Spring Round (2012) #10
Source:
December 4, 2012
Problem Statement
You are at one vertex of a equilateral triangle with side length . All of the edges of the equilateral triangle will reflect the laser beam perfectly (angle of incidence is equal to angle of reflection). Given that the laser beam bounces off exactly edges and returns to the original vertex without touching any other vertices, let be the maximum possible distance the beam could have traveled, and be the minimum possible distance the beam could have traveled. Find .