Cows in the Maze: And Other Mathematical Explorations is reminiscent of the books of the late Martin Gardner. Fun stories. Interesting explorations. Challenging but accessible. That's my summary of Stewart's new book. For those of you who don't know, Stewart is a very prolific writer. He has published over 60 books and he contributes to the monthly Scientific American "Recreational Mathematics" column. The material for this book comes from his columns.
"Cows in the Maze" gets its title from Chapter 13. (There are 21 chapters altogether.) Stewart credits Robert Abbott, author of SuperMazes, for creating the maze called “Where Are the Cows?” Abbott explains the logic puzzle/maze:
It is a flow chart with various boxes connected by a network of paths. Most of the boxes contain questions; there are two paths that exit each box; and the paths are labeled YES and NO. While you’re in this maze you have a pencil in each hand; one pencil points to one box and the other points to another box. On each move you choose one of the pencils, answer the question in the box, then follow the YES path or the NO path. Here’s a sample question: “Does the other pencil point to a box that has green text or has the word ‘green’?” Then there’s this very confusing question: “If you chose the other pencil, would it exit on a path marked NO?” This maze first appeared in Ian Stewart’s Mathematical Games column of the December 1996 Scientific American.
It's interesting to note that Abbott also invented the game Eleusis, which I have blogged about. Oh, and this cow maze logic puzzle is quite diabolical.
What Stewart does particularly well is to add a new twist to an old problem. Chapter 6, for example, Tiling Space with Knots, literally adds such a twist, exploring the world of 3-dimensional tilings. Chapter 1, The Lore and Lure of Dice, goes beyond the familiar discussions of probability to describe a two-player game with a die that has no element of chance. Think Nim meets dice. And, Chapter 10, Cone with a Twist, offers yet another fun twist -- two cones joined together, literally with a twist. And, the construction, a "sphericon," rolls with a wiggle.
Motivated high school students will enjoy "Cows in the Maze." Folks who enjoy Martin Gardner's book will enjoy it as well. Disclaimer: Oxford University Press gave me a review copy.