## Bouncing Ball

#### Problem

A ball is projected from the bottom left corner of unit square $ABCD$ into its interior. We shall assume that the speed of the ball remains constant and it will continue bouncing off the edges until it arrives at a corner. For example, if the ball strikes $\frac{2}{3}$ of the way from $D$ to $C$ it will terminate at $D$.

Where must the ball strike on $DC$ to finish at $A$?

Problem ID: 363 (28 Oct 2009) Difficulty: 3 Star