APMO 1989 Q4: Combinatorics: Upper Secondary Mathematics Competition Question

Let S be a set consisting of m pairs (a, b) of positive integers with the property that 1 ≤ a < b ≤ n. Show that there are at least



triples (a, b, c) such that (a, b), (a, c), and (b, c) belong to S.


[APMO 1989 Q 4]

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