The Island...

A group of people live on an island. They are all perfect logicians -- 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 night.

On this island live 100 blue-eyed people, 100 brown-eyed people, and the Guru. The Guru has green eyes. Everyone on the island knows the rules (but are not given the total numbers) and is constantly aware of everyone else's eye color. Everyone keeps a constant count of the total number they see of each (excluding themselves). However, they cannot otherwise communicate. 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, 100 blue.

The Guru speaks only once in all their endless years on the island. Standing before the islanders, she says the following:

"I can see someone with blue eyes."

Who leaves the island, and on what night?

There are no mirrors or reflecting surfaces, nothing dumb, It is not a trick question, and the answer is logical. It doesn't depend on tricky wording, and it doesn't involve people doing something silly like creating a sign language or doing genetics. The Guru is not making eye contact with anyone in particular; she's simply saying "I count at least one blue-eyed person on this island who isn't me."

And lastly, the answer is not "no one leaves."

This is a pretty tricky logic puzzle. Tim, Jeff, Beth, and I discussed it for about an hour the other night. Tim & Jeff already knew the answer, but we had to work through it to fully understand it. We even acted it out after we thought we had it solved.

My best recommendation is think about it in a small number first, then work up to the 200 people. Good luck!