In the 1930s Jón Guðmundsson was one of the most promising young chess players in Iceland. He three times won the Icelandic Chess Championship (1932, 1936, 1937).
- In 1930, in the 3rd Chess Olympiad in Hamburg (+3, =4, -10),
- In 1937, at second reserve board in the 7th Chess Olympiad in Stockholm (+4, =5, -7),
- In 1939, at third board in the 8th Chess Olympiad in Buenos Aires (+11, =0, -3) and won individual gold medal for group "B", showing a hundred percent result in this group - 10 wins in 10 games.
After this success in 1939 Chess Olympiad, Jón Guðmundsson rarely participated in chess tournaments in the next years.
- Jökulsson, Hrafn (3 August 2014). "Íslendingar með á Ólympíuskákmóti 1930: Frumraun íslenskra skákmanna á erlendri grund!".
- "OlimpBase :: Men's Chess Olympiads :: Jón Guðmundsson". www.olimpbase.org.
- Jón Guðmundsson player profile and games at Chessgames.com
- Jón Guðmundsson chess games at 365chess.com
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