Anneli Lax New Mathematical Library: International Mathematical Olympiads, 1959-1977

Every year, 100 of the most mathematically talented high school students in the country compete in the USA Mathematical Olympiad (USAMO). The USAMO is the third stage of a three-tiered mathematical competition for high school students in the United States and Canada that begins with the AHSME taken by over 400,000 students, continues with the American Invitational Mathematics Exam involving 2,000 students, and culminates with the 100-contestant USAMO. Winners of the USAMO go on to compete in the International Mathematical Olympiad. Compilation of 116 problems of arresting ingenuity given to high school students competing in the International Mathematical Olympiads. All are accessible to secondary school students. The alternative solutions are particularly interesting because they show that there are many ways to solve a problem. The International Olympiad has been held annually since 1959; the U.S. began participating in 1974, when the Sixteenth International Olympiad was held in Erfurt, G.D.R. In 1974 and 1975, the National Science Foundation funded a three week summer training session with Samuel L. Greitzer of Rutgers University and Murray Klamkin of the University of Alberta as the U.S. teams' coaches. Summer training sessions in 1976, 1977 were funded by grants from the Army Research Office and Office of Naval Research. To date the U.S. teams have consistently placed among the top three national second in 1974(the USSR was first), third in 1975 (behind Hungary and the G.D.R) and 1976 (behind the USSR and Great Britain) and first in 1977. Members of U.S. team are selected from the 100 top scorers on the Annual High School Examinations (see NML vols. 5, 17, 25) by subsequent competition in the U.S. Mathematical Olympiad. In this volume the demonstrably effective coach and prime mover in planning the participation of the U.S.A. in the I.M.O., Samuel L. Greitzer, has compiled all the IMO problems from the First through the Nineteenth (1977) IMO and their solutions, some based on the contestants' papers. The problems ae solvable by methods accessible to secondary school students in most nations, but insight and ingenuity are often required. A chronological examination of the questions throws some light on the changes and trends in secondary school mathematics curricula.