Preface

Summary

This volume is a collection of all the problems in the International Mathematical Olympiads (IMO) from the First (1959) through the Nineteenth (1977) together with their solutions.

To explain how the problems are selected and the contests administered, I give a bit of the historical background.

Various countries have conducted national mathematical contests for a long time. The Hungarian Eötvös Competition (begun in 1894, see NML vols. 11 and 12) is a famous example. In 1959 Rumania invited Hungary, Bulgaria, Poland, Czechoslovakia, the German Democratic Republic (G.D.R.) and the U.S.S.R. to participate in the First I.M.O. After a slow start the number of participating nations grew. Finland joined in 1965, Great Britain, France and Italy in 1967; and since then the number of participating nations grew rapidly, reaching twenty-one by 1977.

The U.S.A. first participated in the IMO in 1974. Travel to this competition in Erfurt, G.D.R., was made possible by a generous grant by the Spencer Foundation. Also, the National Science Foundation funded a three-week training session at Rutgers University for the American team prior to its departure. Preparatory work started in 1972 when the Subcommittee on the U.S.A. Mathematical Olympiad of the Mathematical Association of America's Committee on High School Contests organized the first U.S.A. Mathematical Olympiad (USAMO). This contest examination was written by Murray Klamkin of the University of Alberta, Alberta, Canada and administered by this writer to the top 100 scorers (out of 300,000) on the Annual High School Mathematics Examination.