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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What do we know really?
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Well it’s obviously something to do with the hypothetical knowledge of the people who are not oneself. So if I have brown eyes then on the 99th night all the blues should go. Seems like this could be worked out backwards. But I can’t be arsed.
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