The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics (Dover Books on Mathematics)

This book consists of "320 unconventional problems in algebra, arithmetic, elementary number theory and trigonometry." The problems are mathematically accessible to students at the high school level or higher, as they call more upon analytical thinking than upon advanced mathematical techniques. There is a range of difficulties, with harder problems marked with stars in the book. (The hardest problems are marked with double stars.) The problems are divided into twelve sections: "Introductory Problems," "Alterations of Digits in Integers," "The Divisibility of Integers," "Some Problems from Arithmetic," "Equations Having Integer Solutions," "Evaluating Sums and Products," "Miscellaneous Problems from Algebra," "The Algebra of Polynomials," "Complex Numbers," "Some Problems of Number Theory," "Some Distinctive Inequalities," and "Difference Sequences and Sums." Much of the book is devoted to providing hints and solutions, which are both thorough and clear. This is a great resource for preparing for competition, for developing your analytical thinking, or just for having fun (that is, if you are the sort of person who finds solving math problems fun).

The reason I am giving 5 stars to this book is for its unique collection of problems. It has been very entertaining reading the book so far (I have not completed the book). There however are a few errors which can be easily figured out by the reader. The treatment of each problem is unique.

If you like challenging math problems then this book is for you. It's ideal if you want to prepare for a national math olympiad or if you just like hard math problems. Get this book and you won't regret it !!!

This exercise book is great! The collection of the most interessant and exciting problems of elementary Mathematics. Ideal for preparing for the IMO. A must - have book for everybody who likes Math challenge-

This books is what every book on math olympiads should be, it deals with high level problems in a way that readers can easily follow; I also liked it because there are some problems who have many interesting solutions and generalizations