Hexaflexagons and Other Mathematical Diversions: The First Scientific American Book of Mathematical Puzzles and Games by Martin Gardner

Math games and puzzles mostly for the Mensa set

For much of an authorial career that spanned over three-quarters of a century, Martin Gardner (1914–2010) was America’s most popular writer on matters mathematical. He is best known for “Mathematical Games,” a column he wrote in Scientific American magazine for 25 years. The articles from that column were collected into a series of at least 15 books, the first volume being The Scientific American Book of Mathematical Puzzles and Diversions, published in 1959. Many of the books in this series were later republished under different titles. This first book was rereleased in 1988 as Hexaflexagons and Other Mathematical Diversions. The 1988 edition includes additional new content from Gardner in the form of addenda to each chapter and an afterward at the end of the book.

Gardner’s “Mathematical Games” was more than just a brain-teaser-of-the-month. In fact, very few of the chapters in this book are the sort of puzzles you would find in a typical brain teaser book. A couple chapters entitled “Nine Problems” feature such riddles. For the most part, however, a typical Gardner column was more of a recreational exploration into a topic of mathematical interest. The word “Games” in the title is no casually chosen word. Gardner does spend many pages talking about games, those in the abstract strategy category that includes chess, tic tac toe, and everything in between. In this volume he discusses chess, tic tac toe (2D and 3D), Hex, Nim, and Tac Tix. Beyond going over the rules for such games, Gardner might discuss the number of possible moves, play on different board sizes, the winning probabilities of certain opening moves, whether the first or second player has a mathematical advantage, and sure-fire strategies to ensure victory. Other favorite Gardner topics include magic tricks, geometry puzzles, and the branch of mathematics known as topology. Even when he’s discussing card tricks, magic squares, or hand-held sliding-square puzzles, the emphasis is on permutations and probabilities.

It’s amazing how many of the games and puzzles that Gardner features here were created by scientists and mathematicians in some of the most prestigious research institutions in the country. Apparently physicists, when they’re not splitting the atom at MIT or Fermilabs, spent their leisure time on such mathematical diversions. Hexaflexagons are strips of paper that are divided into equilateral triangles and folded into a hexagon-shaped object somewhat like a kid’s paper fortune teller. Yet Gardner tells us that one of the pioneers of hexaflexagons was Richard P. Feynman, the theoretical physicist who won the Nobel in 1965.

Nowadays, Scientific American magazine is aimed at a broad popular audience, but back in Gardner’s day, it was written for a high-IQ clientele. Those same mathematicians and scientists who were fooling around with flexagons, polyominoes, and board games would have been reading the magazine and tuning into Gardner’s column every month. For that reason, this ain’t always easy stuff for the average Joe to wrap his head around. In some cases, that’s because the math may be beyond your level. In others, it’s because Gardner’s explanations are confusing. For the most part, he’s great at explaining higher mathematical concepts to laymen, but sometimes the content is just too complex to be dumbed down for mere mortal mathematical minds like mine.

By its very nature, this book is a grab bag, and as such, some topics will fascinate particular readers more than others. I, for example found the geometry stuff more interesting than the magic tricks. Since a good portion of the book is about abstract strategy games, it helps to have an interest in those, which I do. I can’t say this book was fun and fascinating form start to finish, but it hooked me enough to know that I’ll likely delve into the second volume of Gardner’s Scientific American writings.