This book is a continuation of Mathematical Contests 1997-1998: Olympid Problems and Solutions From Around the World. It contains solutions to challenging problems from algebra, geometry, combinatories, and number theory featured in the earlier book, together with selected questions (without solutions) from 30 national and regional Olympiads given during 1999.
This collection is intended as practice for serious students who wish to improve their performance on the USA Mathematical Olympiad (USAMO). Some of the problems are comparable to the USAMO in that they come from national contests. Others are harder, as some countries first have a national Olympiad, and later one or more exams to select a team for the International Mathematical Olympiad (IMO). And some problems are easier, coming from regional international contests ("mini-IMOs").
Different nations have different mathematical cultures, so you will find some of these questions extremely difficult and some rather easy. We have included a wide variety of problems, especially from those countries that have often done well at the IMO. You will have the chance to work on beautiful mathematical questions. Take them on!