Another Information Theory Riddle The following nice riddle is a quote from the excellent, free-to-download book: Information Theory, Inference, and Learning Algorithms, written by David J.C. MacKay. > In a magic trick, there are three participants: the magician, an assistant, and a volunteer. > > The assistant, who claims to have paranormal abilities, is in a soundproof room. The magician gives the volunteer six blank cards, five white and one blue. The volunteer writes a different integer from 1 to 100 on each card, as the magician is watching. The volunteer keeps the blue card. The magician arranges the five white cards in some order and passes them to the assistant. > > The assistant then announces the number on the blue card. > > How does the trick work?

The five cards are uniquely identified by their numbers (low to high). There are $5!=120$ possible orderings for the five cards, which is more than enough to encode the number on the sixth card. In fact, by orienting the cards carefully, there are 4 ways to orient each card and still make a pile (180 degree rotation, turn upside down), there could be $4^55!=122880$ possibilities. I'd only try this variation with a lot of practice, though.