Lesson 2

Problem. Let \(c_{n}\) be the number of pairs of crossing edges in the graph \(K_{n}\), drawn as a regular \(n\)-gon (with all sides and diagonals). For example, \(c_{4}=1\), \(c_{5}=5\), \(c_{6}=15\) (note that the central point in the drawing of \(K_{6}\) is counted three times, since there are three distinct pairs of edges crossing exactly at it).