If you want a book with over 100 mathematical puzzles for a variety of school grades, contests, bonus activities, or to make your colleagues and friends brain hurt with numbers and logic, Golf on the Moon is for you. Written by Dick Hess, this book is a sequel to Mental Gymnastics. Some of the problems can be solved using mental mathematics and logic, while others require some more thought. As the subtitle Paradoxes and Puzzles suggests, some of the problems are very challenging. See for example problem #116 on Quadragrams — Expert Rules, where Hess says that “some of these are hard enough to find that they’ll make your head spin.”
Hess has divided the book into nine chapters keyed to diverse readers. I see the book being used by high school and college students with an interest in mathematics, geometry, logic, probability, and physics.
The book starts with easier problems and progresses naturally to more complex problems. For example, problems #4 Fast Thinking and #5 Isosceles Triangle are both relatively easy to solve. The Pulley Question, #15, requires more thought. Chapter 7 contains some very nice physics problems, including the problem featured on the books’ title and cover: #101 Golf on the Moon. What is nice about that one is the use of projectile motion, a topic studied by all physics and engineering students.
Chapter 9 contains the MathDice Puzzles. Hess presents Sam Ritchie’s 2004 MathDice game, which is marketed by ThinkFun Inc. The object of the game is to toss dice to determine some “scoring numbers” and a “target number.” The task is to obtain the target number using mathematical expressions that involve each of the scoring numbers. Each scoring number can only be used once. Each of the puzzles gives three or four scoring numbers (from zero to nine) and the player must obtain the target number using certain rules. There are three variants of the game: Beginner Rules, Intermediate Rules, and Expert Rules. Under the Expert Rules, the player may use decimals, factorials, and roots. This, of course, adds a lot more complexity to the problems, which are useful to develop thinking skills and keep one’s brain sharp. These problems can certainly be a perfect fit for a Number Theory course.
The one chapter that feels too short is Chapter 8, Modest Polyomino Puzzles; I would have liked to have seen more of these problems. Perhaps there might be room to include a chapter with a connection to Mathematical Induction. This would prove to be useful for a Discrete Mathematics class.
While reading the book, I started to solve the problems. I didn’t want to look at the solutions in the back of the book, though I was tempted to in multiple instances. If you are reading the book or choosing problems for a classroom or activity, my suggestion is to do the same: first try to solve the problems on your own. They will make you think and you’ll have a broader understanding and respect for mathematics. Then, look up the solutions. Some will leave you asking yourself, “Why didn’t I think of that?”
Peter Olszewski is a Mathematics Lecturer at Penn State Erie, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Pennsylvania Alpha Beta Chapter Advisor of Pi Mu Epsilon. He can be reached at firstname.lastname@example.org. Webpage: www.personal.psu.edu/pto2. Outside of teaching and textbook editing, he enjoys playing golf, playing guitar, reading, gardening, traveling, and painting landscapes.