Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book. The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.
Pablo Soberon (born 1988) is the first Mexican to obtain a gold medal in the International Mathematical Olympiad. After participating in mathematical olympiads, he has also trained Mexican teams for various international mathematical contests. He currently does research in discrete geometry at University College London and enjoys olympiad problem-solving in his free time.
Introduction.- 1 First concepts.- 2 The pigeonhole principle.- 3 Invariants.- 4 Graph theory.- 5 Functions.- 6 Generating Functions.- 7 Partitions.- 8 Hints for the problems.- 9 Solutions to the problems.- Notation.- Further reading.- Index.