A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.

Table of Contents

1. The Invariance Principle

2. Coloring Proofs

3. The Extremal Principle

4. The Box Principle

5. Enumerative Combinatorics

6. Number Theory

7. Inequalities

8. The Induction Principle

9. Sequences

10. Polynomials

11. Functional Equations

12. Geometry

13. Games

14. Further Strategies