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The Mathematics of Various Entertaining Subjects

Jennifer Beineke and Jason Rosenhouse, editors
Publisher: 
Princeton University Press
Publication Date: 
2016
Number of Pages: 
272
Format: 
Hardcover
Price: 
75.00
ISBN: 
9780691164038
Category: 
Proceedings
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Charles Ashbacher
, on
02/6/2016
]

The subtitle of the book, Research in Recreational Mathematics, is very appropriate, for most of the papers in this collection are indeed research rather than simple recreations. The concepts are based on topics generally considered recreational mathematics, yet the treatment is in the form of research papers.

For example, there is the paper “Tic-tac-toe on Affine Planes.” It begins with the simple game and then establishes a set of three axioms for an affine plane that is a set of points and a set of lines. Which, in the simplest form is what the basic game is. By expanding it out and allowing a line to be a curve that wraps around, the game becomes much more complex, both to play and to analyze. A game where all is known becomes complicated and challenging.

There is no puzzle more popular than crossword puzzles, which are a staple in the regular print media as well as a daily mental challenge in the lives of millions. In the paper “Analysis of Crossword Puzzle Difficulty Using a Random Graph Process,” a probability model is developed that can be used to analyze the inherent difficulty of specific puzzles in their raw form. Simulations are also used to create data supporting the value of the model.

There are 17 papers in this collection, covering many areas of recreational math and games. Applications sneak in as well, in the paper “Error Detection and Correction using SET©,” the card game is used to model error correcting codes, a necessary feature of ensuring error-free electronic transmission. In other words, keeping civilization as we know it functioning.

Even if you are someone that does not consider recreational mathematics to be real math, there is no denying the conclusion that this is real math. 


Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, and teaching college classes. In his spare time, he reads about these things and helps his daughter in her lawn care business.

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

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