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.

Jonas Peters is Professor of Statistics at the University of Copenhagen. Nicolai Meinshausen is Professor of Statistics at ETH (Swiss Federal Institute of Technology) in Zurich.

1. HAT COLORS AND HAMMING CODES 1
2. TWENTY BOXES AND PERMUTATIONS 17
3. THE DOVETAIL TRICK AND RISING SEQUENCES 33
4. ANIMAL STICKERS AND CYCLIC GROUPS 55
5. OPERA SINGERS AND INFORMATION THEORY 73
6. ANIMAL MATCHING AND PROJECTIVE GEOMETRY 93 6
7. THE EARTH AND AN EIGENVALUE 109
8. THE FALLEN PICTURE AND ALGEBRAIC TOPOLOGY 123 
A. WHAT DO WE MEAN WHEN WE WRITE …? 139
B. WHAT IS … 143 
C. CHAPTER-SPECIFIC DETAILS 157 
REFERENCES 171
INDEX 175