The IMO Compendium is in its second edition; the first one appeared in 2006 and covered problems from the International Mathematical Olympiads starting with the very first one (1959) through the 45th IMO (2004). The new edition adds 143 problems submitted in the following 5 years, 2005–2009.
The selection of the problems for an olympiad proceeds in several steps. To start with, the participating countries send their proposals to the IMO organizers. These form the so-called long-listed problems. The Problem Committee selects some of the long-listed problems to submit to the IMO Jury that consists of team leaders. These problems are known as short-listed. From the short-listed problems the Jury chooses 6 problems for the IMO. For most olympiads run in the 1960–1980s, the book includes long-listed, short-listed and the olympiad problems. Starting with 1993, only short-listed (which still form a long list) and olympiad problems have been included. This explains the enormous size of the collection and the strange number of problems — 143 — by which the second edition of the book differs from the first one. All short-listed (and in particular, the olympiad) problems come with solutions — many with multiple solutions.
At the time of the first edition, the authors set up a web site to report typos:
If you happen to spot an error, please brag of it to us. All reported errors will be proudly added to the above list and eventually removed from the book (or replaced by some brand new ones).
Far as I can see, the new edition is free of the reported errors, although I did notice a small typo (which I proudly reported) in the formulation of Problem 5 of the first olympiad. I do not know wether the typo has been inherited from the first edition or is brand new.
The book also devotes about 20 pages to a collection of formulas and theorems that the authors judged useful in solving olympiad problems.
There could not be two opinions of the value of the book. I absolutely agree with F. Q. Gouvêa who reviewed the first edition:
The International Mathematical Olympiad, or IMO is the premier international competition for talented high school mathematics students… This book collects statements and solutions of all of the problems ever set in the IMO, together with many problems proposed for the contest… serves as a vast repository of problems at the Olympiad level, useful both to students… and to faculty looking for hard elementary problems. No library will want to be without a copy, nor will anyone involved in mathematics competitions …
The organizers of individual IMOs make every effort to create for the participants an exciting and stimulating event. Working with the IMO Compendium might be the next best thing. Imagine being on the Problem Committee, on the Jury, or just being a participant. There is enough material to fill any shoes.
Alex Bogomolny is a freelance mathematician and educational web developer. He regularly works on his website Interactive Mathematics Miscellany and Puzzles and blogs at Cut The Knot Math. Follow Alex on twitter