2002 AIME I Problems/Problem 11
Problem
Let 
and 
be two faces of a cube with 
. A beam of light emanates from vertex 
and reflects off face at point 
, which is 7 units from 
and 5 units from 
. The beam continues to be reflected off the faces of the cube. The length of the light path from the time it leaves point until it next reaches a vertex of the cube is given by 
, where 
and 
are integers and is not divisible by the square of any prime. Find 
.
Solution
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