Triangles in a Complete Graph

Discrete Mathematics Level 3

A straight-line drawing of a graph $G$ is a drawing of $G$ on the plane such that all its edges are straight line segments.

The maximum number of triangles that can be found in a straight-line drawing of the complete graph $K_4$ is 8, as seen in the image. For $K_5$ , there can be up to 35 triangles.

What is the maximum number of triangles that can be found in a straight-line drawing of the complete graph $K_{10}$ ?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.