A version of billiards is played on a right triangular table, with a pocket in each of the three corners, and one of the acute angles being 30o. A ball is played from just in front of the pocket at the 30o. vertex toward the midpoint of the opposite side. Prove that if the ball is played hard enough, it will land in the pocket of the 60o vertex after 8 reflections. geometrygeometric transformationreflectioncombinatorial geometrycombinatorics