Let M be a set of n≥4 points in the plane, no three of which are collinear. Initially these points are connected with n segments so that each point in M is the endpoint of exactly two segments. Then, at each step, one may choose two segments AB and CD sharing a common interior point and replace them by the segments AC and BD if none of them is present at this moment. Prove that it is impossible to perform n3/4 or more such moves.Proposed by Vladislav Volkov, Russia IMO ShortlistcombinatoricsConvex hull