MathDB

On a plane there is a finite set of

M

points, no three of which are collinear . Some points are joined to others by line segments, with each point connected to no more than one line segment . If we have a pair of intersecting line segments

AB

and

CD

we decide to replace them with

AC

and

BD

, which are opposite sides of quadrilateral

ABCD

. In the resulting system of segments we decide to perform a similar substitution, if possible, and so on . Is it possible that such substitutions can be carried out indefinitely?
(V.E. Kolosov)

Problem Statement