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YouTube // TED-Ed

Can You Solve the Green-Eyed Logic Puzzle?

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YouTube // TED-Ed

If you like logic puzzles, you'll love this. If you dislike logic puzzles, this may frustrate you. Either way, the answer is difficult to sort out, but it is a fascinating bit of inductive reasoning.

In the green-eyed logic puzzle, there is an island of perfectly logical people (or in some variants, dragons) who have green eyes—but they don't know that. They have been imprisoned on this island since birth.

On the island, green-eyed people are allowed to leave, but only under dangerous circumstances—they have to go alone, at night, to a guard booth, where the guard will examine eye color and either let the person go (green eyes) or throw them in the volcano (non-green eyes). The tricks are: people don't know their own eye color; they can never discuss or learn their own eye color (only inference is allowable); they can only leave at night; and they are given only a single hint when someone from the outside visits the island.

Given all these conditions, it's tempting to start thinking that the answer has something to do with genetics, or changing eye colors, or secretly sharing information—but there is really no "trick" here skirting around the no-communication rule. It's all about logic, and specifically the concept of common knowledge (not the kind politicians refer; rather, the kind logicians discuss).

Enjoy this tricky puzzle, and be glad you don't live on a murder-island:

For more, check out this TED-Ed lesson page or check out this io9 puzzle based on the same puzzle (but specifically based on green-eyed dragons, apparently introduced by a Harvard professor).

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