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That's right
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I must not be understanding something! When the visitor goes there, no one is there because everyone has left.
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deleted by author
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ah! ok. If that's the case, I can only see one possibility: using water as a mirror! Ahhah
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Think about the case of just one person having blue eyes. What would they know and do?
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They know there are 200 people on the island, and each person knows the eye color of 199 of them.