The puzzle: A prize is hidden under one of the cups. You pick a cup — then the host (who knows where the prize is) lifts one of the other cups to show it is empty. Now you can Switch to the remaining cup, or Stay with your first choice. Should you switch?

The answer: Always switch! With 3 cups, staying wins 1 in 3 times, but switching wins 2 in 3 times. With N cups, switching wins (N−1)/N of the time.