Ants on a log
Here is a version of a very nice puzzle I first saw in Mathematical Puzzles: A Connoisseur's Collection by Peter Winkler
Thirteen ants are standing on a 1 meter long log, each facing one of the two ends. A bell sounds and all the ants start marching in whichever direction they were looking, traveling at a speed of exactly 2 meters per minute. Of course some of the ants will soon run into each other - if this happens, they will instantly turn around and continue marching in the opposite direction. When an ant comes to the end of the log, they will jump of the end.
How long before you can be sure that every ant has jumped off the log?