1995 AHSME Problems/Problem 15

Problem

Five points on a circle are numbered 1,2,3,4, and 5 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 5, after 1995 jumps it will be on point

$\mathrm{(A) \ 1 } \qquad \mathrm{(B) \ 2 } \qquad \mathrm{(C) \ 3 } \qquad \mathrm{(D) \ 4 } \qquad \mathrm{(E) \ 5 }$

Solution

It moves in a cycle that goes $\{1, 2, 4, 1, 2, 4...\}$ . The cycle has a period of $3$ .

Thus, after $1995=3*665$ jumps, it will be on point $4$ $\Rightarrow \mathrm{(D)}$ .

1995 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Problem 16
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1995 AHSME Problems/Problem 15

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