analysis - How to calculate equivalent resistance?

This is not homework.

Imagine an infinite resistor grid which the picture shows a part of. The question is what's the resistance measured across any of the 1k\$\Omega\$ resistors. I don't want you to tell me the answer, I already know. I want to know how to find the solution. I wish I could show where I got so far, but I'm afraid I don't even get started.

To anyone who wants to try for himself, and doesn't want to know the solution: don't click the link to the solution.