TL;DR
Blue Eyes and Common Knowledge: A canonical quantitative trading interview question at foundation difficulty. Commonly asked at Jane Street, SIG, Optiver.
By Valenke Exam Prep Team·Last updated 2026-06-01
foundationLogic & Constraints
Blue Eyes and Common Knowledge
Asked at: Jane Street, SIG, Optiver
Problem
On an island, 100 people have blue eyes and the rest have brown. Everyone can see others' eye colors but not their own. There are no mirrors. If someone deduces their own eye color, they must leave at midnight. A visitor announces: "At least one of you has blue eyes." When do the blue-eyed people leave, and why does the announcement matter when everyone already sees blue-eyed people?
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