Across the Board: The Mathematics of Chessboard Problems (Princeton Puzzlers) by John J. Watkins (PDF)

Description

Across the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itself–that simple grid of squares so common to games around the world. And, more importantly, the fascinating mathematics behind it. From the Knight’s Tour Problem and Queens Domination to their many variations, John Watkins surveys all the well-known problems in this surprisingly fertile area of recreational mathematics. Can a knight follow a path that covers every square once, ending on the starting square? How many queens are needed so that every square is targeted or occupied by one of the queens? Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery. Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a nice book. The book looks at a small collection of topics, mainly around the classic knight’s tour and queens problems. The presentation is for the general reader, and it is written in a clear, appealing style. Each chapter gives an engaging discussion of a particular topic, with several problems, some old and some new. The chapters conclude with detailed solutions of the problems. I enjoyed reading this book, and I enjoyed doing the problems. The book is remarkably well written, with very nice graphics. The problem solutions are also clearly presented. I only noticed a few typos/slip-ups (in the 2004 edition):1. on the bottom of page 46, when indicating how “Schwenk’s theorem” can be completed, the nine small cases shouldn’t include the 5×5 board (for which a closed tour doesn’t exist) but should include the 5×6 board.2. on the last line of page 76, “the white king moves across to c7” should be “the white queen moves across to c7”. (I understand this was corrected in the 2012 reissue edition)3. for problem 7.1, the solution on page 104 doesn’t strictly speaking satisfy the instruction to move one knight from each group of four. The solution really should be the mirror image of the one given.4. on page 134, the digram on the top right is not correct; square g1 is not covered. There is a covering on this sub-sub-diagonal, but it is not the one shown.My main criticism is that the subtitle “The Mathematics of Chessboard Problems” is very misleading. Perhaps this is the fault of the editor? In any case, it could lead some purchasers to be disappointed. The book is not a thorough treatment of the math of Chessboard problems. There is actually extremely little mathematics in the book. And the “problems” considered are of a somewhat narrow, particular nature. Moreover, the general approach is certainly not that of an exhaustive, academic account. References to the literature are rather minimal. For example, when presenting Schwenk’s theorem in Chapter 3, the book doesn’t mention that the result was stated without proof in Kraitchik’s 1942 book “Mathematical Recreations” and that except for the m = 3 case, a proof had been given by Cull and De Curtins in 1978. Indeed, the bibliography is very brief and not always well chosen: Murray’s awe inspiring book “A history of chess” is not mentioned, but it includes Pickover’s “The Zen of Magic Squares, Circles, and Stars”, which is of poor quality. But to be fair, the aim of the book is clearly not to be an academic treatise, but to be an entertaining account of some beautiful results, and in this the author has certainly been successful. The book would make a very nice present for anyone with an interest in chess.

⭐This book attempts to make a connection between chess and mathematics/mathematical puzzles, by asking several mathematical questions related to chess, the chess board, and chess pieces, such as: how many bishops can be placed on a chess board, without each attacking the other? The author does a good job entertaining the reader with these questions and the answers, although for me (as someone with a degree in mathematics) the level could have been a bit higher. That said, I am probably not the intended and average audience for this book.Pros:+ Well-written, nice read+ One of very few books on the topic of the mathematics of chess+ Pretty affordableCons:- The puzzles are generally not very deep- Ultimately you do not really gain any new insights in chess or mathematics: it is just an interesting read on the topic

⭐good

⭐My order came today, and on having a browse through, was pleased with this book – Which looks, interesting!Good. Thanks.

⭐Lots of interesting things to read and some really good puzzles.

⭐Apenas lo recibí y espero sea una lectura iluminadora que refuerce el bagaje personal en el tema.

⭐

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