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MathNet 2010 — Part 03 Question 36

Math Olympiad Vault · MathNet 2010 — Part 03

Question 36

Given $2009$ points in the plane so that no three points lie on a line, show that there exist at least $1344021$ triangles, each of which is formed by any three of the $2009$ points, and each of the triangles does not contain any of the remaining $2006$ points.