We consider a classic “paradox” where a simple inductive proof seems to clash with intuition. Though the proof makes clear that the naive intuition is wrong, it’s hard to pinpoint exactly where the intuition’s logical error is. After discussing the paradox at some length with my family, we came up with an angle of attack that gives an intuitive framework that matches the math and makes clearer why the naive intuition is wrong.

The situation is as follows. Dragons are a perfectly honest and rational species with color vision and either red or blue eyes. One hundred red-eyed dragons are on an island and are sworn to a two-part pact:

- they will not communicate with each other, look at reflections, or otherwise directly find out what color eyes they have, and
- if they can logically deduce some day that they have red eyes, then they will leave the island that night.

The dragons live for years on the island, each of them seeing ninety-nine red-eyed dragons but none of them able to logically deduce that they too have red eyes. One day, a perfectly honest visitor comes to the island, announces that at least one of the dragons has red eyes, and leaves.

If you haven’t heard this before, try to figure out before continuing: what happens?