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3

Part of 2021 Caucasus Mathematical Olympiad

Problems(1)

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

Source: VI Caucasus Mathematical Olympiad

3/14/2021
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.)
combinatorial geometrycombinatorics