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 thought by Tristan)

The problem states that all are going at the same constant speed.

Posted by Charlie on 2005-01-01 16:57:18