What is the resistance between two points a knights move away on a infinite grid of 1-ohm resistors

Question

On an infinite grid of ideal one-ohm resistors, what's the equivalant resistance between two nodes a knights move away?

_{(please fix the tags, I didn't really know where to put it)}

Answer 1

After Google asked this in their aptitude test, this has become a famous problem.

You can find a nice discussion and a more general solution here: http://www.mathpages.com/home/kmath668/kmath668.htm

I believe the answer for your case is $\displaystyle \dfrac{4}{\pi} - \dfrac{1}{2}$.