MathDB

Let

n \in \mathbb{N}^*

and consider a circle of length

6n

along with

3n

points on the circle which divide it into

3n

arcs:

n

of them have length

1,

some other

n

have length

2

and the remaining

n

have length

3.

Prove that among these points there must be two such that the line that connects them passes through the center of the circle.

Problem Statement