Consider 12 identical resistors connected to form a cube. That is, each resistor lies on the edge of a cube, and there is an electrical connection joining three resistors at each of the cube’s eight vertices.
What is the effective resistance between two vertices across a body diagonal of the cube?
I’ll update this post with my solution (you can probably find solutions all over the internet if you get stuck, but give it a good try if interested!) in a day or two.