Question

12 wires each of resistance 'r' ohm are connected to form a cube. Find the resistance if current enters through one edge and leaves through other corner of the same edge of the cube

Answer 1

I like this question. Draw the figure.

Trail the currents. Let the entering current be 12I, so each branch current is 4I. EAch of those branch currents splits into two currents of 2I each. Now look draw the currents on the diagrams. You see coming into the final node, three currents of 4I each.

Now consider the voltage drop.
first path, voltage drop of 4I*r=4rI.
second path, voltage drop of 2I*r=2rI
final path, voltage drop of 4I*r=4rI

sum of voltage drops=10I

total current=12I

network resistance=V/I=5r/6 ohms

check my thinking.

Answer 2

http://www.rfcafe.com/miscellany/factoids/kirts-cogitations-256.htm