Difference between revisions of "1995 AHSME Problems/Problem 15"
(New page: ==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-num...) |
(→See also) |
||
| Line 8: | Line 8: | ||
==See also== | ==See also== | ||
| + | {{AHSME box|year=1995|num-b=14|num-a=16}} | ||
| + | |||
| + | [[Category:Introductory Number Theory Problems]] | ||
Revision as of 10:57, 29 September 2008
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 1, 2, 4, 1, 2, 4, etc. Thus after 1995=3*665 jumps, it will be on point 4 
.
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 | ||
