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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