ÖMO 2007 Problem 5

38th Austrian Mathematical Olympiad 2007, round 3 problem 5

Given is a convex $n$ -gon with a triangulation, that is a partition into triangles through diagonals that don't cut each other. Show that it's always possible to mark the $n$ corners with the digits of the number $2007$ such that every quadrilateral consisting of $2$ neighbored (along an edge) triangles has got $9$ as the sum of the numbers on its $4$ corners.