MathDB

There are

k

points in the interior of a pentagon. Together with the vertices of the pentagon they form a

(k + 5)

-element set

M

. The area of the pentagon is defined by connecting lines between the points of

M

into sub-areas in such a way that it is divided into sub-areas in such a way that no sub-areas have a point on their interior of

M

and contains exactly three points of

M

on the boundary of each part. None of the connecting lines has a point in common with any other connecting line or pentagon side, which does not belong to

M

. With such a decomposition of the pentagon, there can be an even number of connecting lines (including the pentagon sides) go out? The answer has to be justified.

Problem Statement