Challenging Recreational Mathematics: ▪ Λύσεις Προβλημάτων Διεθνών Μαθηματικών Ολυμπιάδων (στα αγγλικά)

Πέμπτη 2 Φεβρουαρίου 2012

▪ Λύσεις Προβλημάτων Διεθνών Μαθηματικών Ολυμπιάδων (στα αγγλικά)

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

There was no IMO in 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 Marcin Kuczma, Poland
Problem 5 proposed by Hans Zantema, Netherlands
Problem 6 proposed by Morteza Saghafiyan, Iran

2011

2011 IMO (in the Netherlands)
2011 IMO Problems
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 Japan

Πηγή: artofproblemsolving.com

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