Red-eyed Monks Puzzle - Solution
The Puzzle:
If a monk discovers he has red eyes he must leave that night.
All is well until a visitor says "at least one of you has red eyes!"
What happens next?
Our Solution:If there is only one red-eyed monk, he will only see non-red eyed monks, and know he must be the one! He will leave that night.
If there are two red-eyed monks, one will see the other red eye monk. Next morning, when the other monk didn't leave, it must be because he sees another monk with red eyes ... which must be him! So they will both leave on the second night.
If there are three red-eyed monks, they will follow the logic above and realize there must be three red-eyed monks after the second night, so all three will leave on the third night.
And so on!
But if the tourist lied ... they will all leave that night, and the monastery will be deserted.
If there are two red-eyed monks, one will see the other red eye monk. Next morning, when the other monk didn't leave, it must be because he sees another monk with red eyes ... which must be him! So they will both leave on the second night.
If there are three red-eyed monks, they will follow the logic above and realize there must be three red-eyed monks after the second night, so all three will leave on the third night.
And so on!
But if the tourist lied ... they will all leave that night, and the monastery will be deserted.