MathDB

Let

A

be a point in the plane and

3

lines which pass through this point divide the plane in

6

regions. In each region there are

5

points. We know that no three of the

30

points existing in these regions are collinear. Prove that there exist at least

1000

triangles whose vertices are points of those regions such that

A

lies either in the interior or on the side of the triangle.

2