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Hard · Game Theory & Logic · Quant Trader interview question · logic, game-theory, common-knowledge, induction
An island has 100 inhabitants, all perfect logicians. Each inhabitant can see the eye color of every other inhabitant, but they cannot see their own eye color. It is common knowledge that some of the inhabitants have blue eyes, but no one knows how many. In fact, 39 inhabitants have blue eyes. The islanders are forbidden from discussing eye color. One day, a visitor arrives and announces, "I see someone with blue eyes." The visitor speaks truthfully and leaves. Assuming all islanders are perf