Difference between revisions of "2003 AIME II Problems/Problem 13"
m |
m |
||
| Line 1: | Line 1: | ||
| − | |||
== Problem == | == Problem == | ||
| + | A bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls along a side of the triangle to that vertex. Given that the probability that the bug moves to its starting vertex on its tenth move is <math>m/n,</math> where <math>m</math> and <math>n</math> are relatively prime positive integers, find <math>m + n.</math> | ||
== Solution == | == Solution == | ||
| Line 6: | Line 6: | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2003|n=II|num-b=12|num-a=14}} | |
| − | |||
| − | |||
| − | |||
| − | |||
Revision as of 14:41, 21 November 2007
Problem
A bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls along a side of the triangle to that vertex. Given that the probability that the bug moves to its starting vertex on its tenth move is 
where 
and 
are relatively prime positive integers, find 
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 2003 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
