Train Your Brain is an enjoyable way to exercise your brain and spend a few spare minutes during the day. While this collection of math and logic puzzles vary in depth and complexity, they are certainly challenging enough to keep anyone engaged.
I found the structure of Grätzer’s book to be particularly appealing. The contents are broken down into three sections: the problems, hints, and solutions. The first section presents the reader with 52 weeks of puzzles. During the first thirty-six weeks the reader is given 3 puzzles per week to solve while the last 16 weeks, entitled Black Belt, the reader is given only two. As indicated by the name, the puzzles in the last 16 weeks are markedly more difficult than the first 36. To help keep the reader interested, the weekly puzzles vary in difficulty, length and type. The hints section provides the reader with simple hints to help solve some of the more difficult problems. I found this section to be particularly useful. Instead of having to look to the solution for a helpful nudge in the right direction, I was able to use the hints section to keep the problem solving process going and prevent me from inadvertently seeing the solution. The final section of the book contains detailed solutions for each of the posed problems.
The author encourages the reader to solve the problems in the order in which they are presented and to try not to skip or gloss over any. After initially trying to solve problems in a random fashion, I found that the author’s suggestion was right. The insights gained from solving earlier problems helped me solve problems presented later. Even though I don’t believe that this book could be used as the sole textbook in a mathematics course, it does contain numerous interesting problems that could be pulled out and integrated into a class such as probability, problem solving or logic. The task of selecting problems would be difficult, however, since the book is organized to provide the reader with a variety of experiences and not by problem type.
I really enjoyed solving and attempting to solve the puzzles presented in this book. While the puzzles vary in difficulty and mathematical sophistication, most could be solved by anyone from an advanced high school student to a college student with a solid background in mathematics. There is something for everyone in this book.
Janet Shiver is a mathematics educator at Central Washington University in Ellensburg, Washington. In addition to teaching mathematics courses for preservice elementary and middle grades teachers, she keeps busy working on various grants and pursuing her love of gardening.