The Mathematics of Various Entertaining Subjects : Research in Games, Graphs, Counting, and Complexity, Volume 2

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. 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. This book returns with a brand-new compilation of fascinating problems and solutions in recreational mathematics. It 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. Chapters contain new results, and include short expositions on the 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. Contents Foreword Preface and Acknowledgments PART I. PUZZLES AND BRAINTEASERS 1. The Cyclic Prisoners 2. Dragons and Kasha 3. The History and Future of Logic Puzzles 23 Jason Rosenhouse 4. The Tower of Hanoi for Humans 5. Frenicle’s 880 Magic Squares PART II GEOMETRY AND TOPOLOGY 6. A Triangle Has Eight Vertices But Only One Center 7. Enumeration of Solutions to Gardner’s Paper Cutting and Folding Problem 8. The Color Cubes Puzzle with Two and Three Colors 9. Tangled Tangles PART III GRAPH THEORY 10. Making Walks Count: From Silent Circles to Hamiltonian Cycles 11. Duels, Truels, Gruels, and Survival of the Unfittest 12. Trees, Trees, So Many Trees 13. Crossing Numbers of Complete Graphs PART IV GAMES OF CHANCE 14. Numerically Balanced Dice 15. A TROUBLE-some Simulation 16. A Sequence Game on a Roulette Wheel PART V COMPUTATIONAL COMPLEXITY 17. Multinational War Is Hard 18. Clickomania Is Hard, Even with Two Colors and Columns 19. Computational Complexity of Arranging Music About the Editors About the Contributors Index