Taking Sudoku Seriously The Math Behind the

Venues that publish Sudoku puzzles are quick to assure readers that, the presence of numbers notwithstanding, no mathematics is required to solve them. In so doing they perpetuate a tragic misunderstanding of mathematics, one that equates it with the drudgery of rote arithmetic. Though Sudokupuzzles do not directly involve arithmetic, they are all about mathematics. Taking Sudoku Seriously sets out to correct this error by using Sudoku puzzles as the foundation for an introduction to higher mathematics. The clear thinking and logical reasoning used in solving Sudoku are precisely the tools employed by research mathematicians in their work. Questions a curious person might ask about Sudoku lead naturally to ideas in combinatorics, graph theory and algebra. The mechanics of generating interestingpuzzles force you to confront the difficulties inherent in searching large spaces. This book is the very first of its kind to connect Sudoku puzzles with these key mathematical concepts. As both a math book and a puzzle book, it will change the readers look at both Sudoku and mathematics, servingboth as a gateway to mathematics for Sudoku fans and as an exploration of the intricacies of Sudoku for mathematics buffs.Since mathematics is learned by doing, the book includes a large number of intriguing puzzles, many of them novel variations on Sudoku. This visually stunning and elegantly written book will appeal to anyone with a taste for mathematics. Even better, those who claim they do not like mathematicsmight find that they have simply never encountered the real thing. With high school mathematics as the only prerequisite, this book is accessible to nearly anyone.

Jason Rosenhouse is Associate Professor of Mathematics at James Madison University and author of The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser.
Laura Taalman is Professor of Mathematics at James Madison University and co-founder of Brainfreeze Puzzles. She is the author of Integrated Calculus and co-author of three books of original Sudoku puzzles.

Preface	p. ix
Playing the Game: Mathematics as Applied Puzzle-Solving	p. 3
Mathematics and Puzzles	p. 5
Forced Cells	p. 9
Twins	p. 11
X-Wings	p. 13
AriadneÆs Thread	p. 15
Are We Doing Math Yet?	p. 16
Triplets, Swordfish, and the Art of Generalization	p. 19
Starting Over Again	p. 21
Latin Squares: What Do Mathematicians Do?	p. 25
Do Latin Squares Exist?	p. 27
Constructing Latin Squares of Any Size	p. 30
Shifting and Divisibility	p. 33
Jumping in the River	p. 38
Greco-Latin Squares: The Problem of the Thirty-Six Officers	p. 40
Do Greco-Latin Squares Exist?	p. 41
EulerÆs Greco-Latin Square Conjecture	p. 44
Mutually Orthogonal Gerechte Designs	p. 47
Mutually Orthogonal Sudoku Squares	p. 50
Who Cares?	p. 51
Counting: ItÆs Harder than It Looks	p. 56
How to Court	p. 56
Counting Shidoku Squares	p. 61
How Many Sudoku Sudoku Squares Are There?	p. 63
Estimating the Number of Sudoku Squares	p. 66
From Two Million to Forty-Four	p. 68
Enter the Computer	p. 70
A Note on Problem-Solving	p. 71
Equivalence Classes: The Importance of Being Essentially Identical	p. 75
They Might as Well Be the Same	p. 76
Transformations Preserving Sudokuness	p. 77
Equivalent Shidoku Squares	p. 79
Why the Natural Approach Fails	p. 81
Groups	p. 82
Burnside's Lemma	p. 87
Bringing It Home	p. 93
Searching: The Art of Finding Needles in Haystacks	p. 96
The Sudoku Stork	p. 97
A Stork with GPS	p. 99
How to Search	p. 101
Searching for Eighteen-Clue Sudoku	p. 103
Measuring Difficulty	p. 111
Ease and Interest Are Inversely Correlated	p. 115
Sudoku with an Extra Something	p. 117
Graphs: Dots, Lines, and Sudoku	p. 123
A Physics Lesson	p. 123
Two Mathematical Examples	p. 124
Sudoku as a Problem in Graph Coloring	p. 127
The Four-Color Theorem	p. 131
Many Roads to Rome	p. 133
Book Embeddings	p. 137
Polynomials: WeFinallyEoundaUseforAlgebra	p. 141
Sums and Products	p. 141
The Perils of Generalization	p. 144
Complex Polynomials	p. 147
The Rise of Experimental Mathematics	p. 150
Extremes: Sudoku Pushed to Its Limits	p. 152
The Joys of Going to Extremes	p. 152
Maximal Numbers of Clues	p. 153
Three Amusing Extremes	p. 161
The Rock Star Problem 164
Is There "Evidence" in Mathematics?	p. 170
Sudoku Is Math in the Small	p. 171
Epilogue: You Can Never Have Too Many Puzzles	p. 172
Extra Regions	p. 172
Adding Value	p. 178
Comparison Sudoku	p. 182
.And Beyond	p. 187
Solutions to Puzzles	p. 192
Bibliography	p. 206
Index	p. 209
Table of Contents provided by Ingram. All Rights Reserved.

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Taking Sudoku Seriously The Math Behind the World's Most Popular Pencil Puzzle

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