A group of people live on an island. They are all perfect logicians â€” if a conclusion can be logically deduced, they will do it instantly. No one knows the color of their eyes. Every night at midnight, a ferry stops at the island. If anyone has figured out the color of their own eyes, they must leave the island that midnight.
On this island live 100 blue-eyed people, 100 brown-eyed people, and the Guru. The Guru has green eyes, and does not know her own eye color (if she did, she would have to leave). Everyone on the island knows the rules and is constantly aware of everyone elseâ€™s eye color, and keeps a constant count of the total number of each (excluding themselves). So any given blue-eyed person can see 100 people with brown eyes and 99 people with blue eyes, but that does not tell them their own eye color; it could be 101 brown and 99 blue. Or 100 brown, 99 blue, and the one could have red eyes.
No one on the island can speak except the Guru. The Guru speaks only once (letâ€™s say at noon), on one day in all their endless years on the island. Standing before the islanders, she says the following: â€œI can see someone with blue eyes.â€?
Who leaves the island, and how many night after the Guru makes her proclamation?
There are no mirrors or reflecting surfaces, nothing dumb, It is not a trick question, and the answer is logical. It doesnâ€™t depend on tricky wording, and it doesnâ€™t involve people doing something silly like creating a sign language or doing genetic tests. The Guru is not making eye contact with anyone in particular; sheâ€™s simply saying â€œI count at least one blue-eyed person on this island who isnâ€™t me.â€?