List

OBM Problems and Solutions

Brazil's national olympiad, first organised by the Brazilian Mathematical Society in 1979. From 1998 it ran in three phases at three school levels, with a university level added in 2001. Since 2017 the school levels qualify through OBMEP and sit a single final, and the university level followed in 2020.

2016

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2015

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2014

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2013

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2012

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University2 problems
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2011

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2010

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2009

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2008

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2007

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2006

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2005

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2004

Brazil

Phase 1
Level 11 problemAll problemsProblemSolution
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblemSolution
Phase 2
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblemSolution
Level 31 problemAll problemsProblemSolution
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2003

Brazil

Phase 1
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
University1 problemAll problemsProblem
Phase 2
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2002

Brazil

Phase 1
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
University1 problemAll problemsProblem
Phase 2
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2001

Brazil

Phase 1
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
University1 problemAll problemsProblem
Phase 2
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
University1 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

2000

Brazil

Phase 1
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
Phase 2
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

1999

Brazil

Phase 1
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
Phase 2
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem

1998

Brazil

Phase 1
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
Phase 2
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem
Phase 3
Level 11 problemAll problemsProblem
Level 21 problemAll problemsProblem
Level 31 problemAll problemsProblem