In the house that math built, there are many rooms. The Unilluminable Room is one of the strangest. How do you build a room that is guaranteed to have one spot of complete darkness? Here's the weird solution to this 26 year mystery.

Imagine a room where all the walls are covered in floor-to-ceiling mirrors. If someone were to light a match in this room, no matter how big or how complicated it was - with little side passages and oddly shaped foyers - you would always see it. The light would bounce off mirrors until it hit every spot in the room. Likewise, if someone were to launch an inexhaustible rubber ball at one of the walls, eventually it would bounce around until it hit you. But what if there were a room in which this wasn't possible? What would it take to create a room that had at least one spot of darkness when a candle was placed in it?

This question was posed in the sixties, and it was puzzled over for decades. As long as all the walls of the room were straight, it seemed impossible to find a mirrored room that a light couldn't illuminate fully.