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International Mathematical Olympiad

The International Mathematical Olympiad (IMO) is an annual contest for high school students. It is the oldest of the science olympiads.

The first IMO was held in Romania in 1959. Since then it has been held every year except 1980. About 80 countries send teams of (at most) 6 students each (plus one team leader, one deputy leader and observers). Teams are not officially recognized - all scores are given only to individual contestants. Constestants must be under the age of 20 and must not have any post-secondary school education. Subject to these conditions, an individual may participate any number of times in the IMO.

The paper consists of 6 problems, with each problem being worth 7 points. The total score is thus 42 points. The examination is held over two consecutive days; the contestants have 4.5 hours to solve 3 problems on each day. The problems chosen are from various areas of secondary school mathematics, broadly classifiable as Geometry, Number theory, Algebra, and Combinatorics. They require no knowledge of higher mathematics, and often admit of short and elegant solutions. Finding them, however, requires exceptional ingenuity and mathematical ability.

Each participating country other than the host country may submit suggested problems to a Problem Selection Committee provided by the host country, which reduces the submitted problems to a shortlist. The team leaders arrive at the IMO a few days in advance of the contestants and form the IMO Jury which is responsible for all the formal decisions relating to the contest, starting with selecting the 6 problems from that shortlist. As the leaders know the problems in advance of the contestants, they are kept strictly separated from the contestants until the second examination has finished; the contestants are accompanied to the IMO by their deputy leaders.

Each country's marks are agreed between that country's leader and deputy leader and Co-ordinators provided by the host country (the leader of the team whose country submitted the problem in the case of the marks of the host country), subject to the ultimate decision of the Jury if any disputes cannot otherwise be resolved.


Selection process

United States

In the United States, all high school students may opt to take the American Mathematics Competition 10 or 12 (AMC). The highest possible score on this examination is 150. Those who score over 100 or in the top 5% of the AMC 12, or those who score in the top 1% in the AMC 10 are invited to take the American Invitational Mathematics Examination (AIME). This consists of 15 questions, each worth 10 points.

Unlike the AMC, which has five possible answers to each question, questions on the AIME are stuctured so that the answers will always be whole integers from 1-999. This makes obtaining points by guessing randomly much less likely, although it has sometimes been rumored that the number 17 appears as an answer with disproportionate frequency.

The total score a student achieves on the AIME is added to the total on the AHSME. Those who score over 200 (?) points collectively then take the USAMO. The top six scorers on the USAMO then represent the United States at the IMO.


The participants are ranked based on their individual scores.

  • Gold medals will be awarded to the top 1/12 of the contestants.
  • Silver medals will be awarded to the next 2/12.
  • Bronze medals will be awarded to the next 3/12.
  • Participants who don't win a medal but who score 7 points on at least one problem will get an honorable mention.

Special prizes may be awarded for solutions of outstanding elegance or involving good generalisations of a problem. This last happened in 1995 and 1988, but was more frequent up to the early 1980s.

Current and Future IMOs

  • The 46th IMO will be held in Mérida, Mexico in 2005. [1]
  • The 47th IMO will be held in Slovenia in 2006.
  • The 48th IMO will be held in Viet Nam in 2007.
  • The 49th IMO will be held in Spain in 2008.
  • The 50th IMO will be held in Bremen, Germany in 2009.

Past IMOs

Sources differ about the cities hosting some of the early IMOs. This may be partly because leaders are generally housed well away from the students, and partly because after the competition the students did not always stay based in one city for the rest of the IMO. The exact dates cited may also differ, because of leaders arriving before the students, and at more recent IMOs the IMO Advisory Board arriving before the leaders.

External links

  • Central IMO web site
  • IMO problems and solutions
  • IMO scores
  • IMO winners Hall of Fame - IMO winners who have won Fields Medal or Nevanlinna Prize
  • IMO contestants who have won 3 or more gold medals

Last updated: 03-09-2005 19:44:02