MathDB

Consider a system of infinitely many spheres made of metal, with centers at points

(a, b, c) \in \mathbb Z^3

. We say that the system is stable if the temperature of each sphere equals the average temperature of the six closest spheres. Assuming that all spheres in a stable system have temperatures between

0^\circ C

and

1^\circ C

, prove that all the spheres have the same temperature.

Problem Statement