IMO 1985 LL NOR61

Consider the set A = {0, 1, 2, . . ., 9} and let (B1, B2, . . . , Bk)

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IMO 1985 LL NOR61

Origin: NOR

Problem

Consider the set A = {0, 1, 2, . . ., 9} and let (B1, B2, . . . , Bk) be a collection of nonempty subsets of A such that Bi \capBj has at most two elements for i ̸= j. What is the maximal value of k?