Brown Eyes and Red Eyes Solution
There is an island of monks where everyone has either brown eyes or red eyes. Monks who have red eyes are cursed, and are supposed to leave the next morning. However, no one ever talks about what color eyes they have, because the monks have a vow of silence. Thus, no one knows their own eye color; they can only see the eye colors of other people, and not mention them.
Every day, the monks enjoy a silent brunch together at a round table. One day, a tourist visits the island monastery, and, unaware that he's not supposed to talk about eyes, says "At least one of you has red eyes." Having acquired this new information, something dramatic happens among the monks. What happens?
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.