Problem:
Five points on a circle are numbered , and in clockwise order. A bug jumps in a clockwise direction from one point to another around the circle; if it is on an odd-numbered point, it moves one point, and if it is on an even-numbered point, it moves two points. If the bug begins on point , after jumps it will be on point
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Answer Choices:
A.
B.
C.
D.
E.
Solution:
With the first jump, the bug moves to point , with the second to , with the third to and with the fourth it returns to . Thereafter, every third jump it returns to . Thus, after jumps, the bug will be on or , depending on whether is of the form or , respectively. Since , the bug will be on point after jumps.
