An island has 100 inhabitants who all have either blue eyes or brown eyes, but nobody knows their own eye color. They are forbidden from speaking about eye color. Every day at noon, a ferry arrives to take away anyone who has deduced their own eye color. A visitor arrives and publicly announces: "At least one person here has blue eyes." If exactly 3 people on the island have blue eyes, on which day will they leave?
On the third day
If 1 person had blue eyes, they would see 0 blue-eyed people and leave on Day 1. If 2 people had blue eyes, each would see 1 blue-eyed person, expect them to leave on Day 1, and when they didn't, both would leave on Day 2. With 3 blue-eyed people, each sees 2 blue-eyed people and expects them to leave on Day 2. When nobody leaves on Day 2, all 3 realize they also have blue eyes and leave on Day 3.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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