Charles R. DePrima Memorial Lecture in Mathematics

We are guests at the Midnight Ball, amongst infinitely many friends, and everyone has a natural number written on their forehead. We can see the other numbers, but not our own. The Queen of the Ball is chosen, and she alone is allowed to change her number to whatever she likes. At midnight, we are to shout our best guess for our own number. With advance planning—but no communication after we have our numbers—how well can we do? Find out at the talk, where we shall also explore many other puzzles. We shall meet the blue-eyed islanders and the pirates dividing their treasure. Some solutions rely on the axiom of choice. I shall conclude with the nearly perfect prediction theorem, showing how to predict the current and future values of an unknown (possibly discontinuous) function on the real numbers, with almost-everywhere perfect accuracy, based solely on the history of prior values.