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2000 HMMT RMT Team #13 max no of intersections inside convex n-gon

Source:

March 8, 2024
combinatoricscombinatorial geometrygeometry

Problem Statement

Let P1,P2,...,PnP_1, P_2,..., P_n be a convex nn-gon. If all lines PiPjP_iP_j are joined, what is the maximum possible number of intersections in terms of nn obtained from strictly inside the polygon?
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