Saturday, September 5, 2009

 

The Blue-Eyed Islander Puzzle

Here is a well-known puzzle that I will probably be teaching next week. An island starts with 2 blue-eyed people and 48 green-eyed, but the people do not know these numbers. If a person ever decides his eyes are blue, he must leave the island at dawn the next day. There are no mirrors and people may not talk about eye color, but they see each others' faces.

What will happen? -- nobody leaves.

Now an outsider comes to the island and says, "At least one of you has blue eyes".

The next dawn, nobody leaves, but on the second dawn, both blue-eyed people leave.

The reason: Both blue-eyed people realize there are either 1 or 2 blue-eyed people. When nobody leaves on the first dawn, each realizes that there must be 2-- and he is one of them.

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