The Raven's Hat

The Raven's Hat

Fallen Pictures, Rising Sequences, and Other Mathematical Games

By Jonas Peters and Nicolai Meinshausen

Games that show how mathematics can solve the apparently unsolvable.





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.


$24.95 T ISBN: 9780262044516 192 pp. | 5.375 in x 8 in 25 color illus., 5 b&w illus.


  • “A book of intriguing problems that are simple to state and yet seem impossible to solve. Each problem has been carefully chosen to illustrate an important mathematical concept. The lucid explanations provide aha moments that connect the problems to key ideas in a wide variety of undergraduate courses. A wonderful book for someone who likes mathematics and likes to be challenged!”

    Chris Bernhardt

    author of Quantum Computing for Everyone

  • “This is a fantastic book! It's full of clever and carefully constructed puzzles that will entertain any mathematically curious reader, from novice to expert.”

    Richard J. Samworth

    Professor of Statistical Science, University of Cambridge


  • Choice 2021 Outstanding Academic Title