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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)

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 Subject Author Date re(9): weighing in | Hint Percy 2006-01-01 06:41:42 re(8): weighing in | Hint Tristan 2005-12-15 17:59:27 re(7): weighing in | Hint Percy 2005-12-15 10:07:50 re(6): weighing in (my error) Jer 2005-11-26 13:22:32 re(6): weighing in on the gravity solution (full solution?) Mindy Rodriguez 2005-11-23 00:56:59 re(5): weighing in on the gravity solution (full solution?) Tristan 2005-11-22 18:51:21 re(4): weighing in on the gravity solution (full solution?) Jer 2005-11-22 07:48:04 re(3): weighing in on the gravity solution (full solution?) Tristan 2005-11-21 19:05:33 Link and Check CeeAnne 2005-11-21 13:18:35 re(2): weighing in on the gravity solution (full solution?) Jer 2005-11-21 10:07:18 Look At This Again CeeAnne 2005-11-20 12:23:10 re: What do you think? Percy 2005-11-19 14:26:21 re: weighing in on the gravity solution (full solution?) Tristan 2005-11-18 23:11:54 What do you think? CeeAnne 2005-11-18 18:35:50 Without Gravity Thought Bractals 2005-11-18 10:21:58 weighing in on the gravity solution (full solution?) Jer 2005-11-18 09:53:51 top? Cory Taylor 2005-11-18 01:04:43 re: Angle Percy 2005-11-17 23:46:58 Add gravity... Tristan 2005-11-17 19:54:03 re(2): Think of this ... CeeAnne 2005-11-17 17:13:44 re: Think of this ... Vernon Lewis 2005-11-17 16:50:23 Solution of space version. Charlie 2005-11-17 14:57:22 Think of this ... CeeAnne 2005-11-17 13:56:16 Second Path CeeAnne 2005-11-17 13:14:00 Initial Thoughts CeeAnne 2005-11-17 12:44:59 Angle owl 2005-11-17 11:09:06

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