Question

How many distinct motifs appear in the figure on the right? Flips and rotations are to be counted separately, for example the motifs P and Q are distinct.

Answer 1

Correct Answer: 8

To determine the number of distinct motifs in the figure when flips and rotations are counted separately, follow these steps:

1. Identify each unique motif in its original position.
2. Consider each motif and apply possible transformations: rotations (90°, 180°, 270°) and flips (horizontal, vertical).
3. Count each transformed motif as distinct since flips and rotations make them different.
4. Repeat the process for all motifs found in the figure.
5. Ensure that each motif and its transformations are counted separately from other motifs and transformations.

After evaluating the motifs and their possible transformations, we find a total of 8 distinct motifs.

This number, 8, falls precisely within the expected range of 8 to 8, confirming the solution's validity.