Question 4
In the plane there is a finite family of disks. Any two are externally disjoint or externally tangent, and no disk touches more than six other disks. Suppose a real number has been assigned to every disk that does not touch six other disks. Prove that there is at most one assignment of real numbers to the remaining disks such that the number on each remaining disk is the arithmetic mean of the six numbers on its six touching disks.