Difference between revisions of "1995 AIME Problems/Problem 3"
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| + | Starting at <math>\displaystyle (0,0),</math> an object moves in the coordinate plane via a sequence of steps, each of length one. Each step is left, right, up, or down, all four equally likely. Let <math>\displaystyle p</math> be the probability that the object reaches <math>\displaystyle (2,2)</math> in six or fewer steps. Given that <math>\displaystyle p</math> can be written in the form <math>\displaystyle m/n,</math> where <math>\displaystyle m</math> and <math>\displaystyle n</math> are relatively prime positive integers, find <math>\displaystyle m+n.</math> | ||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
| + | * [[1995_AIME_Problems/Problem_2|Previous Problem]] | ||
| + | * [[1995_AIME_Problems/Problem_4|Next Problem]] | ||
* [[1995 AIME Problems]] | * [[1995 AIME Problems]] | ||
Revision as of 21:58, 21 January 2007
Problem
Starting at 
an object moves in the coordinate plane via a sequence of steps, each of length one. Each step is left, right, up, or down, all four equally likely. Let 
be the probability that the object reaches 
in six or fewer steps. Given that can be written in the form 
where 
and 
are relatively prime positive integers, find 
