3035
Cached	0	0