Taking Sudoku Seriously facts for kids

Taking Sudoku Seriously: The Math Behind the World's Most Popular Pencil Puzzle is a book about the mathematics of Sudoku. It was written by Jason Rosenhouse and Laura Taalman. The Oxford University Press published it in 2011. This book was suggested for college math libraries by the Mathematical Association of America. In 2012, it won a PROSE Awards for popular science and math books.

Exploring Math with Sudoku Puzzles

This book uses Sudoku puzzles to teach many different math topics. It starts with simple examples you can solve by hand. Then, it shows how these ideas apply to bigger Sudoku problems using computers. The book also talks about what mathematics is and how computers help mathematicians.

How the Book is Organized

The book begins by explaining Sudoku puzzles and how to solve them. It also briefly mentions Euler tours and Hamiltonian cycles. After the first chapter, there are eight more chapters and a final section called an epilogue.

Latin Squares and Sudoku

Chapters two and three discuss Latin squares. A Latin square is a grid where each number appears only once in every row and every column. This is similar to how a solved Sudoku puzzle works. The book also covers the thirty-six officers problem and Leonhard Euler's ideas about Graeco-Latin squares.

Latin squares have a long history. They were studied in mathematics in medieval Islam. Benjamin Franklin even played with them for fun. Today, they are used in important areas like design of experiments and error correction codes. Sudoku puzzles are a special kind of Latin square. They also require each number to appear once in certain square blocks. This makes them a specific design called a gerechte design.

Counting Sudoku Puzzles

Chapters four and five explore how many different completed Sudoku puzzles exist. They look at this before and after grouping puzzles that are similar due to symmetry. This involves using a math idea called Burnside's lemma from group theory.

Chapter six looks for the smallest number of starting clues that make a Sudoku puzzle have only one solution. Soon after the book came out, people used these methods. They found that the fewest clues a Sudoku puzzle can have is 17.

Solving Sudoku with Advanced Math

The next two chapters show two different ways to think about solving Sudoku puzzles using advanced math. One way uses graph coloring, which is like assigning colors to parts of a picture. The other way uses something called the Gröbner basis method to solve systems of equations.

The last chapter explores questions in extremal combinatorics that are inspired by Sudoku. The book includes 76 Sudoku puzzles throughout its pages. The epilogue offers 20 more puzzles, including some harder and different types of Sudoku.