In the six chapters of the book, selected problems at a Mathematical Olympiad level are solved. The first chapter, “Strategies in problem solving”, explains in detail the main strategic steps in solving a concrete problem. The following five chapters contain solutions to many problems from number theory, algebra, analysis, and Euclidean and analytic geometry. The sixth chapter, “Sundry examples”, is dedicated to interesting (and quite funny) problems that have something in common with combinatorics and game theory. At the end of some solved problems, there are additional exercises whose solutions can be obtained in a similar manner. It is an important feature of the book that problems are not only solved but that various solving strategies and methods are also demonstrated, which make problems easier and help to find the best route towards a solution. Without any exaggeration, I can say that the book gave me enormous pleasure. It not only portrays the author’s enthusiasm for the beauty of mathematics but also his ability to explain problems and their solutions to young people who are at the beginning of their mathematical career. And this is one of the reasons why the book will be useful for pupils and students who are interested in mathematics. It can also be recommended to mathematics teachers working with gifted students and will undoubtedly make their lectures more attractive.

Reviewer:

ec