Two points A and B are fixed on a plane. A beetle, starting at point Psub0, crawls to the point A, turns right 90 degrees and then walks to a point Psub1 the same distance from A as Psub0 was. Next the beetle walks to B, turns right 90 degrees and walks to a point Psub2 the same distance from B as Psub1 was. The beetle repeated this motion, alternating between points A and B. Show that the beetle is guaranteed to return to start. (In how many moves?)

Question