Question

The image is a ceramic tile of dimension 20 cm × 20 cm. How many distinct patterns can you create by using two such ceramic tiles in a rectangular patch of 40 cm × 20 cm on the wall?

Answer 1

Correct Answer: 16

To determine how many distinct patterns can be created using two 20 cm × 20 cm ceramic tiles on a 40 cm × 20 cm patch, we must consider how tiles can be arranged. Each tile can have different orientations: tile rotated 0°, 90°, 180°, or 270°. This results in 4 possible orientations per tile.
1. **Tile A Placements:** Each tile (A) has 4 possible orientations.
2. **Tile B Placements:** Similarly, the second tile (B) also has 4 possible orientations independently of the first tile.

Therefore, the total number of distinct patterns is:

Patterns = Orientations_A × Orientations_B
= 4 × 4 = 16

This solution matches the expected range of [16,16], confirming that our computation is accurate. Thus, there are 16 distinct patterns possible.