The Mathematics of Various Entertaining Subjects

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