This problem was one I was assigned in my math class:
On a certain island live 1000 persons, all well acquainted with one another, of whom some have blue eyes and the rest brown eyes. It is an absolute taboo on this island to convey any information on eye color, and mirrors are unknown. It is furthermore an absolutely accepted rule that any person who is able to prove that his/her eyes are blue must, at midnight of the day on which such proof first becomes available, commit suicide. Finally, there is on the island an infallible oracle, whose pronouncements are attended every day at noon by all inhabitants of the island. On one fateful day the oracle stated: "There is at least one blue-eyed person on this island." What, if anything, ensues?

Try and figure it out for yourself - it's pretty damn satisfying to do so... like finally getting that damn squirrel out of your birdseed or something.