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Invitation to a Mathematical Festival

Ivan Yashchenko
Mathematical Sciences Research Institute/American Mathematical Society
Publication Date: 
Number of Pages: 
MSRI Mathematical Circles Library 35
Problem Book
[Reviewed by
Charles Ashbacher
, on

The Mathematical Festival is a mathematical competition that has been held in Moscow since 1990. It is attended by Russian middle school students. Creating problems for this competition poses significant challenges, since they must be accessible to students at that level of mathematical maturity as well as challenging enough to be worthy of a competition. This book is a collection of the problems that were used in the years 1990–2011.

The problems cover a wide spectrum of topics, most of which have appeared in other collections of problems and puzzles. Some examples are cryptarithms, liar/truth teller puzzles, dissections, simple tournaments, prime numbers and other basic number theory problems. I found myself stopping and thinking about the problems; while some answers were immediate, others required a bit of thought and more in-depth analysis. Sections containing hints and in-depth solutions are included.

This book is an enormous storehouse of problems that middle school math teachers can use in their classes. Most of the problems are what could be categorized as “fun” and the solution of many requires nothing more than simple persistence rather than significant mathematical insight. People that home-school will also find it very valuable in presenting challenging problems to their students. These are also great problems for classes designed to teach future elementary and middle school math teachers. Even mathematical veterans will find the mathematical components of their brains challenged a bit as they read through these problems.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.