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

by Jennifer Beineke (Editor), Jason Rosenhouse (Editor)

Overview

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.

Product Details

ISBN-13:	9780691171920
Publisher:	Princeton University Press
Publication date:	09/05/2017
Pages:	408
Product dimensions:	6.10(w) x 9.30(h) x 1.40(d)

About the Author

Jennifer Beineke is professor of mathematics at Western New England University. Jason Rosenhouse is professor of mathematics at James Madison University. Beineke and Rosenhouse are the coeditors of The Mathematics of Various Entertaining Subjects: Research in Recreational Math (Princeton).

Table of Contents

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

What People are Saying About This

From the Publisher

"Every essay in this collection can be appreciated by math enthusiasts of all levels, from high school students to research mathematicians. With work from leading mathematicians such as John Conway, Richard Guy, Bob Bosch, Peter Winkler, Tanya Khovanova, and Erik Demaine, what's not to love?"—Arthur Benjamin, author of The Magic of Math: Solving for x and Figuring out Why

"Recreational math is an important branch of mathematics. The contributions in The Mathematics of Various Entertaining Subjects are of a very high quality and almost all contain new results."—Anany Levitin, coauthor of Algorithmic Puzzles

"The fascinating essays in this collection are written by top scholars who employ diverse mathematical and computational techniques to find surprising answers to intriguing questions. With a nice balance of context and background information, new results, and surveys of known and related results, this book will be useful to a wide array of mathematicians and readers interested in recreational mathematics."—David Richeson, author of Euler's Gem: The Polyhedron Formula and the Birth of Topology

"As enticing as a Rubik's Cube, this rigorous and inviting book is a treat to the eyes and mind. The list of contributors is an all-star lineup ready to welcome you into their mathematical rec rooms. Pull up a chair and grab a friend, it’s time to be entertained with various mathematical subjects."—Tim Chartier, author of Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing

"The fascinating essays in this collection are written by top scholars who employ diverse mathematical and computational techniques to find surprising answers to intriguing questions. With a nice balance of context and background information, new results, and surveys of known and related results, this book will be useful to a wide array of mathematicians and readers interested in recreational mathematics."—David Richeson, author of Euler's Gem: The Polyhedron Formula and the Birth of Topology

Editorial Reviews

"The editors once again have brought together an extraordinary list of authors to produce nineteen engaging papers, split into five groups: puzzles and brainteasers, geometry and topology, graph theory, games of chance, and computational complexity. . . . It is often deeply challenging mathematically and, as a result, all the more fun. Each reader will find chapters that appeal to them."

MAA Reviews

"[This book] is beautiful in that just about every problem could be explained to anybody with almost no mathematics background at all, but the methods of solving them take you deeply into many complex areas of mathematics. The books gathers together problems which pop up through what one might consider 'silly' or 'frivolous' questions, but which lead to new ways of thinking and have applications in enormously wide-ranging areas of mathematics."—-Jonathan Shock, Mathemafrica

From the Publisher

"In the second volume of this engaging series, Beineke . . . and Rosenhouse . . . deliver another fantastic collection of essays dealing with popular mathematics. . . . Anyone who enjoys reading about recreational mathematics will find plenty to enjoy and discover in this second volume."

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