The Mathematics of Various Entertaining Subjects, Volume 1: Research in Recreational Math

Foreword by Raymond M. Smullyan 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. Contributors Show How Sophisticated Mathematics Can Help You 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--provided By Publisher. Part I Vignettes: Should You Be Happy? / Peter Winkler -- One-move Puzzles With Mathematical Content / Anany Levitin -- Minimalist Approaches To Figurative Maze Design / Robert Bosch, Tim Chartier, And Michael Rowan -- Some Abcs Of Graphs And Games / Jennifer Beineke And Lowell Beineke -- Part Ii Problems Inspired By Classic Puzzles: Solving The Tower Of Hanoi With Random Moves / Max A. Alekseyev And Toby Berger -- Groups Associated To Tetraflexagons / Julie Beier And Carolyn Yackel -- Parallel Weighings Of Coins / Tanya Khovanova -- Analysis Of Crossword Puzzle Difficulty Using A Random Graph Process / John K. Mcsweeney -- From The Outside In: Solving Generalizations Of The Slothouber-graatsma-conway Puzzle / Derek Smith -- Part Iii Playing Cards: Gallia Est Omnis Divisa In Partes Quattuor / Neil Calkin And Colm Mulcahy -- Heartless Poker / Dominic Lanphier And Laura Taalman -- An Introduction To Gilbreath Numbers / Robert W. Vallin -- Part Iv Games: Tic-tac-toe On Affine Planes / Maureen T. Carroll And Steven T. Dougherty -- Error Detection And Correction Using Set / Gary Gordon And Elizabeth Mcmahon -- Connection Games And Sperner’s Lemma / David Molnar -- Part V Fibonacci Numbers: The Cookie Monster Problem / Leigh Marie Braswell And Tanya Khovanova -- Representing Numbers Using Fibonacci Variants / Stephen K. Lucas. Edited By Jennifer Beineke & Jason Rosenhouse ; With A Foreword By Raymond Smullyan. Includes Bibliographical References And Index. Content: Cover Title Copyright Contents Foreword Preface and Acknowledgments PART I VIGNETTES 1 Should You Be Happy? 2 One-Move Puzzles with Mathematical Content 3 Minimalist Approaches to Figurative Maze Design 4 Some ABCs of Graphs and Games PART II PROBLEMS INSPIRED BY CLASSIC PUZZLES 5 Solving the Tower of Hanoi with Random Moves 6 Groups Associated to Tetraflexagons 7 Parallel Weighings of Coins 8 Analysis of Crossword Puzzle Difficulty Using a Random Graph Process 9 From the Outside In: Solving Generalizations of the Slothouber-Graatsma-Conway Puzzle PART III PLAYING CARDS 10 Gallia Est Omnis Divisa in Partes Quattuor11 Heartless Poker 12 An Introduction to Gilbreath Numbers PART IV GAMES 13 Tic-tac-toe on Affine Planes 14 Error Detection and Correction Using SET^® 15 Connection Games and Sperner's Lemma PART V FIBONACCI NUMBERS 16 The Cookie Monster Problem 17 Representing Numbers Using Fibonacci Variants About the Editors About the Contributors Index