An electricity and magnetism problem by Jonathan Schirmer

We can see from symmetry that the potential at the center should be a linear combination of the potential on each face. Since it is a cube weight factor of each face is 1/6. Therefore potential at center is $5/6 \times 0$ + $1/6\times20$ . Why linear combination and not quadratic or higher? That would violate consistency.

I thought I did it wrong. Since the cube has six conducting plates, hence the potential is $\displaystyle \frac{20}{6} \text{V} = \frac{10}{3} \text{V}.$ Therefore, the required answer is $\displaystyle 10 + 3 = 13.$

$\frac{20}{6}=\frac{10}{3}$

$(a+b)=\fbox{13}$

Clearly, the answer is $\dfrac {20}{6} \, \text{V} = \dfrac {10}{3} \, \text{V} \rightarrow \boxed {13}$ .