Imagine you are playing handball in outer space (don't think too hard about this... just go with me for a second). You are floating without any gravity in a 10 foot by 10 foot by 10 foot perfectly square room. In front of you is a grid of squares numbered 1 through 25, as in the picture. The back and side walls also have a grid - but the ceiling and floor is blank. You have a rubber ball in your hand.
If you started in the exact center of the room, and threw the ball directly in front of you (and then got out of the way), the ball would hit the middle of the 13 square in front of you, return without friction to the exact center of the room, and then hit the exact center of the wall behind you, before repeating this sequence over and over forever.
Here is some notation to describe the motion of the ball:
F = Front wall
B = Back wall
L = Left wall
R = Right wall
U = Up, the ceiling
D = Down, the floor
So, you can say "F13" which is the middle tile of the front wall. Or, "R25", which is the southeastern-most tile of the right hand wall. Note that there is no "U5" or "U6"... if the ball hits the ceiling, it is just noted as "U".
Also, you can use an apostrophe to represent endless repeating. In this notation, the ball traveled in the first example a path of: (F13 B13)' which is another way of saying F13 B13 F13 B13 F13 B13... (etc.)
What would the result be if you started at the exact center of the room, and threw the ball at the exact middle of the F23 tile?
(F23 D U B3)'
How about throwing the ball from the the exact center of the room to F15? (Scroll for answer)
Center to F15 =
(F15 R11 L11 B15)'
Now, how about the exact center to F14? Answer in a screened comment, and I will post the answer tomorrow night at 11:59 PM Friday (May 14, 2010) with the people who got it correct.
Finally, I can't figure out the exact center to F20. Does anybody want to solve it for me?