TED-Ed: The famously difficult green-eyed logic puzzle - Alex Gendler

A group of 100 prisoners with green eyes are trapped by a dictator. They can only escape if they know their eye color, but they can't communicate or see their own eyes. A visitor tells them, 'At least one of you has green eyes.' Using logic and inductive reasoning, they deduce their own eye color over 100 days and escape. The key is common knowledge, where each prisoner knows that everyone else is aware of the same information.

What is the unique rule that allows prisoners to escape?

• They must solve a riddle given by the guards.

• They must win a game of chess against the dictator.

• They can leave if they have green eyes.

• They need to find a hidden key.

Why do Adria and Bill not leave on the first night?

• They are afraid of the dark.

• They are waiting for a signal from the narrator.

• They are unsure if the guards are watching.

• They each see one person with green eyes and are unsure about their own eye color.

What new information do Adria and Bill gain on the second morning?

• They find a note from the narrator.

• They discover a hidden mirror.

• They understand that the other person also sees a green-eyed person.

• They realize the guards have left the island.

How does the presence of a third prisoner, Carl, change the deduction process?

• It requires them to wait an additional night to confirm their own eye color.

• It causes confusion and they decide not to leave.

• It makes it impossible for anyone to leave.

• It allows them to leave immediately.

What is the key concept that allows all prisoners to eventually escape?

• The dictator changes the rules.

• The concept of common knowledge.

• The prisoners find a way to communicate secretly.

• The guards fall asleep.