Difference between revisions of "2014 AIME I Problems/Problem 11"
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== Problem 11 == | == Problem 11 == | ||
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| + | A token starts at the point <math>(0,0)</math> of an <math>xy</math>-coordinate grid and them makes a sequence of six moves. Each move is 1 unit in a direction parallel to one of the coordinate axes. Each move is selected randomly from the four possible directions and independently of the other moves. The probability the token ends at a point on the graph of <math>|y|=|x|</math> is <math>\frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. | ||
== Solution == | == Solution == | ||
Revision as of 18:16, 14 March 2014
Problem 11
A token starts at the point 
of an 
-coordinate grid and them makes a sequence of six moves. Each move is 1 unit in a direction parallel to one of the coordinate axes. Each move is selected randomly from the four possible directions and independently of the other moves. The probability the token ends at a point on the graph of 
is 
, where 
and 
are relatively prime positive integers. Find 
.
