Question 18
In a regular $n$-gon, either $0$ or $1$ is written at each vertex. Using non-intersecting diagonals, Juku divides this polygon into triangles. Then he writes into each triangle the sum of the numbers at its vertices. Prove that Juku can choose the diagonals in such a way that the maximal and minimal number written into the triangles differ by at most $1$. (Seniors.)