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An estimate for the number of triangles with vertices in given points

Source: VI Caucasus Mathematical Olympiad

March 14, 2021
combinatorial geometrycombinatorics

Problem Statement

Let n≥3n\ge 3 be a positive integer. In the plane nn points which are not all collinear are marked. Find the least possible number of triangles whose vertices are all marked.
(Recall that the vertices of a triangle are not collinear.)
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