Question 26
There are $n$ lines $(n\gt 2)$ given in the plane. No two of the lines are parallel and no three of them intersect at one point. Every point of intersection of these lines is labelled with a natural number between $1$ and $n-1$. Prove that, if and only if $n$ is even, it is possible to assign the labels in such a way that every line has all the numbers from $1$ to $n-1$ at its points of intersection with the other $n-1$ lines.