The IMO Compendium: A Collection of Problems Suggested for the International Mathematical Olympiads: 1959-2009

by Dušan Djukić, Vladimir Janković, Ivan Matić

"The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems and is an invaluable resource not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates mathematics. The International Mathematical Olympiad (IMO), nearing its 50th anniversary, has become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for high school students to measure up with students from the rest of the world. Until the first edition of this book appearing in 2006, it has been almost impossible to obtain a complete collection of the problems proposed at the IMO in book form. "The IMO Compendium" is the result of a collaboration between four former IMO participants from Yugoslavia, now Serbia and Montenegro, to rescue these problems from old and scattered manuscripts, and produce the ultimate source of IMO practice problems. This book attempts to gather all the problems and solutions appearing on the IMO through 2009. This second edition contains 143 new problems, picking up where the 1959-2004 edition has left off.

Genres: Mathematics

823 pages, Hardcover

First published January 1, 1900

Reviews

[Rodolphe Gintz · Rating 5 out of 5]

Il ne s’agit pas d’une lecture comme les autres mais entretenir son 🧠 en faisant des mathématiques est une excellente gymnastique !
En la matière, ceci est probablement l’Everest : le recueil des exercices et problèmes des olympiades internationales de mathématiques
L’épreuve consiste, pour des élèves de fin de terminale, à résoudre deux séries de trois problèmes issus de la géométrie plane, de l’arithmétique, des inégalités, de la combinatoire, des équations fonctionnelles et de l’algèbre qui sont proposés par les pays organisateurs.
Je n’avais clairement pas le niveau (ni l’entraînement 😅) en fin de terminale ; désormais, j’y arrive un peu mieux (à part la géométrie) !
Mon problème préféré (voyons si vous avez la solution) est celui proposé par l’Iran en 2000 : « Ten gangsters are standing on a flat surface, and the distances between them are all distinct. At twelve o’clock, when the church bells start chiming, each of them fatally shoots the one among the other nine gangsters who is the nearest. At least how many gangsters will be killed? ».