Question 58
One of the numbers $0$ or $1$ is assigned to every vertex of a regular polygon. Rudi divides the polygon to triangles by drawing some diagonals that intersect each other only in the vertices of the polygon, and then inside each triangle writes the sum of the numbers assigned to its vertices. Prove that Rudi can choose the diagonals to draw in such a way that the minimal and the maximal number inside the triangles differ by at most $1$. (Estonia 2010)