The international mathematical olympiad (IMO) is an international maths competition (probably the most important one).
In the 1st IMO (in Romania, 1959) only a few sovbloc countries participated. Since then the IMO has been held yearly (with the exception of 1980) and the number of particpating countries has increased over the years to 82 in the 41st IMO (South Korea, 2000).

Each particpating country sends a team consisting of a leader, a deputy leader and up to six contestants. The contest must be less than 20 years of age and must not be enrolled at any university.
The competition consists of two papers of three questions each. The time allowed for each paper is 4,5 hours. The only permitted instruments are writing and drawing equipment.
Each solution is assessed and awarded with up to 7 points, and final score calculated for each contestant. Prizes are awarded to those with the highest scores. The ratio between first, second and third prizes is approximately 1:2:3 with less than half the contestants obtaining prizes. Anyone not receiving a prize who has solved at least one problem completely receives an honourable mention. Special awards are sometimes given for outstanding solutions.

The problems in the IMO are difficult but do not really require any knowledge outside secondary school maths syllabuses.