MathNet 2021 — Part 07 Question 52

Let $n$ be a positive integer. Prove that in a regular $6 n$-gon, we can draw $3 n$ diagonals with pairwise distinct ends and partition the drawn diagonals into $n$ triplets so that:

- the diagonals in each triplet intersect in one interior point of the polygon and

- all these $n$ intersection points are distinct.