Potential Inside Cube: What Is the Center's Potential?

[EFuzzy]

A cube has 5 sides grounded, and an insulated sixth side at potential x. What is the potential at the center of the cube?

The solution states that the potential at the center must be a linear combination of the potentials of the six sides. Why is that?

Thanks,
EFuzzy

 

[Persia]

I guess using principle of superposition...
V=c(v1+v2+...+v6)for each side, where c is a constant . assuming they have the same potential... V=c6V so c=1/6
now v1=0=v2=...=v5 and v6=V'
so V=1/6(0+0+..+0+V')=1/6V'