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.

Explain the concept of common knowledge as it relates to the prisoners' situation.

What could you have said to spare the prisoners additional days on the island?