Problems from olympiads (main page)

Problem Collection for Balkan Mathematical Olympiad


The Balkan Mathematical Olympiad (BMO) is a mathematical competition for high-school students from the region of Balkan.

The first BMO was organized in Greece in 1984. That year four countries competed: Bulgaria, Cyprus, Greece and Romania. Since then, the competition has been held annually. Nowadays there are ten member coutries of BMO: Albania, Bosnia & Herzegovina, Bulgaria, Cyprus, Greece, FYR Macedonia, Moldova, Romania, Serbia & Montenegro, Turkey. However, the hosting country may invite guest teams to participate.

The Competition

Each country sends up to six contestants, a team leader and a deputy leader. Like the IMO, this is an individual competition. On the competition students are given 4.5 hours to solve 4 problems. Each problem is worth 10 points, making 40 the maximum possible score.


Successful contestants are awarded first, second, and third prizes. A honorable mention is awarded to each student who does not receive a prize, but who has obtained 10 points on at least one question. The total number of prizes should not exceed 2/3 of participans, and the first, second, and third prizes are distributed approximately in the ratio 1:2:3.


The total number of available problems is 104.

Year BMO
1984 BMO
1985 BMO
1986 BMO
1987 BMO
1988 BMO
1989 BMO
1990 BMO
1991 BMO
1992 BMO
Year BMO
1993 BMO
1994 BMO
1995 BMO
1996 BMO
1997 BMO
1998 BMO
1999 BMO
2000 BMO
2001 BMO
Year BMO
2002 BMO
2003 BMO
2004 BMO
2005 BMO
2006 BMO
2007 BMO
2008 BMO
2009 BMO