How about we consider the edges to be resistances (equal of course) and then think about the current distribution? That is one way of doing the specific case I mentioned, so it might help in the general case too.
Current is constant and uniform. No specific details about current/current density were given so I believe it's supposed to be constant and uniform(like no variations whatsoever). Current flows along the edges only.
Basically, any two completely random points on the edges of the cube. The...
I could solve a similar (rather, a specific case of the above) where the current entered through a
corner and left from the corner opposite to it along the body diagonal of the cube. For this specific case, I was able to easily exploit symmetry to deduce the answer (0). However, I cannot think...