Question

A regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during the rotation?

Answer 1

A regular octagon has 8 sides, so it would coincide exactly each time the vertices fall into the same places. In one full 360-degree rotation, any "selected" vertex would fall into all 7 other vertices one after the other, before going back to its original position. Therefore, there would be 8 times during the rotation that the octagon coincides with the preimage.