HardBrain Teasers
The Blue-Eyed Islanders
Jane StreetTwo Sigma
On an island live 100 blue-eyed people and some brown-eyed people. Nobody knows their own eye colour, everyone sees everyone else’s, and anyone who deduces their own colour must leave that midnight. All islanders are perfect logicians and this is common knowledge. One day a visitor announces to everyone: “At least one of you has blue eyes.” On which night do the blue-eyed islanders leave?
Approach
Solve it for 1 and 2 blue-eyed islanders first.
Ask what the announcement changes if everyone already sees blue eyes.
Answer
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