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 Angle by owl)

Owl, I was just referring to the incoming and outgoing angles the motion makes with the surface in each individual bounce. The problem was not intended to give any info about the angles that the ball enters and leaves the box. Sorry for any confusion.

Also I should point out that the sentence "(All conditions are the same except the ball is now affected by gravity.)" Was intended to imply that the condition: "The ball travels in a perfectly straight line" is no longer true. Hopefully this is obvious? Just want to be precise.

Posted by Percy on 2005-11-17 23:46:58