# 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 2011
- 54 2012
- 55 2013
- 56 2014
- 57 2015
- 58 Comment
- 59 See also

## 1959

- 1959 IMO (in Romania)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- Problem 1 proposed by Severino Gervacio and 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- Problem 1 proposed by Charles Leytem, Luxembourg
- Problem 2 proposed by Ravi 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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)
- 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 Marcin Kuczma, Poland
- Problem 5 proposed by Hans Zantema, Netherlands
- Problem 6 proposed by Morteza Saghafiyan, Iran

## 2011

- 2011 IMO (in the Netherlands)
- Problem 1 proposed by Fernando Campos, Mexico
- Problem 2 proposed by Geoff Smith, United Kingdom
- Problem 3 proposed by Igor Voronovich, Belarus
- Problem 4 proposed by Morteza Saghafiyan, Iran
- Problem 5 proposed by Seyedmahyar Sefidgaran, Iran
- Problem 6 proposed by Japanese PSC, Japan

## 2012

- 2012 IMO (in Argentina)
- Problem 1 proposed by Evangelos Psychas, Greece
- Problem 2 proposed by Angelo di Pasquale, Australia
- Problem 3 proposed by David Arthur, Canada
- Problem 4 proposed by Liam Baker, South Africa
- Problem 5 proposed by Josef Tkadlec, Czech Republic
- Problem 6 proposed by Dušan Djukić, Serbia

## 2013

- 2013 IMO (in Colombia)
- Problem 1 proposed by Japanese PSC, Japan
- Problem 2 proposed by Ivan Guo, Australia
- Problem 3 proposed by Alexander A. Polyansky, Russia
- Problem 4 proposed by Warut Suksompong and Potcharapol Suteparuk, Thailand
- Problem 5 proposed by Nikolai Nikolov, Bulgaria
- Problem 6 proposed by Alexander S. Golovanov and Mikhail A. Ivanov, Russia

## 2014

- 2014 IMO (in South Africa)
- Problem 1 proposed by Gerhard Woeginger, Austria
- Problem 2 proposed by Tonči Kokan, Croatia
- Problem 3 proposed by Iran
- Problem 4 proposed by Giorgi Arabidze, Georgia
- Problem 5 proposed by Luxembourg
- Problem 6 proposed by Gerhard Woeginger, Austria

## 2015

- 2015 IMO (in Thailand)
- Problem 1 proposed by Merlijn Staps, Netherlands
- Problem 2 proposed by Dušan Djukić, Serbia
- Problem 3 proposed by Danylo Khilko and Mykhailo Plotnikov, Ukraine
- Problem 4 proposed by Silouanos Brazitikos and Evangelos Psychas, Greece
- Problem 5 proposed by Dorlir Ahmeti, Albania
- Problem 6 proposed by Ross Atkins and Ivan Guo, Australia

## 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.