''Taking Sudoku Seriously: The math behind the world's most popular pencil puzzle'' is a book on the mathematics of Sudoku. It was written by Jason Rosenhouse and

Laura Taalman Laura Anne Taalman, also known as mathgrrl, is an American mathematician known for her work on the mathematics of Sudoku and for her mathematical 3D printing models. Her mathematical research concerns knot theory and singular algebraic geometry; ...

, and published in 2011 by the Oxford University Press. The Basic Library List Committee of the

Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure a ...

has suggested its inclusion in undergraduate mathematics libraries. It was the 2012 winner of the PROSE Awards in the popular science and popular mathematics category.

Topics

The book is centered around Sudoku puzzles, using them as a jumping-off point "to discuss a broad spectrum of topics in mathematics". In many cases these topics are presented through simplified examples which can be understood by hand calculation before extending them to Sudoku itself using computers. The book also includes discussions on the nature of mathematics and the use of computers in mathematics. After an introductory chapter on Sudoku and its deductive puzzle-solving techniques (also touching on Euler tours and Hamiltonian cycles), the book has eight more chapters and an epilogue. Chapters two and three discuss Latin squares, the

thirty-six officers problem In combinatorics, two Latin squares of the same size (''order'') are said to be ''orthogonal'' if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are ...

, Leonhard Euler's incorrect conjecture on Graeco-Latin squares, and related topics. Here, a Latin square is a grid of numbers with the same property as a Sudoku puzzle's solution of having each number appear once in each row and once in each column. They can be traced back to mathematics in medieval Islam, were studied recreationally by Benjamin Franklin, and have seen more serious application in the design of experiments and in error correction codes. Sudoku puzzles also constrain square blocks of cells to contain each number once, making a restricted type of Latin square called a gerechte design. Chapters four and five concern the combinatorial enumeration of completed Sudoku puzzles, before and after factoring out the symmetries and

equivalence class In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set S into equivalence classes. These equivalence classes are constructed so that elements a ...

es of these puzzles using

Burnside's lemma Burnside's lemma, sometimes also called Burnside's counting theorem, the Cauchy–Frobenius lemma, the orbit-counting theorem, or the Lemma that is not Burnside's, is a result in group theory that is often useful in taking account of symmetry when ...

in group theory. Chapter six looks at combinatorial search techniques for finding small systems of givens that uniquely define a puzzle solution; soon after the book's publication, these methods were used to show that the minimum possible number of givens is 17. The next two chapters look at two different mathematical formalizations of the problem of going from a Sudoku problem to its solution, one involving

graph coloring In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices o ...

(more precisely,

precoloring extension In graph theory, precoloring extension is the problem of extending a graph coloring of a subset of the vertices of a graph, with a given set of colors, to a coloring of the whole graph that does not assign the same color to any two adjacent vertices ...

of the

Sudoku graph In the mathematics of Sudoku, the Sudoku graph is an undirected graph whose vertices represent the cells of a (blank) Sudoku puzzle and whose edges represent pairs of cells that belong to the same row, column, or block of the puzzle. The problem ...

) and another involving using the Gröbner basis method to solve systems of polynomial equations. The final chapter studies questions in

extremal combinatorics Extremal combinatorics is a field of combinatorics, which is itself a part of mathematics. Extremal combinatorics studies how large or how small a collection of finite objects (numbers, graphs, vectors, sets, etc.) can be, if it has to satisfy ce ...

motivated by Sudoku, and (although 76 Sudoku puzzles of various types are scattered throughout the earlier chapters) the epilogue presents a collection of 20 additional puzzles, in advanced variations of Sudoku.

Audience and reception

This book is intended for a general audience interested in recreational mathematics, including mathematically inclined high school students. It is intended to counter the widespread misimpression that Sudoku is not mathematical, and could help students appreciate the distinction between mathematical reasoning and rote calculation. Reviewer Mark Hunacek writes that "a person with very limited background in mathematics, or a person without much experience solving Sudoku puzzles, could still find something of interest here". It can also be used by professional mathematicians, for instance in setting research projects for students. It is unlikely to improve Sudoku puzzle-solving skills, but Keith Devlin writes that Sudoku players can still gain "a deeper appreciation for the puzzle they love". However, reviewer Nicola Tilt is unsure of the book's audience, writing that "the content may be deemed a little simplistic for mathematicians, and a little too diverse for real puzzle enthusiasts". Reviewer David Bevan calls the book "beautifully produced", "well written", and "highly recommended". Reviewer Mark Hunacek calls it "a delightful book which I thoroughly enjoyed reading". And (despite complaining that the section on graph coloring is "abstract and demanding" and overly US-centric in its approach), reviewer Donald Keedwell writes "This well-written book would be of interest to anyone, mathematician or not, who likes solving Sudoku puzzles."

References

{{reflist, refs= {{citation , last = Bevan , first = David , author-link = David Bevan (mathematician) , date = November 2013 , doi = 10.1017/S0025557200000589 , issue = 540 , journal = The Mathematical Gazette , jstor = 24496749 , pages = 574–575 , title = Review of ''Taking Sudoku Seriously'' , volume = 97 {{citation , last = Devlin , first = Keith , author-link = Keith Devlin , date = January 28, 2012 , newspaper = The Wall Street Journal , title = The numbers game (review of ''Taking Sudoku Seriously'') , url = https://www.wsj.com/articles/SB10001424052970204301404577173022950738492 {{citation , last = Hösli , first = Hansueli , journal = zbMATH , title = Review of ''Taking Sudoku Seriously'' , zbl = 1239.00014 {{citation , last = Hunacek , first = Mark , date = January 2012 , journal = MAA Reviews , publisher =

, title = Review of ''Taking Sudoku Seriously'' , url = https://www.maa.org/press/maa-reviews/taking-sudoku-seriously-the-math-behind-the-worlds-most-popular-pencil-puzzle {{citation , last = Keedwell , first = Donald , date = February 2018 , doi = 10.1017/mag.2018.39 , issue = 553 , journal = The Mathematical Gazette , pages = 186–187 , title = Review of ''Taking Sudoku Seriously'' , volume = 102 {{citation , last = Li , first = Aihua , journal =

Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also pu ...

, mr = 2859240 , title = Review of ''Taking Sudoku Seriously'' {{citation , last = Tilt , first = Nicola , date = February 2013 , doi = 10.1111/j.1740-9713.2013.00640.x , issue = 1 , journal = Significance , page = 43 , publisher = Royal Statistical Society , title = Review of ''Taking Sudoku Seriously'' , volume = 10, doi-access = {{citation, title=2012 Award Winners, work= PROSE Awards, publisher=Association of American Publishers, url=https://proseawards.com/winners/2012-award-winners/, accessdate=2018-05-14 Sudoku Popular mathematics books 2011 non-fiction books Puzzle books Oxford University Press books