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?
Hmmm ... Bractals has a point.
Reviewing this ... that would mean all reflections would lie in a plane ... thus for them to contact each face just once they would be tangent points of a circle larger than the inscribed circle of a side but within some range of nearly fitting.
This would mean just 4 distinct positions for the circle and 4 distinct ways of bouncing the ball ... unless you count starting counterclockwise instead of clockwise ... in that case there's 8 distinct ways to bounce it and being on Earth with gravity should make no difference.
So, 8 ways either way.
What do you think? Cee

Posted by CeeAnne
on 20051118 18:35:50 