Mock AIME 6 2006-2007 Problems/Problem 11
Problem
Each face of an octahedron is randomly colored blue or red. A caterpillar is on a vertex of the octahedron and wants to get to the opposite vertex by traversing the edges. The probability that it can do so without traveling along an edge that is shared by two faces of the same color is 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
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