100 brown-eyed and 100 blue-eyed perfect logicians live on an island, but none knows the color of their own eyes. There are no mirrors on the island, and communicating is forbidden. If any of them works out the color of their eyes, they must leave the island in the night.
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One day a visitor comes to the island and says, "I see at least one person with blue eyes". What happens next? The surprising result is that nothing happens for a hundred days, then all the blue-eyed people leave, and the next night all the brown-eyed people leave.
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Replying to @propensive
I think all the brown-eyed people shall remain in the island until a visitor says "I see at least one person with brown eyes". 'Cause as you said not everyone knows that everyone knows that everyone knows... there's someone with brown eyes.
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I think it should work if everyone knows there are only two possible eye colors... when all the blue-eyed people leave in one night, that's equivalent to someone saying "I see 100 people with not-blue eyes" and there are only 99 other people on the island. But I'm not certain. ;)
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