## 29 Sep 2013

### 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

$\frac{4m}{3n}.\left&space;(&space;m-\frac{n^{2}}{4}&space;\right&space;)$

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

[APMO 1989 Q 4]

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