003 • Response

puzzle_id:

5-150deff5

description:

example_3

timestamp:

24.356.195518

call_count:

3

model:

gemini-2.0-flash-thinking-exp-1219

The user has provided a third example for the same task. I need to analyze this example and see if it aligns with the natural language program developed so far.

Input Grid Analysis (Example 3):

• Dimensions: 8x9

• Colors: White (0) and Gray (5)

• Objects: A single contiguous block of gray pixels, forming a shape similar to a ‘C’ rotated 90 degrees clockwise.

Output Grid Analysis (Example 3):

• Dimensions: 8x9 (same as input)

• Colors: White (0), Azure (8), and Red (2)

• Objects: The gray object has been transformed. The outer boundary is azure, and the inner part is red.

Comparison with Previous Examples:

The pattern of transforming a gray object into an azure border and a red interior seems consistent across all three examples.

Verifying the Natural Language Program:

The refined natural language program should work for this example as well. Let’s mentally walk through it.

1. Identify gray components: One connected component of gray pixels.

2. Identify boundary pixels: The gray pixels adjacent to white pixels.

3. Color boundary pixels azure: This should create the azure outline in the output.

4. Identify interior pixels: The remaining gray pixels.

5. Color interior pixels red: This should create the red interior in the output.

The program seems to hold.

Let’s generate the YAML blocks and then the natural language program.

observations

The input grid shows a gray shape on a white background. The output grid shows a similar shape, but with the outer layer colored azure and the inner part colored red.

input:
  width: 9
  height: 8
  colors:
    0: 52
    5: 20
  objects:
    - color: gray
      shape: C-like (rotated)
      pixels: 20
      positions: Determined by the coordinates of the gray pixels

output:
  width: 9
  height: 8
  colors:
    0: 52
    8: 10
    2: 10
  objects:
    - color: azure
      shape: outer boundary of the original gray shape
      pixels: 10
      positions: Determined by the coordinates of the azure pixels
    - color: red
      shape: inner part of the original gray shape
      pixels: 10
      positions: Determined by the coordinates of the red pixels

differences:
  cells_changed: 20
  colors_changed: gray to azure and red
  transformation:
    - Identify the connected component of gray pixels.
    - Change the color of the outermost layer of this component to azure.
    - Change the color of the inner part of this component to red.

Natural Language Program:

1. Create an output grid by copying the input grid.

2. Identify all connected components of gray (5) pixels in the input grid.

3. For each connected component of gray pixels:

   1. Identify the boundary pixels of the component. A boundary pixel is a gray pixel that is horizontally or vertically adjacent to a non-gray pixel.

   2. Change the color of all boundary pixels in the output grid to azure (8).

   3. Identify the interior pixels of the component. These are the gray pixels that are not boundary pixels.

   4. Change the color of all interior pixels in the output grid to red (2).

time

response time	total elapsed
7.394	32.308

usage

token type	call count	total used
Prompt	7696	15270
Response	777	3756
Total	8473	19026
Cached	0	0

See also

• 003 • History

• 003 • Response