A problem by Chandler West

Level pending

Nine nodes are arranged on a three by three grid. You randomly place wires of resistance \(R\) between adjacent nodes (see image), and measure the resistance between the bottom left and top right nodes. It can be shown that out of 4096 possible configurations, 1135 form a valid circuit, in which it is possible to make this measurement. Assuming that you ignore any invalid circuits, the expected value of the equivalent resistance between the bottom left and top right nodes (node \(A\) and node \(I\)) can be written in the form

\(\frac{nR}{d}\)

What is the sum of the digits of \(n + d\)?

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