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Box bounce (Posted on 2005-11-17) Difficulty: 4 of 5
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: ( You must be logged in to post comments.)
  Subject Author Date
re(9): weighing in | HintPercy2006-01-01 06:41:42
re(8): weighing in | HintTristan2005-12-15 17:59:27
re(7): weighing in | HintPercy2005-12-15 10:07:50
re(6): weighing in (my error)Jer2005-11-26 13:22:32
re(6): weighing in on the gravity solution (full solution?)Mindy Rodriguez2005-11-23 00:56:59
re(5): weighing in on the gravity solution (full solution?)Tristan2005-11-22 18:51:21
re(4): weighing in on the gravity solution (full solution?)Jer2005-11-22 07:48:04
re(3): weighing in on the gravity solution (full solution?)Tristan2005-11-21 19:05:33
Link and CheckCeeAnne2005-11-21 13:18:35
re(2): weighing in on the gravity solution (full solution?)Jer2005-11-21 10:07:18
SolutionLook At This AgainCeeAnne2005-11-20 12:23:10
re: What do you think?Percy2005-11-19 14:26:21
re: weighing in on the gravity solution (full solution?)Tristan2005-11-18 23:11:54
What do you think?CeeAnne2005-11-18 18:35:50
Some ThoughtsWithout Gravity ThoughtBractals2005-11-18 10:21:58
Solutionweighing in on the gravity solution (full solution?)Jer2005-11-18 09:53:51
top?Cory Taylor2005-11-18 01:04:43
re: AnglePercy2005-11-17 23:46:58
SolutionAdd gravity...Tristan2005-11-17 19:54:03
re(2): Think of this ...CeeAnne2005-11-17 17:13:44
Questionre: Think of this ...Vernon Lewis2005-11-17 16:50:23
SolutionSolution of space version.Charlie2005-11-17 14:57:22
Think of this ...CeeAnne2005-11-17 13:56:16
Second PathCeeAnne2005-11-17 13:14:00
Initial ThoughtsCeeAnne2005-11-17 12:44:59
QuestionAngleowl2005-11-17 11:09:06
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