Question

Count the number of unique patterns in the given grid.

Hint:

When asked for “unique patterns,” ignore location and frequency—just list distinct textures/tones (treat rotations of the same hatch as the same only if stated).

Answer 1

Step 1: Identify distinct fill styles (ignoring position and repetition).
To begin, we analyze the various fill styles used across the grid. We must identify the unique fill patterns without considering their positions or repetitions. Here are the distinct styles used:
1. Plain white: This refers to the absence of any texture or fill, where the cell is simply left blank, showing no patterns at all.
2. Solid light grey: A uniform fill with a light grey color, which gives the cell a plain, soft tone that is visually distinct from both white and darker shades.
3. Solid medium/dark grey (solid tone): A uniform, solid grey fill, but in a darker shade compared to light grey. It contrasts more with other lighter fills.
4. Dense cross-hatch / mesh (dot-like): A pattern filled with closely spaced dots or cross-hatch lines, providing a dense mesh look. This is visually distinct and stands out from plain colors.
5. Diagonal hatch left (/ slant): This fill style uses a diagonal line pattern running from the top left to the bottom right. It creates a slanted appearance of parallel lines.
6. Diagonal hatch right (\ slant): Similar to the previous style but with the slant running in the opposite direction, from top right to bottom left. This creates a mirrored pattern compared to the left slant.
7. Horizontal/vertical line hatch (single-direction grid): This fill consists of parallel lines that run either horizontally or vertically, creating a grid-like structure that gives the cell a very structured, regular appearance.

Each of these fills is distinct, and by ignoring their repetitions or positions on the grid, we can clearly see that these 7 styles are the only unique ones in use. Step 2: Count the distinct styles.
After analyzing the grid and identifying the unique fill styles, we can count that there are exactly 7 distinct fill patterns used. All other squares in the grid are simply repetitions of these 7 styles, appearing in different positions throughout the layout.
Thus, the total number of distinct fill styles used in the grid is: \(\boxed{7}\).