Taking Sudoku Seriously · The Math Behind the World's Most Popular Pencil Puzzle by Rosenhouse, Jason -- Read -- Imperial Library of Trantor

Index

Cover Page Title Page Copyright Page Dedication Contents Preface 1. Playing the Game: Mathematics as Applied Puzzle-Solving

1.1 Mathematics and Puzzles 1.2 Forced Cells 1.3 Twins 1.4 X-Wings 1.5 Ariadne’s Thread 1.6 Are We Doing Math Yet? 1.7 Triplets, Swordfish, and the Art of Generalization 1.8 Starting Over Again

2. Latin Squares: What Do Mathematicians Do?

2.1 Do Latin Squares Exist? 2.2 Constructing Latin Squares of Any Size 2.3 Shifting and Divisibility 2.4 Jumping in the River

3. Greco-Latin Squares: The Problem of the Thirty-Six Officers

3.1 Do Greco-Latin Squares Exist? 3.2 Euler’s Greco-Latin Square Conjecture 3.3 Mutually Orthogonal Gerechte Designs 3.4 Mutually Orthogonal Sudoku Squares 3.5 Who Cares?

4. Counting: It’s Harder than It Looks

4.1 How to Count 4.2 Counting Shidoku Squares 4.3 How Many Sudoku Squares Are There? 4.4 Estimating the Number of Sudoku Squares 4.5 From Two Million to Forty-Four 4.6 Enter the Computer 4.7 A Note on Problem-Solving

5. Equivalence Classes: The Importance of Being Essentially Identical

5.1 They Might as Well Be the Same 5.2 Transformations Preserving Sudokuness 5.3 Equivalent Shidoku Squares 5.4 Why the Natural Approach Fails 5.5 Groups 5.6 Burnside’s Lemma 5.7 Bringing It Home

6. Searching: The Art of Finding Needles in Haystacks

6.1 The Sudoku Stork 6.2 A Stork with GPS 6.3 How to Search 6.4 Searching for Eighteen-Clue Sudoku 6.5 Measuring Difficulty 6.6 Ease and Interest Are Inversely Correlated 6.7 Sudoku with an Extra Something

7. Graphs: Dots, Lines, and Sudoku

7.1 A Physics Lesson 7.2 Two Mathematical Examples 7.3 Sudoku as a Problem in Graph Coloring 7.4 The Four-Color Theorem 7.5 Many Roads to Rome 7.6 Book Embeddings

8. Polynomials: We Finally Found a Use for Algebra

8.1 Sums and Products 8.2 The Perils of Generalization 8.3 Complex Polynomials 8.4 The Rise of Experimental Mathematics

9. Extremes: Sudoku Pushed to Its Limits

9.1 The Joys of Going to Extremes 9.2 Maximal Numbers of Clues 9.3 Three Amusing Extremes 9.4 The Rock Star Problem 9.5 Is There “Evidence” in Mathematics? 9.6 Sudoku Is Math in the Small

10. Epilogue: You Can Never Have Too Many Puzzles

10.1 Extra Regions 10.2 Adding Value 10.3 Comparison Sudoku 10.4 … And Beyond

Solutions to Puzzles Bibliography Index