Question 185
Given a convex polyhedron with 2022 faces. On 3 arbitrary faces, the numbers 26, 4 and 2022 are already written (each face contains one number). One wants to write in each other face a real number which is the arithmetic mean of all the numbers in the faces that share a common edge with that face. Prove that there is exactly one way to fill in all the numbers of that polyhedron.