© 2006

The IMO Compendium

A Collection of Problems Suggested for the International Mathematical Olympiads: 1959–2004


  • The definitive source for IMO problems

  • Concise solutions and hints for all problems


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

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Pages 1-3
  3. Pages 27-332
  4. Pages 333-730
  5. Back Matter
    Pages 731-740

About this book


The International Mathematical Olympiad (IMO) has within its almost 50-year-old history 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.

The IMO has sparked off a burst of creativity among enthusiasts in creating new and interesting mathematics problems. In an extremely stiff competition, only six problems are chosen each year to appear on the IMO. The total number of problems proposed for the IMOs up to this point is staggering and, as a whole, this collection of problems represents a valuable resource for all high school students preparing for the IMO.

Until now 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 two year long 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, as well as the so-called "short-lists", a total of 864 problems. In addition, the book contains 1036 problems from various "long-lists" over the years, for a grand total of 1900 problems.

In short, "The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems. It will be an invaluable resource, not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates math.


Mathematica calculus combinatorics geometry history of mathematics mathematics number theory

Authors and affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Department of MathematicsUniversity of BelgradeBelgradeSerbia and Montenegro
  3. 3.Department of MathematicsBerkeleyUSA
  4. 4.Institute of PhysicsBelgradeSerbia and Montenegro

About the authors

* Dusan Djukic, IMO: gold, 2 silver, B.Sc. in Mathematics at Belgrade

University, Serbia and Montenegro

* Vladimir Jankovic, Ph.D. in Mathematics, Associate Professor at the

Belgrade University, Serbia and Montenegro

* Ivan Matic, IMO: silver, B.Sc. in Mathematics at Belgrade University,

Serbia and Montenegro

* Nikola Petrovic, IMO: 2 silver, bronze, B.Sc. in Mathematics and in

Physics at MIT, USA

Bibliographic information

  • Book Title The IMO Compendium
  • Book Subtitle A Collection of Problems Suggested for the International Mathematical Olympiads: 1959–2004
  • Authors Dušan Djukić
    Vladimir Janković
    Ivan Matić
    Nikola Petrović
  • Series Title Problem Books in Mathematics
  • DOI
  • Copyright Information Springer Science+Business Media, Inc. 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-24299-6
  • Softcover ISBN 978-1-4419-2027-0
  • eBook ISBN 978-0-387-33430-1
  • Series ISSN 0941-3502
  • Edition Number 1
  • Number of Pages XIV, 746
  • Number of Illustrations 200 b/w illustrations, 0 illustrations in colour
  • Topics Mathematics, general
  • Buy this book on publisher's site
Industry Sectors
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From the reviews:

"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)