“This book is for lovers of mathematics, lovers of puzzles, lovers of challenge. Most of all, it if for those who think that the world of mathematics is orderly, logical, and intuitive — and are ready to learn otherwise!” Who could resist that kind of opening? Mathematical Mind-Benders is Winkler’s second book of recreational mathematics. Winkler states that the problems presented in this book are “elegant and entertaining”, and that the solutions are “illuminating”. He claims that no special mathematical training is required to do these problems, and in fact, that more mathematical training might be a detriment to answering the problems. Along with his opening entreaty stated above, I took this as a challenge! I dove in right there and then to find out! What I found was that the author’s claims are right on, for the most part. I was smiling with the very first problem, and was almost late to teach my next course.
Problems are grouped based on what kind of solution they require, and in general get harder with each chapter. For example, the second chapter, entitled “Stretching the Imagination” is made up of problems that require one to formulate a plan and use creativity.
In general, the problems require creative thinking and little or no paper and pencil. That said, some chapters, such as “Two Dimensions and Three” do require real proofs, with pencil and paper and some prior mathematical training. At least the solutions provided by the author are of that nature. But even these more “professional” problems can provide fun and enlightening mental exercises without resorting to rigorous proof.
My favorite sections were, “Warm-ups”, “Stretching the Imagination”, “Numerical Conundrums” and “New Visits to Old Friends”, which required a lot of creativity and little paper. These kinds of problems keep you busy while stuck in traffic, or might even make you the cause of a traffic jam if you are not careful. Mathematical Mind-Benders contains problems or all types, levels and styles that are accessible to everyone, mathematician or not. You are sure to find something in this volume to make you say “a-ha!”, and smile!
Amy Shell-Gellasch is a Faculty Fellow at Pacific Lutheran University in Tacoma, WA. She is actively involved with the MAA and its History of Mathematics SIGMAA as chairperson to several committees. She enjoys researching and promoting the use of history in the teaching of mathematics through editing books and organizing meetings. She received her bachelor’s degree from the University of Michigan in 1989, her master’s degree from Oakland University in Rochester, Michigan in 1995, and her doctor of arts degree from the University of Illinois at Chicago in 2000.