The Raven's Hat: Fallen Pictures, Rising Sequences, and Other Mathematical Games

Games that show how mathematics can solve the apparently unsolvable.

This book presents a series of engaging games that seem unsolvable—but can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high school–level math, to experience the joy of mathematical discovery.

The authors set up each game, specifying the number of players and props needed, and show readers how mathematical language reveals the problem's underlying structure. They explain the mathematical concepts with many examples, describe the history of the problem, and offer practical advice. Colorful and clever illustrations, featuring a flock of mathematically inclined ravens, help clarify things. All of the games can be presented to an audience; each one runs from sixty to ninety minutes, suitable for seminar presentations or lectures. The authors aim at maintaining mathematical precision while avoiding overly complex notation. Appendixes go into more detail, reviewing frequently used mathematical symbols, providing further information on a range of mathematical concepts, and offering chapter-specific mathematical explanations.