MathDB

Let

n_1, n_2

be positive integers. Consider in a plane

E

two disjoint sets of points

M_1

and

M_2

consisting of

2n_1

and

2n_2

points, respectively, and such that no three points of the union

M_1 \cup M_2

are collinear. Prove that there exists a straightline

g

with the following property: Each of the two half-planes determined by

g

E

(

g

not being included in either) contains exactly half of the points of

M_1

and exactly half of the points of

M_2.

Problem Statement