MathDB

Let

n

and

k

be positive integers. Let

A

be a set of

2n

distinct points on the Euclidean plane such that no three points in

A

are collinear. Some pairs of points in

A

are linked with a segment so that there are

n^2 + k

distinct segments on the plane. Prove that there exists at least

\frac{4}{3}k^{3/2}

distinct triangles on the plane with vertices in

A

and sides as the aforementioned segments.
Proposed by Ho-Chien Chen

Problem Statement