Consider a system of infinitely many spheres made of metal, with centers at points (a,b,c)∈Z3. 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∘C and 1∘C, prove that all the spheres have the same temperature. geometry3D geometryspherecombinatorics unsolvedcombinatorics