Step 1: Understanding the Concept:
The task is to count the number of unique patterns present in the 8x8 grid. The problem specifies that rotated patterns are considered distinct (e.g., vertical stripes are different from horizontal stripes). We must carefully scan the grid and identify every unique design.
Step 2: Key Formula or Approach:
The approach is to systematically categorize and list each pattern found in the grid, ensuring no duplicates are counted. We can group patterns by type (e.g., solid, striped, geometric shapes) to maintain a clear count.
Step 3: Detailed Explanation:
Let's list the unique patterns by scanning the grid row by row.
Clearly Distinguishable Patterns:
Solid Fills:
1. White square
2. Black square
Geometric Shapes:
3. Black circle
4. Black diamond
5. Central black dot
Bordered Patterns:
6. White square with a full border
Corner Patterns (4 distinct rotations):
7. Black corner (top-left)
8. Black corner (top-right)
9. Black corner (bottom-left)
10. Black corner (bottom-right)
Single Line Patterns (2 distinct rotations):
11. Single diagonal line (/)
12. Single diagonal line (\textbackslash)
Grid/Checkerboard Patterns:
13. Crosshatch (thin grid lines)
14. 2x2 checkerboard
15. Dithered pattern (fine 4x4 or 8x8 checkerboard)
Striped Patterns:
16. Three vertical bars
17. Three horizontal bars
18. Diagonal stripes (
)
19. Diagonal stripes (//)
Step 4: Final Answer:
By identifying all clearly distinct patterns, we find 19.