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 Box bounce (Posted on 2005-11-17)
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?

 No Solution Yet Submitted by Sir Percivale Rating: 4.1429 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(8): weighing in | Hint | Comment 25 of 26 |
(In reply to re(7): weighing in | Hint by Sir Percivale)

I hate to be a killjoy, but I'm fairly sure I already proved that a tilted box doesn't work any better, however unclear my proof might have been.  It's simply a matter of breaking the gravity vector into x, y, and z vectors.

However, if the gravitational field were uneven... you've got yourself 5! combinations.

 Posted by Tristan on 2005-12-15 17:59:27

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