There are n>2 lines 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. modular arithmeticgraph theorycombinatorics proposedcombinatorics