In honour of Patricia C. Wrede
Today at work we bandied about an interesting logic puzzle, and understanding the answer totally blew my mind. It goes like this:
All dragons have either red eyes or green eyes. If a dragon ever knows its own eye color, it will die on the next stroke of midnight. Moreover, dragons, like all mythical beasts, are perfect logicians. That is to say, if it is possible to infer a fact from what is already known, dragons cannot help but make this deduction.
There is a town in which n dragons live, where n is small enough that every day, every dragon interacts with every other dragon. One day, an oracle, renowned for always speaking the truth, comes to the town. She gathers together all the dragons, looks at each one, and then loudly proclaims, “At least one dragon here has red eyes!”
- What happens in the town?
- Suppose that at least three dragons have red eyes. Now, not only does every dragon already know that at least one dragon has red eyes, they also know that every other dragon knows this, too. What information does the oracle add that the dragons didn’t have already?