Equivalent resistance of 2015 points

[jbriggs444]

is it that there is no potential difference across A and B

I assume that your two terminals are the nodes in the upper left and upper right. Yes, since there is no potential difference between A and B (by a symmetry argument), one can remove the direct connection between A and B without modifying the resistance of the network.

With that link removed, one can see that there are exactly three parallel paths. Two of length 2 and one of length 1.

Similarly for any number of nodes greater than 4. Since all of the intermediate nodes are at the same potential, one can remove all of their direct connections to one another without modifying the resistance of the network. One is left with n-1 parallel paths. n-2 of length 2 and one of length 1.

 

[timetraveller123]

i was thinking of that too and i realized that was how you derived your symetry method really smart