MathDB

There are

n

dots on the plane such that no three dots are collinear. Each dot is assigned a

0

or a

1

. Each pair of dots is connected by a line segment. If the endpoints of a line segment are two dots with the same number, then the segment is assigned a

0

. Otherwise, the segment is assigned a

1

. Find all

n

such that it is possible to assign

0

's and

1

's to the

n

dots in a way that the corresponding line segments are assigned equally many

0

's as

1

's.

Problem Statement