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?
(In reply to
re(4): weighing in on the gravity solution (full solution?) by Jer)
The y coordinate of a bouncing ball (without friction) is not
described by the equation abs( h  1/2*g*tē ) as your drawing seems to
imply. If it were, the ball would bounce twice, and then
accelerate infinitely in the direction opposite gravity.
The force of gravity is such that whether we go backwards or forwards
in time, the force of gravity affects the path of a ball the same
way. The path of the ball should be symmetrical about the
vertical line going through the bouncing point. So your
"unfolded" drawing is more correctly drawn this way:
_ _
XXXXXXXXXXXXXXXXXXXXXXXXXX 
X __ X X X__
X  X X 
X  X  X
X X  X  X
X X  X  X
X X  X X
X X VX X
XXXXXXXXXXXXXXXXXXXXXXXXXXXX
If you still think that gravity creates more possibilities, show me
a counterexample. Give me a gravity vector, an initial velocity
vector, and an initial position on the "open" face of the box (2d or
3d). I take physics, I know how to calculate these things.

Posted by Tristan
on 20051122 18:51:21 