The Mathematics of Various Entertaining Subjects:
Research in Recreational Math

Jennifer Beineke + Jason Rosenhouse (editors)

Princeton University Press 2016
A book review by Danny Yee © 2016
This is a fairly random ("various") collection of essays on the mathematics of various recreations. The essays are "popular" in that they treat games and puzzles, but the presentation is rigorous and assumes, if not much formal mathematics, a general familiarity with mathematical thinking and notation. So the obvious audience is curious university students and graduates — perhaps high school students, but more plausibly their teachers.

Some of the pieces are broad and others are much more specific. The first essay surveys "One-Move Puzzles" in the areas of divination, weighing, dissection, rearrangement and folding, for example, while the second applies travelling salesman and minimum spanning tree algorithms to figurative maze design.

The topics touched on include the Tower of Hanoi, mazes, crossword puzzles, assembly problems, tetraflexagons, coin weighing puzzles, poker, tic-tac-toe, SET, Hex and other connection games, the Cookie Monster problem, and Fibonacci numbers. The mathematics deployed comes from probability, combinatorics, optimisation, packing, graph theory, affine geometry, and coding theory. Some of the pieces use games as motivation for teaching some mathematics, some use mathematics to explore games, most do a combination of both.

I particularly enjoyed essays on the Slothouber-Graatsma-Conway puzzle and Fibonacci coding of numbers, but I ended up reading most of the pieces in The Mathematics of Various Entertaining Subjects in full and at least skimming through the rest. Everyone's preferences here are likely to differ and, given its diversity, it is hard to see that this really makes sense as a book, in a world where shorter pieces can so easily be distributed individually. Unless there's a cheaper paperback coming, most people will probably prefer to borrow this from a library.

October 2016

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%T The Mathematics of Various Entertaining Subjects
%S Research in Recreational Math
%E Beineke, Jennifer
%E Rosenhouse, Jason
%I Princeton University Press
%D 2016
%O hardcover, index
%G ISBN-13 9780691164038
%P 272pp