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**The mathematics of various entertaining subjects. Volume 2. Research in games, graphs, counting, and complexity. With a foreword by Ron Graham.**
*(English)*
Zbl 1386.00005

Princeton, NJ: Princeton University Press (ISBN 978-0-691-17192-0/hbk; 978-1-4008-8913-6/ebook). xviii, 390 p. (2017).

This book is the hard-copy version of the 2015 MOVES conference, “MOVES” being an acronym for (among other things) the title of the book. This conference, the second in a series, was held in honor of Elwyn Berlekam, John H. Conway, and Richard Guy. It is unsurprising, then, that the book is in the same spirit as the various books generated by the “Gathering for Gardner” conferences.

The late Martin Gardner, however, was an autodidact, and the G4G books have tended to mathematics that was solid but light and accessible. MOVES is the honors course: while the reader is by no means thrown in at the deep end, a solid grounding in undergraduate mathematics is generally assumed. The result is a challenging and exciting book that complements the more familiar (and unconnected) series.

There is a distinct concentration on unfamiliar aspects of familiar games: Stockmeyer gives a new view of the Towers of Hanoi, Demaine et al. analyze Tangles, Bosch et al. design better gaming dice, and Weed shows that the children’s card game War, (than which, nothing but 1x1 tic-tac-toe could be much simpler) becomes, if slightly generalized, PSPACE-hard.

A sociobibliographical aside: it is a known phenomenon, first described by Carroll (1876), that the more frivolous or bizarre a significant problem appears at first glance, the larger the group of recreational mathematicians that will assemble for the hunt. Of the nineteen papers in this book, three have six authors each.

Two of the three guests of honor are represented in the book; Conway (with Norton and Ryba) presents a wonderful article on magic squares studded with truly dreadful puns, and Guy (whose impending hundredth birthday was honored by another chapter) produces special points from an ordinary triangle with the verve of a magician pulling paper streamers out of a hat.

Other topics include graph theory, number theory, paper folding, and dragons fighting over kasha. My only warning about this book is that it truly is not as elementary as the G4G series that it resembles. To anybody with at least the moiety of a math degree, the present book will be at least as interesting and possibly more so, but it might not be as appropriate for the high school reader.

The late Martin Gardner, however, was an autodidact, and the G4G books have tended to mathematics that was solid but light and accessible. MOVES is the honors course: while the reader is by no means thrown in at the deep end, a solid grounding in undergraduate mathematics is generally assumed. The result is a challenging and exciting book that complements the more familiar (and unconnected) series.

There is a distinct concentration on unfamiliar aspects of familiar games: Stockmeyer gives a new view of the Towers of Hanoi, Demaine et al. analyze Tangles, Bosch et al. design better gaming dice, and Weed shows that the children’s card game War, (than which, nothing but 1x1 tic-tac-toe could be much simpler) becomes, if slightly generalized, PSPACE-hard.

A sociobibliographical aside: it is a known phenomenon, first described by Carroll (1876), that the more frivolous or bizarre a significant problem appears at first glance, the larger the group of recreational mathematicians that will assemble for the hunt. Of the nineteen papers in this book, three have six authors each.

Two of the three guests of honor are represented in the book; Conway (with Norton and Ryba) presents a wonderful article on magic squares studded with truly dreadful puns, and Guy (whose impending hundredth birthday was honored by another chapter) produces special points from an ordinary triangle with the verve of a magician pulling paper streamers out of a hat.

Other topics include graph theory, number theory, paper folding, and dragons fighting over kasha. My only warning about this book is that it truly is not as elementary as the G4G series that it resembles. To anybody with at least the moiety of a math degree, the present book will be at least as interesting and possibly more so, but it might not be as appropriate for the high school reader.

Reviewer: Robert Dawson (Halifax)

### MSC:

00A08 | Recreational mathematics |

97A20 | Recreational mathematics, games (education) (MSC2010) |

### Citations:

Zbl 1328.00020
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XMLCite

\textit{J. Beineke} (ed.) and \textit{J. Rosenhouse} (ed.), The mathematics of various entertaining subjects. Volume 2. Research in games, graphs, counting, and complexity. With a foreword by Ron Graham. Princeton, NJ: Princeton University Press (2017; Zbl 1386.00005)

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