Mock AIME 3 2006-2007 Problems/Problem 8

Problem

A cube has vertices $(0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0)$ , and $(1,1,1)$ . At $t=0$ , a particle is at $(12,12,0)$ . After one second, the particle travels to $(\frac{9}{16},\frac{5}{8},\frac{1}{13})$ . The particle bounces until it hits an edge or a corner at which point it stops. If the particle travels in straight lines with uniform speed, find the time (in seconds) when the particle stops motion.

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Mock AIME 3 2006-2007 Problems/Problem 8

Problem