Question 132
Let $n$ be a positive integer and let $C$ be a circle whose circumference is equal to $6n$. The circle $C$ is divided by $3n$ points into $3n$ small arcs such that $n$ of them have the lengths equal with $1$, other $n$ have the lengths equal with $2$ and the remaining $n$ arcs have the lengths equal with $3$. Prove that among the given $3n$ points there are two which are antipodal.