There is an infinite ladder-shaped grid of 1Ω resistors connecting adjacent nodes as follows:

What is the electrical resistance between (a) and (b)? Note: in the image, every resistor is 1Ω.

(In reply to re: Solution by Federico Kereki)

No recurrence is needed. The whole configuration can be thought of as a consisting of four resistors: The one right next to a, the one right next to b, the first vertical one and all the rest, "all the rest" being identical to the original configuration. The latter two are in parallel, the others in serial. So if the whole configuration has resitance x, then

x=1+1+1/(1/1+1/x)

Solve for x and you get x=1+sqrt(3). 

Posted by JLo on 2006-11-03 11:30:37