# Maximize resistance in a 3 ring symmetrical circuit

I came up with this question as I tried to extend the problem of maximizing the resistance in a circle by selecting two points where to connect the electrodes. The solution for this problem is obvious - antipodal points, however, naturally my other problem is more complex, and I don't know how to go about solving it.

I have a circuit which looks like this:

All the rings are connected at all intersection points and all have equal crossectional area and density.

The problem: Where would you connect two electrodes so that the effective resistance of the circuit would be maximal?

I know you could try doing some complex mathematics with Kirchhoff laws, but is there a simpler way?

• Interesting problem. I think that using symmetry arguments it may be possible to topologically simplify that mess of intersecting wires in the middle to just a Y-shaped connection consisting of three resistors of equal value. But I still don't see a simple solution to the problem. – Samuel Weir May 15 '17 at 22:17