The International Mathematical Olympiad (IMO) is a widely renowned international competition in high school mathematics that has been conducted annually since 1959 (with the single exception of the year 1980). Several hundred incredibly gifted high school students from several dozen countries compete each year, taking a two-day examination consisting of three truly difficult problems to be solved each day. The IMO is a challenge to the mental skills of its participants. There are those who win medals and those who, while losing in the narrow sense, gain immeasurably from the intensity of the effort and the competition. This book is a sequel to two earlier MAA publications (NML27 and NML31) by Samuel L. Greitzer and Murray S. Klamkin, which covered the first twenty-six International Mathematical Olympiads. This volume includes all of the Olympiad problems from 1986 through 1999. Each problem is given with a solution (and often more than one). Occasionally, solutions are accompanied by remarks, in which alternative approaches, generalizations of the problem, or the relevance of the problem to some mathematical theory are given. The book is addressed mainly to high school students preparing for participating in mathematics competitions, and to their teachers. However, anyone interested in problem solving will enjoy these problems.