# IMO Problems and Solutions

This page lists the authors and the proposing countries of the problems of the IMO.

## Contents

- 1 1959
- 2 1960
- 3 1961
- 4 1962
- 5 1963
- 6 1964
- 7 1965
- 8 1966
- 9 1967
- 10 1968
- 11 1969
- 12 1970
- 13 1971
- 14 1972
- 15 1973
- 16 1974
- 17 1975
- 18 1976
- 19 1977
- 20 1978
- 21 1979
- 22 1980
- 23 1981
- 24 1982
- 25 1983
- 26 1984
- 27 1985
- 28 1986
- 29 1987
- 30 1988
- 31 1989
- 32 1990
- 33 1991
- 34 1992
- 35 1993
- 36 1994
- 37 1995
- 38 1996
- 39 1997
- 40 1998
- 41 1999
- 42 2000
- 43 2001
- 44 2002
- 45 2003
- 46 2004
- 47 2005
- 48 2006
- 49 2007
- 50 2008
- 51 2009
- 52 2010
- 53 Comment
- 54 See also

## 1959

- 1959 IMO (in Romania)
- 1959 IMO Problems
- Problem 1 proposed by Poland
- Problem 2 proposed by Constantin Ionescu-Tiu, Romania
- Problem 3 proposed by Hungary
- Problem 4 proposed by Hungary
- Problem 5 proposed by Cezar Cosnita, Romania
- Problem 6 proposed by Czechoslovakia

## 1960

- 1960 IMO (in Romania)
- 1960 IMO Problems
- Problem 1 proposed by Bulgaria
- Problem 2 proposed by Hungary
- Problem 3 proposed by Gheorghe D. Simionescu, Romania
- Problem 4 proposed by Hungary
- Problem 5 proposed by Czechoslovakia
- Problem 6 proposed by Bulgaria
- Problem 7 proposed by East Germany

## 1961

- 1961 IMO (in Hungary)
- 1961 IMO Problems
- Problem 1 proposed by Hungary
- Problem 2 proposed by Poland
- Problem 3 proposed by Bulgaria
- Problem 4 proposed by East Germany
- Problem 5 proposed by Czechoslovakia
- Problem 6 proposed by Gheorghe D. Simionescu, Romania

## 1962

- 1962 IMO (in Czechoslovakia)
- 1962 IMO Problems
- Problem 1 proposed by Poland
- Problem 2 proposed by Hungary
- Problem 3 proposed by Czechoslovakia
- Problem 4 proposed by Cezar Cosnita, Romania
- Problem 5 proposed by Bulgaria
- Problem 6 proposed by East Germany
- Problem 7 proposed by USSR

## 1963

- 1963 IMO (in Poland)
- 1963 IMO Problems
- Problem 1 proposed by Czechoslovakia
- Problem 2 proposed by USSR
- Problem 3 proposed by Hungary
- Problem 4 proposed by USSR
- Problem 5 proposed by Wolfgang Engel, East Germany
- Problem 6 proposed by Hungary

## 1964

- 1964 IMO (in USSR)
- 1964 IMO Problems
- Problem 1 proposed by Czechoslovakia
- Problem 2 proposed by Hungary
- Problem 3 proposed by Yugoslavia
- Problem 4 proposed by Hungary
- Problem 5 proposed by Gheorghe D. Simionescu, Romania
- Problem 6 proposed by Poland

## 1965

- 1965 IMO (in East Germany)
- 1965 IMO Problems
- Problem 1 proposed by Yugoslavia
- Problem 2 proposed by Poland
- Problem 3 proposed by Czechoslovakia
- Problem 4 proposed by USSR
- Problem 5 proposed by Gheorghe D. Simionescu, Romania
- Problem 6 proposed by Poland

## 1966

- 1966 IMO (in Bulgaria)
- 1966 IMO Problems
- Problem 1 proposed by USSR
- Problem 2 proposed by Hungary
- Problem 3 proposed by Bulgaria
- Problem 4 proposed by Yugoslavia
- Problem 5 proposed by Czechoslovakia
- Problem 6 proposed by Poland

## 1967

- 1967 IMO (in Yugoslavia)
- 1967 IMO Problems
- Problem 1 proposed by Poland
- Problem 2 proposed by Czechoslovakia
- Problem 3 proposed by United Kingdom
- Problem 4 proposed by Tullio Viola, Italy
- Problem 5 proposed by USSR
- Problem 6 proposed by Hungary

## 1968

- 1968 IMO (in USSR)
- 1968 IMO Problems
- Problem 1 proposed by Unknown Author, Romania (taken from a Romanian problem book)
- Problem 2 proposed by Czechoslovakia
- Problem 3 proposed by Bulgaria
- Problem 4 proposed by Poland
- Problem 5 proposed by East Germany
- Problem 6 proposed by David Monk, United Kingdom

## 1969

- 1969 IMO (in Romania)
- 1969 IMO Problems
- Problem 1 proposed by Wolfgang Engel, East Germany
- Problem 2 proposed by Hungary
- Problem 3 proposed by Poland
- Problem 4 proposed by Netherlands
- Problem 5 proposed by A. Mekei, Mongolia
- Problem 6 proposed by USSR

## 1970

- 1970 IMO (in Hungary)
- 1970 IMO Problems
- Problem 1 proposed by Poland
- Problem 2 proposed by Dumitru Batinetzu, Romania
- Problem 3 proposed by Åke Samuelsson, Sweden
- Problem 4 proposed by Czechoslovakia
- Problem 5 proposed by Bulgaria
- Problem 6 proposed by USSR

## 1971

- 1971 IMO (in Czechoslovakia)
- 1971 IMO Problems
- Problem 1 proposed by Hungary
- Problem 2 proposed by USSR
- Problem 3 proposed by Poland
- Problem 4 proposed by Netherlands
- Problem 5 proposed by Bulgaria
- Problem 6 proposed by Sweden

## 1972

- 1972 IMO (in Poland)
- 1972 IMO Problems
- Problem 1 proposed by USSR
- Problem 2 proposed by Netherlands
- Problem 3 proposed by United Kingdom
- Problem 4 proposed by Netherlands
- Problem 5 proposed by Bulgaria
- Problem 6 proposed by United Kingdom

## 1973

- 1973 IMO (in USSR)
- 1973 IMO Problems
- Problem 1 proposed by Czechoslovakia
- Problem 2 proposed by Poland
- Problem 3 proposed by Åke Samuelsson, Sweden
- Problem 4 proposed by Ðorde Dugošija, Yugoslavia
- Problem 5 proposed by Poland
- Problem 6 proposed by Åke Samuelsson, Sweden

## 1974

- 1974 IMO (in East Germany)
- 1974 IMO Problems
- Problem 1 proposed by Murray Klamkin, USA
- Problem 2 proposed by Matti Lehtinen, Finland
- Problem 3 proposed by Ciprian Borcea, Romania
- Problem 4 proposed by Bulgaria
- Problem 5 proposed by Jan van de Craats, Netherlands
- Problem 6 proposed by Sweden

## 1975

- 1975 IMO (in Bulgaria)
- 1975 IMO Problems
- Problem 1 proposed by Czechoslovakia
- Problem 2 proposed by United Kingdom
- Problem 3 proposed by Jan van de Craats, Netherlands
- Problem 4 proposed by USSR
- Problem 5 proposed by USSR
- Problem 6 proposed by David Monk, United Kingdom

## 1976

- 1976 IMO (in Austria)
- 1976 IMO Problems
- Problem 1 proposed by Czechoslovakia
- Problem 2 proposed by Matti Lehtinen, Finland
- Problem 3 proposed by Jan van de Craats, Netherlands
- Problem 4 proposed by Murray Klamkin, USA
- Problem 5 proposed by Jan van de Craats, Netherlands
- Problem 6 proposed by Robert Lyness and David Monk, United Kingdom

## 1977

- 1977 IMO (in Yugoslavia)
- 1977 IMO Problems
- Problem 1 proposed by Jan van de Craats, Netherlands
- Problem 2 proposed by Phan Duc Chinh, Vietnam
- Problem 3 proposed by Jan van de Craats, Netherlands
- Problem 4 proposed by David Monk, United Kingdom
- Problem 5 proposed by Hermann Frasch, West Germany
- Problem 6 proposed by Ivan Prodanov, Bulgaria

## 1978

- 1978 IMO (in Romania)
- 1978 IMO Problems
- Problem 1 proposed by Cuba
- Problem 2 proposed by Murray Klamkin, USA
- Problem 3 proposed by United Kingdom
- Problem 4 proposed by Murray Klamkin, USA
- Problem 5 proposed by France
- Problem 6 proposed by Jan van de Craats, Netherlands

## 1979

- 1979 IMO (in United Kingdom)
- 1979 IMO Problems
- Problem 1 proposed by Arthur Engel, West Germany
- Problem 2 proposed by Nickolay Khadzhiivanov and Nedjalko Nenov, Bulgaria
- Problem 3 proposed by Nikolai Vasil'ev and Igor F. Sharygin, USSR
- Problem 4 proposed by Murray Klamkin, USA
- Problem 5 proposed by Joe Gillis, Israel
- Problem 6 proposed by Arthur Engel, West Germany

## 1980

## 1981

- 1981 IMO (in USA)
- 1981 IMO Problems
- Problem 1 proposed by David Monk, United Kingdom
- Problem 2 proposed by Arthur Engel, West Germany
- Problem 3 proposed by Jan van de Craats, Netherlands
- Problem 4 proposed by Belgium
- Problem 5 proposed by USSR
- Problem 6 proposed by Juha Oikkonen, Finland

## 1982

- 1982 IMO (in Hungary)
- 1982 IMO Problems
- Problem 1 proposed by David Monk, United Kingdom
- Problem 2 proposed by Jan van de Craats, Netherlands
- Problem 3 proposed by Alexander N. Grishkov, USSR
- Problem 4 proposed by David Monk, United Kingdom
- Problem 5 proposed by Jan van de Craats, Netherlands
- Problem 6 proposed by Van Nhu Cuong, Vietnam

## 1983

- 1983 IMO (in France)
- 1983 IMO Problems
- Problem 1 proposed by David Monk, United Kingdom
- Problem 2 proposed by Igor F. Sharygin, USSR
- Problem 3 proposed by Arthur Engel, West Germany
- Problem 4 proposed by Belgium
- Problem 5 proposed by Marcin Kuczma, Poland
- Problem 6 proposed by Murray Klamkin, USA

## 1984

- 1984 IMO (in Czechoslovakia)
- 1984 IMO Problems
- Problem 1 proposed by Michael Stoll and Bruno Haible, West Germany
- Problem 2 proposed by Aiko Tiggelaar, Netherlands
- Problem 3 proposed by Ioan Tomescu, Romania
- Problem 4 proposed by Laurentiu Panaitopol, Romania
- Problem 5 proposed by Tserendorj Dashdorj, Mongolia
- Problem 6 proposed by Poland

## 1985

- 1985 IMO (in Finland)
- 1985 IMO Problems
- Problem 1 proposed by Frank Budden, United Kingdom
- Problem 2 proposed by George Szekeres, Australia
- Problem 3 proposed by Jan van de Craats, Netherlands
- Problem 4 proposed by R. Gonchigdorj, Mongolia
- Problem 5 proposed by Igor F. Sharygin, USSR
- Problem 6 proposed by Åke Samuelsson, Sweden

## 1986

- 1986 IMO (in Poland)
- 1986 IMO Problems
- Problem 1 proposed by Arthur Engel, West Germany
- Problem 2 proposed by Gengzhe Chang and Dongxu Qi, China
- Problem 3 proposed by Elias Wegert, East Germany
- Problem 4 proposed by Sven Sigurðsson, Iceland
- Problem 5 proposed by David Monk, United Kingdom
- Problem 6 proposed by Konrad Engel, East Germany

## 1987

- 1987 IMO (in Cuba)
- 1987 IMO Problems
- Problem 1 proposed by Horst Sewerin, West Germany
- Problem 2 proposed by I.A. Kushnir, USSR
- Problem 3 proposed by Arthur Engel, West Germany
- Problem 4 proposed by Nguyen Minh Duc, Vietnam
- Problem 5 proposed by Hans-Dietrich Gronau, East Germany
- Problem 6 proposed by Vsevolod F. Lev, USSR

## 1988

- 1988 IMO (in Australia)
- 1988 IMO Problems
- Problem 1 proposed by Lucien Kieffer, Luxembourg
- Problem 2 proposed by Czechoslovakia
- Problem 3 proposed by David Monk, United Kingdom
- Problem 4 proposed by Finbarr Holland, Ireland
- Problem 5 proposed by Dimitris Kontogiannis, Greece
- Problem 6 proposed by Stephan Beck, West Germany

## 1989

- 1989 IMO (in West Germany)
- 1989 IMO Problems
- Problem 1 proposed by Jose Marasigan, Philippines
- Problem 2 proposed by Esther Szekeres, Australia
- Problem 3 proposed by Harm Derksen, Netherlands
- Problem 4 proposed by Eggert Briem, Iceland
- Problem 5 proposed by Bernt Lindström, Sweden
- Problem 6 proposed by Marcin Kuczma, Poland

## 1990

- 1990 IMO (in China)
- 1990 IMO Problems
- Problem 1 proposed by C.R. Pranesachar, India
- Problem 2 proposed by Pavol Černek, Czechoslovakia
- Problem 3 proposed by Laurentiu Panaitopol, Romania
- Problem 4 proposed by Albert Erkip, Turkey
- Problem 5 proposed by Hagen von Eitzen, West Germany
- Problem 6 proposed by Harm Derksen, Netherlands

## 1991

- 1991 IMO (in Sweden)
- 1991 IMO Problems
- Problem 1 proposed by Arkadii Skopenkov, USSR
- Problem 2 proposed by Laurentiu Panaitopol, Romania
- Problem 3 proposed by Chengzhang Li, China
- Problem 4 proposed by Cecil Rousseau, USA
- Problem 5 proposed by Johan Yebbou, France
- Problem 6 proposed by Harm Derksen, Netherlands

## 1992

- 1992 IMO (in Russia)
- 1992 IMO Problems
- Problem 1 proposed by Achim Zulauf, New Zealand
- Problem 2 proposed by Belur Jana Venkatachala, India
- Problem 3 proposed by Chengzhang Li, China
- Problem 4 proposed by Johan Yebbou, France
- Problem 5 proposed by Stefano Mortola, Italy
- Problem 6 proposed by Tony Gardiner, United Kingdom

## 1993

- 1993 IMO (in Turkey)
- 1993 IMO Problems
- Problem 1 proposed by Tom Laffey, Ireland
- Problem 2 proposed by David Monk, United Kingdom
- Problem 3 proposed by Kerkko Luosto, Finland
- Problem 4 proposed by Donco Dimovski, Macedonia
- Problem 5 proposed by Elias Wegert, Germany
- Problem 6 proposed by Nicholas de Bruijn, Netherlands

## 1994

- 1994 IMO (in Hong Kong)
- 1994 IMO Problems
- Problem 1 proposed by Vincent Lafforgue, France
- Problem 2 proposed by Hans Lausch, Australia and Garnik Tonoyan, Armenia (independently)
- Problem 3 proposed by Gabriel Istrate, Romania
- Problem 4 proposed by Hans Lausch, Australia
- Problem 5 proposed by David Monk, United Kingdom
- Problem 6 proposed by Kerkko Luosto, Finland

## 1995

- 1995 IMO (in Canada)
- 1995 IMO Problems
- Problem 1 proposed by Borislav Mihailov, Bulgaria
- Problem 2 proposed by Nazar Agakhanov, Russia
- Problem 3 proposed by Jaromír Šimša, Czech Republic
- Problem 4 proposed by Marcin Kuczma, Poland
- Problem 5 proposed by Alastair McNaughton, New Zealand
- Problem 6 proposed by Marcin Kuczma, Poland

## 1996

- 1996 IMO (in India)
- 1996 IMO Problems
- Problem 1 proposed by Kerkko Luosto, Finland
- Problem 2 proposed by Jeffrey Grossman, Canada
- Problem 3 proposed by Mircea Becheanu, Romania
- Problem 4 proposed by Alexander S. Golovanov, Russia
- Problem 5 proposed by Nairi Sedrakyan, Armenia
- Problem 6 proposed by Laurent Rosaz, France

## 1997

- 1997 IMO (in Argentina)
- 1997 IMO Problems
- Problem 1 proposed by Igor Akylich and Igor Voronovich, Belarus
- Problem 2 proposed by David Monk, United Kingdom
- Problem 3 proposed by Oleg Bogopolsky, Russia
- Problem 4 proposed by Ebadollah S. Mahmoodian and Mohammad Mahdian, Iran
- Problem 5 proposed by Petr Kanovsky, Czech Republic
- Problem 6 proposed by Giedrius Alkauskas, Lithuania

## 1998

- 1998 IMO (in Taiwan)
- 1998 IMO Problems
- Problem 1 proposed by Charles Leytem, Luxembourg
- Problem 2 proposed by R.B. Bapat, India
- Problem 3 proposed by Igor Voronovich, Belarus
- Problem 4 proposed by David Monk, United Kingdom
- Problem 5 proposed by Vyacheslav Yasinsky, Ukraine
- Problem 6 proposed by Oleg Mushkarov and Nikolai Nikolov, Bulgaria

## 1999

- 1999 IMO (in Romania)
- 1999 IMO Problems
- Problem 1 proposed by Jan Willemson, Estonia
- Problem 2 proposed by Marcin Kuczma, Poland
- Problem 3 proposed by Eugenii Barabanov and Igor Voronovich, Belarus
- Problem 4 proposed by Liang-Ju Chu, Taiwan
- Problem 5 proposed by Pavel Kozhevnikov, Russia
- Problem 6 proposed by Tetsuya Ando, Japan

## 2000

- 2000 IMO (in South-Korea)
- 2000 IMO Problems
- Problem 1 proposed by Sergei Berlov, Russia
- Problem 2 proposed by Titu Andreescu, USA
- Problem 3 proposed by Sergei Shikh and Igor Voronovich, Belarus
- Problem 4 proposed by Sándor Dobos, Hungary
- Problem 5 proposed by Valerii Senderov, Russia
- Problem 6 proposed by Lev and Tatiana Emelianovii, Russia

## 2001

- 2001 IMO (in USA)
- 2001 IMO Problems
- Problem 1 proposed by Hojoo Lee, South Korea
- Problem 2 proposed by Hojoo Lee, South Korea
- Problem 3 proposed by Christian Bey, Germany
- Problem 4 proposed by Bill Sands, Canada
- Problem 5 proposed by Shay Gueron, Israel. (Also: Problem 2501 in Crux Mathematicorum, February 2000)
- Problem 6 proposed by Aleksander Ivanov, Bulgaria

## 2002

- 2002 IMO (in United Kingdom)
- 2002 IMO Problems
- Problem 1 proposed by Federico Ardila, Colombia
- Problem 2 proposed by Hojoo Lee, South Korea
- Problem 3 proposed by Laurentiu Panaitopol, Romania
- Problem 4 proposed by Mihai Manea, Romania
- Problem 5 proposed by Belur Jana Venkatachala, India
- Problem 6 proposed by Vyacheslav Yasinsky, Ukraine

## 2003

- 2003 IMO (in Japan)
- 2003 IMO Problems
- Problem 1 proposed by Carlos Gustavo Moreira, Brazil
- Problem 2 proposed by Aleksander Ivanov, Bulgaria
- Problem 3 proposed by Waldemar Pompe, Poland
- Problem 4 proposed by Matti Lehtinen, Finland
- Problem 5 proposed by Finbarr Holland, Ireland
- Problem 6 proposed by Johan Yebbou, France

## 2004

- 2004 IMO (in Greece)
- 2004 IMO Problems
- Problem 1 proposed by Dinu Serbanescu and Valentin Vornicu, Romania
- Problem 2 proposed by Hojoo Lee, South Korea
- Problem 3 proposed by Jan Willemson, Estonia
- Problem 4 proposed by Hojoo Lee, South Korea
- Problem 5 proposed by Waldemar Pompe, Poland
- Problem 6 proposed by Mohsen Jamaali and Armin Morabbi, Iran

## 2005

- 2005 IMO (in Mexico)
- 2005 IMO Problems
- Problem 1 proposed by Bogdan Enescu, Romania
- Problem 2 proposed by Nicholas de Bruijn, Netherlands
- Problem 3 proposed by Hojoo Lee, South Korea
- Problem 4 proposed by Mariusz Skalba, Poland
- Problem 5 proposed by Waldemar Pompe, Poland
- Problem 6 proposed by Radu Gologan and Dan Schwarz, Romania

## 2006

- 2006 IMO (in Slovenia)
- 2006 IMO Problems
- Problem 1 proposed by Hojoo Lee, South Korea
- Problem 2 proposed by Dušan Djukić, Serbia
- Problem 3 proposed by Finbarr Holland, Ireland
- Problem 4 proposed by Zuming Feng, USA
- Problem 5 proposed by Dan Schwarz, Romania
- Problem 6 proposed by Dušan Djukić, Serbia

## 2007

- 2007 IMO (in Vietnam)
- 2007 IMO Problems
- Problem 1 proposed by Michael Albert, New Zealand
- Problem 2 proposed by Charles Leytem, Luxembourg
- Problem 3 proposed by Vasily Astakhov, Russia
- Problem 4 proposed by Marek Pechal, Czech Republic
- Problem 5 proposed by Kevin Buzzard and Edward Crane, United Kingdom
- Problem 6 proposed by Gerhard Woeginger, Netherlands

## 2008

- 2008 IMO (in Spain)
- 2008 IMO Problems
- Problem 1 proposed by Andrey Gavrilyuk, Russia
- Problem 2 proposed by Walther Janous, Austria
- Problem 3 proposed by Kęstutis Česnavičius, Lithuania
- Problem 4 proposed by Hojoo Lee, South Korea
- Problem 5 proposed by Bruno Le Floch and Ilia Smilga, France
- Problem 6 proposed by Vladimir Shmarov, Russia

## 2009

- 2009 IMO (in Germany)
- 2009 IMO Problems
- Problem 1 proposed by Ross Atkins, Australia
- Problem 2 proposed by Sergei Berlov, Russia
- Problem 3 proposed by Gabriel Carroll, USA
- Problem 4 proposed by Hojoo Lee, Peter Vandendriessche and Jan Vonk, Belgium
- Problem 5 proposed by Bruno Le Floch, France
- Problem 6 proposed by Dmitry Khramtsov, Russia

## 2010

- 2010 IMO (in Kazakhstan)
- 2010 IMO Problems
- Problem 1 proposed by Pierre Bornsztein, France
- Problem 2 proposed by Tai Wai Ming and Wang Chongli, Hong Kong
- Problem 3 proposed by Gabriel Carroll, USA
- Problem 4 proposed by Poland
- Problem 5 proposed by Netherlands
- Problem 6 proposed by Morteza Saghafiyan, Iran

## Comment

This page lists the authors and the proposing countries of the problems of the IMO.

For many problems, the composers do not have the nationality of the proposing country. For instance, problem 2009/4 was proposed by Belgium, but only two of the three problem authors were Belgian, whereas the third is from South-Korea.

To the current moment, there is only a single IMO problem that has two distinct proposing countries: The if-part of problem 1994/2 was proposed by Australia and its only-if part by Armenia.