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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See also
2002 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |