The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects now returns with a brand-new compilation of fascinating problems and solutions in recreational mathematics.This latest volume gathers together the top experts in recreational math and presents a compelling look at board games, card games, dice, toys, computer games, and much more. The book is divided into five parts: puzzles and brainteasers, geometry and topology, graph theory, games of chance, and computational complexity. Readers will discover what origami, roulette wheels, and even the game of Trouble can teach about math. Essays contain new results, and the contributors include short expositions on their topic's background, providing a framework for understanding the relationship between serious mathematics and recreational games. Mathematical areas explored include combinatorics, logic, graph theory, linear algebra, geometry, topology, computer science, operations research, probability, game theory, and music theory.Investigating an eclectic mix of games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.

Foreword by Ron Graham vii
Preface and Acknowledgments xi
I PUZZLES AND BRAINTEASERS
1 The Cyclic Prisoners 3
Peter Winkler
2 Dragons and Kasha 11
Tanya Khovanova
3 The History and Future of Logic Puzzles 23
Jason Rosenhouse
4 The Tower of Hanoi for Humans 52
Paul K. Stockmeyer
5 Frenicle's 880 Magic Squares 71
John Conway, Simon Norton, and Alex Ryba
II GEOMETRY AND TOPOLOGY
6 A Triangle Has Eight Vertices But Only One Center 85
Richard K. Guy
7 Enumeration of Solutions to Gardner's Paper Cutting and Folding Problem 108
Jill Bigley Dunham and Gwyneth R. Whieldon
8 The Color Cubes Puzzle with Two and Three Colors 125
Ethan Berkove, David Cervantes-Nava, Daniel Condon, Andrew Eickemeyer, Rachel Katz, and Michael J. Schulman
9 Tangled Tangles 141
Erik D. Demaine, Martin L. Demaine, Adam Hesterberg, Quanauan Liu, Ron Taylor, and Ryuhei Uehara
III GRAPH THEORY
10 Making Walks Count: From Silent Circles to Hamiltonian Cycles 157
Max A. Alekseyev and Gérard P. Michon
11 Duels, Truels, Gruels, and Survival of the Unfittest 169
Dominic Lanphier
12 Trees, Trees, So Many Trees 195
Allen J. Schwenk
13 Crossing Numbers of Complete Graphs 218
Noam D. Elkies
IV GAMES OF CHANCE
14 Numerically Balanced Dice 253
Robert Bosch, Robert Fathauer, and Henry Segerman
15 A TROUBLE-some Simulation 269
Geoffrey D. Dietz
16 A Sequence Game on a Roulette Wheel 286
Robert W. Vallin
V COMPUTATIONAL COMPLEXITY
17 Multinational War Is Hard 301
Jonathan Weed
18 Clickomania Is Hard, Even with Two Colors and Columns 325
Aviv Adler, Erik D. Demaine, Adam Hesterberg, Quanquan Liu, and Mikhail Rudoy
19 Computational Complexity of Arranging Music 364
Erik D. Demaine and William S. Moses
About the Editors 379
About the Contributors 381
Index 387