Difference between revisions of "1995 AHSME Problems/Problem 15"
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==Solution== | ==Solution== | ||
| − | It moves 1, 2, 4, 1, 2, 4 | + | It moves in a cycle that goes <math>\{1, 2, 4, 1, 2, 4...\}</math>. The cycle has a period of <math>3</math>. |
| + | |||
| + | Thus, after <math>1995=3*665</math> jumps, it will be on point <math>4</math> <math>\Rightarrow \mathrm{(D)}</math>. | ||
==See also== | ==See also== | ||
Revision as of 16:43, 18 August 2011
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
Solution
It moves in a cycle that goes 
. The cycle has a period of 
.
Thus, after 
jumps, it will be on point 
.
See also
| 1995 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
