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Medium · Game Theory & Logic · Quant Trader interview question · game-theory, logic, common-knowledge, mutual-knowledge
Consider the classic Blue Eyes puzzle: On an island, there are 100 people. Everyone can see everyone else, but no one can see their own eye color. It is known that some people have blue eyes. Islanders are forbidden from discussing eye color. However, if an islander knows they have blue eyes, they must leave the island at dawn the next day. All islanders are perfectly logical and know that all other islanders are perfectly logical (and know that all other islanders know this, and so on). One day