Head Games

Image: Wikimedia Commons

Or how about this amazing result. Each of a million men puts his hat into a very large box. Every hat has its owner’s name on it. The box is given a good shaking, and then each man, one after the other, randomly draws a hat out of the box. What’s the probability that at least one of the men gets his own hat back? Most people would answer with ‘pretty slim,’ but in fact the answer is the astonishingly large 0.632! Who would have guessed that?

— Paul J. Nahin, Will You Be Alive 10 Years From Now?, 2014