Nine points

[witzar]

Nine points are given on the plane, no three of which are collinear.
Each pair of points is connected with segment, that is painted either white or black.
Prove that there exists either quadrilateral with white sides and diagonals or triangle with black sides.

[bonanova]

Nine points are given on the plane, no three of which are collinear.

Each pair of points is connected with segment, that is painted either white or black.

Prove that there exists either quadrilateral with white sides and diagonals or triangle with black sides.

Sounds like a Ramsey's Theory question. Prove:

In any group of nine people there are either four people who all know each other or three who are mutual strangers.