IMO Shortlist 2001 problem C8

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2. travnja 2012.
Twenty-one girls and twenty-one boys took part in a mathematical competition. It turned out that each contestant solved at most six problems, and for each pair of a girl and a boy, there was at least one problem that was solved by both the girl and the boy. Show that there is a problem that was solved by at least three girls and at least three boys.
Izvor: Međunarodna matematička olimpijada, shortlist 2001