The game of trilliards is just like billiards except that it is played on a triangular table.  Of course, as in regular billiards, balls rebound off the bumpers by the usual light-reflection rules:  the angle of reflection equals the angle of incidence.  

In the trilliards game shown on the left, the table is in the shape of an isosceles triangle with the angle at B measuring 30° and the other two angles equal.  Suppose a ball is placed at corner A and shot toward side BC.  (The sketch shows an example of a one path the ball might follow, with the outbound path (1,2,3) in red and the return path (3,4,5) in green.) 

At what initial angle (measured from side AC) should you hit the ball toward side BC so as to maximize the number of rebounds the ball will make before it again reaches side AC?   (The ball in the diagram makes three rebounds before reaching side AC.)

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ã2003 Alberto L. Delgado