- There's a monastery that is inhabited by Monks.
- 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.
- One day the head monk shows up to inform them that at least one of them is possessed by Satan. (The head monk can talk, obviously.)
- They are informed that if one is possessed it will be indicated with an X on the forehead.
- A possessed monk must leave the monastery.
- Day 1 goes by, no one leaves. Day 2 arrives, no one has left. Day 3, all have left.
Update: the solution