The IMO Compendium

A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2009 Second Edition

  • Dušan Djukić
  • Vladimir Janković
  • Ivan Matić
  • Nikola Petrović

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Dušan Djukić, Vladimir Janković, Ivan Matić, Nikola Petrović
    Pages 1-3
  3. Dušan Djukić, Vladimir Janković, Ivan Matić, Nikola Petrović
    Pages 5-25
  4. Dušan Djukić, Vladimir Janković, Ivan Matić, Nikola Petrović
    Pages 27-346
  5. Dušan Djukić, Vladimir Janković, Ivan Matić, Nikola Petrović
    Pages 347-790
  6. Back Matter
    Pages 791-809

About this book


The IMO Compendium is the ultimate collection of challenging high school level mathematics problems. It is an invaluable resource, not only for students preparing for competitions, but for anyone who loves and appreciates math. Training for mathematical olympiads is enjoyed by talented students throughout the world. Olympiads have become one of the primary ways to recognize and develop talented youth with a potential to excel in areas that require abstract thinking. Although the problems appearing at IMO do not involve advanced mathematics, they must be difficult and their solutions must arise from creative and clever insights rather than tedious calculations.

In preparation for the distinguished International Mathematical Olympiad (IMO) competition, each participating country selects the top six high school students every year through a series of national olympiads. These students are invited to participate in the IMO, usually held in July. The IMO is a two-day contest where each day competitors are given three problems which they work on independently. The IMO host country appoints a special committee to which each country submits up to six problems. From this composite “longlist” of problems, a “shortlist” of 25-30 problems is created. The jury, consisting of one professor from each country, makes the final selection from the shortlist a few days before the IMO begins.

The IMO has sparked a burst of creativity among enthusiasts to create new and interesting mathematics problems. It can be safely said that the IMO and shortlisted problems are among the well-crafted problems created in a given year. This book attempts to gather all of these problems with their solutions. In addition, the book contains all the available longlist problems, for a total of more than 2000 problems.

From the reviews of the first edition:

"The International Mathematical Olympiad, or IMO is the premier international competition for talented high school mathematics students. … This book collects statements and solutions of all of the problems ever set in the IMO, together with many problems proposed for the contest. … serves as a vast repository of problems at the Olympiad level, useful both to students … and to faculty looking for hard elementary problems. No library will want to be without a copy, nor will anyone involved in mathematics competitions …"

— (Fernando Q. Gouvêa, MathDL, March, 2006)


IMO International Mathematical Olympiad Mathematical Problem-Solving Mathematics Competition

Authors and affiliations

  • Dušan Djukić
    • 1
  • Vladimir Janković
    • 2
  • Ivan Matić
    • 3
  • Nikola Petrović
    • 4
  1. 1., Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2., Department of MathematicsUniversity of BelgradeBelgradeSerbia
  3. 3., Department of MathematicsDuke UniversityDurhamUSA
  4. 4., Science DepartmentTexas A&M UniversityDohaQatar

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-9853-8
  • Online ISBN 978-1-4419-9854-5
  • Series Print ISSN 0941-3502
  • About this book