There's a spaceperson with a very bouncy ball and a rigid box in the form of a cube with one face missing. One day she throws the ball into the box and notices the ball bounces off each face exactly once before exiting through the missing face.

(The ball travels in a perfectly straight line, being unaffected by air resistance, spin or any other forces other than the reactions with the box. Also the ball bounces symmetrically such that the incoming angle is identical to the outgoing angle and again is unaffected by spin. Also, the box cannot be moved while the ball is in motion.)

How many different combinations are there of the order in which the ball can bounce off all five faces?

On returning to Earth our spaceperson notices that new combinations are possible.

(All conditions are the same except the ball is now affected by gravity.)
How many different combinations are there of the order in which the ball can bounce off all five faces now?

(In reply to re(5): weighing in on the gravity solution (full solution?) by Tristan)

I was the one making a wrong assumption.  Namely that the ball loses energy when it hits the bottom of the box.

I now agree that my idea does not work with a flat box.

It probably will I the box is tilted somewhat to 'simulate' a loss of energy.  This may be beyond my abilities, but I plan to try it.  I know I won't be able to ascii a picture...

I'll just see what I can do.

Posted by Jer on 2005-11-26 13:22:32