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Maximum and minimum number of intersection

Source: Iranian third round 2019 finals Combinatorics exam problem 2

August 27, 2019
combinatorics

Problem Statement

Let TT be a triangulation of a 100100-gon.We construct P(T)P(T) by copying the same 100100-gon and drawing a diagonal if it was not drawn in TT an there is a quadrilateral with this diagonal and two other vertices so that all the sides and diagonals(Except the one we are going to draw) are present in TT.Let f(T)f(T) be the number of intersections of diagonals in P(T)P(T).Find the minimum and maximum of f(T)f(T).
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