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?

    ... with straight line motion ... all reflections lie in a plane and on the circumference of a circle. The box doesn't really have cardinal points so there's just two distinct cases for a circle to fit: one tilted to touch side/side/bottom/side/side and the other along the box's diagonal to touch 2 sides/bottom/2 sides.

    In space, ball speed isn't critical and goes the direction she throws it but back on Earth our SpacePerson needs to adjust her throw to make the ball bounce the way she wants.  Cee

Posted by CeeAnne on 2005-11-20 12:23:10