Line segments OA and OB meet at O with an angle of 1 degree. Points C and D bisect OA and OB respectively. For the purists, the line segments are all defined to include their leftmost point, but exclude their rightmost point. For example, CA includes the point at C, but not the point at A.

Imagine that the segments CA and DB act as reflective mirrors, and that a light ray in the plane enters the larger opening AB, bounces back and forth between the two mirrors for a while and then exits. What is the maximum number of reflections that are possible?

The applet below illustrates the reflection pattern for various wedge angles. Don't toggle the "Show Solution" button unless you really want to see the solution and spoil your fun.