003 • Response

puzzle_id:: 2-0ca9ddb6
description:: example_3
timestamp:: 24.329.071439
call_count:: 3
model:: models/gemini-exp-1114

observations This example introduces a magenta cell (color 6), which, like the azure cell in the previous example, remains unchanged in the output. The red (2) and blue (1) cells continue to generate yellow (4) and orange (7) cells respectively, following the established pattern. The magenta cell doesn’t seem to influence the placement of any new cells.

Analysis

I will use Python to confirm the positions and counts of each color and the changes between the input and output grids.

code_execution:

import numpy as np

input_grid_3 = np.array([
    [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, 6, 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]
])

output_grid_3 = np.array([
    [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, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 6, 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]
])


input_positions_3 = np.argwhere(input_grid_3 != 0)
print("Non-zero positions in input grid 3:", input_positions_3)

new_cells_positions_3 = np.argwhere((output_grid_3 != 0) & (input_grid_3 == 0))
print("New cells in output grid 3:", new_cells_positions_3)
print("Colors of new cells 3:", output_grid_3[tuple(new_cells_positions_3.T)])

code_execution_result: 1

Non-zero positions in input grid 3: [[2 2]
 [5 6]
 [7 3]]
New cells in output grid 3: [[1 1]
 [1 3]
 [3 1]
 [3 3]
 [6 3]
 [7 2]
 [7 4]
 [8 3]]
Colors of new cells 3: [4 4 4 4 7 7 7 7]

Input

input:
  width: 9
  height: 9
  colors:
    - 0: 78
    - 1: 1
    - 2: 1
    - 6: 1
  objects:
    - 1x1, position (2,2), color red
    - 1x1, position (5,6), color magenta
    - 1x1, position (7,3), color blue

Output

output:
  width: 9
  height: 9
  colors:
    - 0: 70
    - 1: 1
    - 2: 1
    - 4: 4
    - 6: 1
    - 7: 4
  objects:
    - 1x1, position (2,2), color red
    - 1x1, position (5,6), color magenta
    - 1x1, position (7,3), color blue
    - 1x1, positions (1,1), (1,3), (3,1), (3,3), color yellow
    - 1x1, positions (6,3), (7,2), (7,4), (8,3), color orange

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
  - magenta cell remains unchanged and doesn't influence new cell placement

Transformation

This example reinforces the previously observed pattern. Red cells generate yellow cells two cells away in the cardinal directions, and blue cells generate orange cells one cell away in the cardinal directions. Cells of other colors (magenta in this case) are unaffected by the transformation and do not influence the placement of new cells.

The natural language program remains consistent:

For each red cell, place yellow cells two cells away in the north, south, east, and west directions unless the position is already occupied by a non-zero cell. For each blue cell, place orange cells one cell away in the north, south, east, and west directions unless the position is already occupied by a non-zero cell.

time
response time	total elapsed
29.992	160.465

usage
token type	call count	total used
Prompt	7801	15171
Response	535	3092
Total	8336	18263
Cached	0	0