Happy Birthday to Martin Gardner! Mr. Gardner is 90; as a tribute to him the editors of this book compiled this collection of articles. It is a lovely tribute indeed.
The articles include puzzles, personal recollections of the authors’ friendships with Gardner, and historical pieces. The personalized articles are wonderfully done and give the reader insight into Gardner’s inquisitive nature. I suspect, however, that his fans already know him as inquisitive from his myriad columns and books on mathematics. But, did you know he has had a penchant for magic tricks since he was young boy?
There are twenty-five articles in all so let me give a short description of just a few. As an historical reference, “Tangram: The World’s First Puzzle Craze” by Jerry Slocum ranks high, giving a history of the tangram and pictures of artifacts and modern day renditions. “De Viribus Quantitatis by Luca Pacioli: The First Recreational Mathematics Book,” by David Singmaster, is filled with details, pictures, and reproductions of book pages that show puzzles have happily been with us for a very long time.
I was struck by M. Oskar van Deventer’s article “Mechanical Mazes.” He describes not the popular two-dimensional mazes, but three-dimensional mazes and puzzles. Speaking of three dimensions, Frans de Vreugd’s “Extreme Puzzles” describes three dimensional shapes, such as cubes with holes, and interlocking puzzles. The trick here is to design these cube-like shapes such that it takes many moves (say, 23 or more!) to get a piece out of the puzzle. Then once the first piece is removed, it again requires many moves to get the second piece out. I recall these sorts of puzzles from my childhood, but only now did I realize there is a science to them and design behind the twisty and irregular puzzle pieces.
For logic, Raymond Smullyan’s “Memories and Inconsistencies” asks the reader the stretch his thinking in a Gödelian way. Perhaps the best article is “NetWords: A Fascinating New Pencil-Paper Game.” The article is about a word game two (or more) people play based on connecting letters in an undirected graph. You can learn some topology by playing the game. It is well written and the authors guide you into their game with a well-developed example. I was halfway through it and thought about how well-written the article is. Only then did I look at the authors: Mamikon Mnatsakanian, Gwen Roberts, and I should have known, Martin Gardner!
Each of the articles can be read independently so if you don’t like one, simply move to another. My only complaint is that the figures are all black and white. For most of the illustrations that is fine, but there are some figures for which color would have been better. Nonetheless, the book is a fine tribute to Mr. Gardner. Happy Birthday.
David S. Mazel is a practicing engineer in Washington, DC. His research interests are in the dynamics of billiards, signal processing, and cellular automata.