Let $n \ge 3$ be an integer. A finite number of disjoint arcs with the total sum of length $1 -\frac{1}{n}$ are given on a circle of perimeter $1$. Prove that there is a regular $n$-gon whose all vertices lie on the considered arcs
Source: Romania IMO TST 1991 p6
Tags: combinatorics, combinatorial geometry
Let $n \ge 3$ be an integer. A finite number of disjoint arcs with the total sum of length $1 -\frac{1}{n}$ are given on a circle of perimeter $1$. Prove that there is a regular $n$-gon whose all vertices lie on the considered arcs