Question 18
Let $n$ be a positive integer coprime to $6$. We colour the vertices of a regular $n$-gon with three colours in such a way that for each colour the number of vertices coloured with it is odd.
Prove that there is always an isosceles triangle whose vertices are vertices of the $n$-gon and are all coloured differently.
Prove that there is always an isosceles triangle whose vertices are vertices of the $n$-gon and are all coloured differently.