Over dinner last night with two math professors / yoga partners, one brought up a similar puzzle:
An order of perfectly logical monks lives isolated in their monastery. They are sworn not to communicate with each other in any way. They have no mirrors, and no other means by which a monk can see his own face. They see each other only once each day when they all gather together for afternoon prayers.
There is a demon loose in the land - the relativity demon. If a person becomes possessed by this demon, the demon's sign (e=mc2) appears on his forehead. The monks know that this is a very powerful demon -- one that can never be exorcised -- and so, if a monk would discover that he bore this mark, that evening, in the privacy of his cell, he would commit suicide.
One afternoon, a visitor (one who is not sworn to silence) comes to the prayer meeting. He looks around the room, announces "At least one monk in this room has the demon's mark on his forehead", and immediately leaves. The monks all look around, examining each other's foreheads. Nothing unusual happens that evening.
At the second day's prayer meeting the monks all look at each other, but again that evening nothing unusual occurs.
...and so on for the third, fourth, fifth, and sixth days.
But on the seventh evening, all the monks commit suicide.
What happened? How many monks were there? How many had the demon's mark?
(copied from "gnome"'s post at Physics Forums)
I like this one because it's funny. Poor monks!
I think I ran across these puzzles years ago when I was reading fun books by Hofstadter, Gardner, and Smullyan instead of doing my assigned problem sets. Good times.