This book is different! Most "problem books" contain many difficult and thought-provoking problems that are usually tackled with pencil and paper. The problems contained in such books tend to be at the level of the Mathematics Olympiad. As an example of such a text I refer you to Mathematical Olympiad Challenges by Andreescu and Gelca (Birkhäuser, 2000). As the subtitle of the book under review indicates, the problems in this book are more activity-oriented. Some use pencil and paper, but most require that the students actually move around.
For example, an activity labeled "Laundry Math" involves the topological aspects of turning a shirt or pair of pants inside out. This kind of problem is not to be found in most texts. Another activity called "Get Knotted" presents three activities referred to as "party tricks". We even see photographs of students performing these "tricks".
Before you get the wrong idea, be aware that there is serious mathematics being presented here. In addition to the laundry quandary mentioned above, topology shows up in some Möbius constructions, slicing a bagel and coloring a map on a torus We also encounter probability questions along the way. Chapter 25 is entitled Weird Lotteries and certainly lives up to that title. Graph theory appears in a few places, including Chapter 30 on Chessboard Maneuvers.
The book is full of photographs of students actually taking part in these activities. What a nice touch! Instead of merely describing the problem in words we actually see people riding bicycles (Chapter 9), turning pants inside out (Chapter 17) and blowing bubbles (Chapter 21).
The author has kindly included extensive hints and solutions in Part II of the book. These are clearly written and very informative.
If you are looking for a book to help students prepare for the Mathematical Olympiad or the Putnam Exam, this one is not for you. If, on the other hand, you want a book with a bounty of activities that you could use in your mathematics classroom or as part of a mathematics club try this one. We as mathematicians are always looking for ways to stimulate interest in mathematics in others. In particular, if one were to visit a high school mathematics classroom and want to show the students that mathematics can actually be FUN, look to this book for some wonderful ideas.
Herbert E. Kasube (firstname.lastname@example.org) is associate professor of mathematics at Bradley University. His mathematical interests include number theory, discrete mathematics and the history of mathematics. When not doing mathematics he can often be found jogging around the streets of Peoria.
Part I: Activities and Problem Statements
1. Distribution Dilemmas
2. Weird Shapes
3. Counting the Odds…and Evens
4. Dicing, Slicing and Avoiding the Bad Bits
5. "Impossible" Paper Tricks
6. Tiling Challenges
7. Things that Won't Fall Down
8. Mobius Madness: Tortuous Twists on a Classic Theme
9. The Infamous Bicycle Problem
10. Making Surfaces in 3- and 4-Dimensional Space
11. Paradoxes in Probability Theory
12. Don't Turn Around Just Once!
13. It's All in a Square
14. Bagel Math
15. Capturing Chaos
16. Who Has the Advantage?
17. Laundry Math
18. Get Knotted!
19. Tiling and Walking
20. Automata Antics
21. Bubble Trouble
22. Halves and Doubles
23. Playing with Playing Cards
24. Map Mechanics
25. Weird Lotteries
26. Flipped Out
27. Parts That Do Not Add to Their Whole
28. Making the Sacrifice
29. Problems in Parity
30. Chessboard Maneuvers
Part II: Hints, Solutions and Further Thoughts
Part III: Solutions and Discussions