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There is little need to introduce the International Mathematical Olympiad to the readers. The IMO is the most prestigious of all international competitions in high school mathematics. It has been conducted annually since 1959 (with the single exception of the year 1980). In contrast to physical sports, the game of the IMO is to challenge the mental skills of its participants. Like a game, there are precise regulations, scores, results, and medals. 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. Several hundred incredibly gifted 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.
This book focuses on the mathematics of the IMO, leaving the sporting aspects of the event to the media. It is a continuation of the two previous MAA publications that comprised the first twenty-six contests: International Mathematical Olympiads 1959–1977, NML vol. 27, by Samuel L. Greitzer, and International Mathematical Olympiads 1979–1985 and forty supplementary problems, NML vol. 31, by Murray S. Klamkin. Accordingly, this volume takes up the series, starting from the 27th IMO in Poland (incidentally, the author's native country) and ending up with the 40th IMO in Romania.
The reader will find all the problems of those fourteen IMOs compiled here. There is true mathematical beauty in many of them. I have had the good luck to be present at the IMO in various roles: many years ago, as a contestant; then, several times, as the delegation leader of my country, hence a Jury member; and also, four times, as a member of the Problem Selection Committee. So I have had the chance to witness the process of selection, preliminary and ultimate, of the contest problems. Each time, the work on the problem proposals coming from the participating countries was a fascinating intellectual adventure. In so many cases, we could only regret that there was room for no more than six contest problems, so that one or another tiny mathematical treasure had to be left out.
Each problem in this book is given with a solution, sometimes more than one.
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