Some bumper cars are moving around a circular track at the same constant speed. However, they are not all going in the same direction. Collisions are perfectly elastic, so that two colliding cars instantaneously change directions (and continue at the same speed).

Show that at some point in the future, all the cars will be back to their starting positions and directions. Assume that each car has no length.

(In reply to Solution by Larry)

Quote="Larry":So once N periods have gone by, there should be at least one time when each car was at its original starting location.

Well, to be frank, I too have the same thought that after a certain period, after an infinite collisions, the cars would indeed return return to their original positions. But, I see no prove to this, thought I do believe this is true. In addition, after INFINITE collisions... I too believe this is true. But to be fair, a prove is still needed, and the number of times, must be finite.

Posted by Vee-Liem Veefessional on 2004-12-31 07:52:09