Problem

Source: Bundeswettbewerb Mathematik 2023, Round 2 - Problem 4

Tags: combinatorics, combinatorics proposed, construction



Exactly $n$ chords (i.e. diagonals and edges) of a regular $2n$-gon are coloured red, satisfying the following two conditions: (1) Each of the $2n$ vertices occurs exactly once as the endpoint of a red chord. (2) No two red chords have the same length. For which positive integers $n \ge 2$ is this possible?