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IMO 2007 — Complete Shortlist Question 15

IMO Shortlist · IMO 2007 — Complete Shortlist

Question 15

Given a convex $n$-gon $P$ in the plane. For every three vertices of $P$, consider the triangle determined by them. Call such a triangle good if all its sides are of unit length.

Prove that there are not more than $\frac{2}{3} n$ good triangles.