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 exploring puzzles and brainteasers, research in recreational mathematics has often been neglected.
The Mathematics of Various Entertaining Subjects brings together authors from a variety of specialties to present fascinating problems and solutions in recreational mathematics.
Contributors to the book show how sophisticated mathematics can help construct mazes that look like famous people, how the analysis of crossword puzzles has much in common with understanding epidemics, and how the theory of electrical circuits is useful in understanding the classic Towers of Hanoi puzzle. The card game SET is related to the theory of error-correcting codes, and simple tic-tac-toe takes on a new life when played on an affine plane. Inspirations for the book's wealth of problems include board games, card tricks, fake coins, flexagons, pencil puzzles, poker, and so much more.
Looking at a plethora of eclectic games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.
Author(s): Jennifer Beineke, Jason Rosenhouse, Raymond M. Smullyan
Publisher: Princeton University Press
Year: 2015
Language: English
Pages: 288
City: New Jersey
Tags: Math Games;Puzzles & Games;Humor & Entertainment;History;Mathematics;Science & Math
Foreword by Raymond Smullyan vii
Preface and Acknowledgments x
PART I VIGNETTES
1 Should You Be Happy? 3
Peter Winkler
2 One-Move Puzzles with Mathematical Content 11
Anany Levitin
3 Minimalist Approaches to Figurative Maze Design 29
Robert Bosch, Tim Chartier, and Michael Rowan
4 Some ABCs of Graphs and Games 43
Jennifer Beineke and Lowell Beineke
PART II PROBLEMS INSPIRED BY CLASSIC PUZZLES
5 Solving the Tower of Hanoi with Random Moves 65
Max A. Alekseyev and Toby Berger
6 Groups Associated to Tetraflexagons 81
Julie Beier and Carolyn Yackel
7 Parallel Weighings of Coins 95
Tanya Khovanova
8 Analysis of Crossword Puzzle Difficulty Using a Random Graph Process 105
John K. McSweeney
9 From the Outside In: Solving Generalizations of the Slothouber-Graatsma-Conway Puzzle 127
Derek Smith
PART III PLAYING CARDS
10 Gallia Est Omnis Divisa in Partes Quattuor 139
Neil Calkin and Colm Mulcahy
11 Heartless Poker 149
Dominic Lanphier and Laura Taalman
12 An Introduction to Gilbreath Numbers 163
Robert W. Vallin
PART IV GAMES
13 Tic-tac-toe on Affine Planes 175
Maureen T. Carroll and Steven T. Dougherty
14 Error Detection and Correction Using SET 199
Gary Gordon and Elizabeth McMahon
15 Connection Games and Sperner's Lemma 213
David Molnar
PART V FIBONACCI NUMBERS
16 The Cookie Monster Problem 231
Leigh Marie Braswell and Tanya Khovanova
17 Representing Numbers Using Fibonacci Variants 245
Stephen K. Lucas
About the Editors 261
About the Contributors 263
Index 269
