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Intersecting diagonals in an n-gon

Source: All Russian-2014 Grade 9 Day 1 P3

May 17, 2014
inductiongeometrycombinatorics proposedcombinatorics

Problem Statement

In a convex nn-gon, several diagonals are drawn. Among these diagonals, a diagonal is called good if it intersects exactly one other diagonal drawn (in the interior of the nn-gon). Find the maximum number of good diagonals.