Solve the 2011-Point Resistance Challenge!

[ashishsinghal]

This is a fun question I found and wanted to share. Please, do not bother to tell me that I need to post equations or show my attempt as I have solved it myself. As I liked this question I am sharing it on PF.
Here it goes:

There are 2011 points randomly chosen and a resistance R is connected between every possible pair of points. Any two points are taken and marked as a and b. Find net resistance between a and b.

Do not right the solutions so as to preserve the question.

 

[ashishsinghal]

Here 2011 is taken to mark the year that's all...

 

[ashishsinghal]

Hey, come on has no one try to do this question. Or is it that no is posting any comment?
I thought it would be fun...

 

[brocks]

Well, you said not to post the answer, so what exactly do you want?

 

[Quinzio]

mmm... it's a very beautiful problem.
I have come to the solution, but it's quite hard to break down.
I think many people here wants to have their homework done, that's it.
Anyway, once you "see" how the current splits in the branches, it looks very "amazing".
I'm tempted to write the solution, I'm not even sure it's correct, btw.

I think I saw it again time ago, but I didn't got any solution at that time.

Thank you... nice food for thoughts (it took me one hour !).

 

[ashishsinghal]

Well, you said not to post the answer, so what exactly do you want?

Well, I asked not to post a solution. You can post your answer with a spoiler alert wrapped over it.

 

[ashishsinghal]

It is like a riddle closely related to the subject. So I could not find any place better than this. The main reason why I am urging to post is that without posts the thread will be soon lost and I wanted the question to spread. For the sake of Physics...