Physics Cup - 2017, Problem 2

For this problem, there were several slightly different approaches which could be used, and I decided to give a bonus to the best-written solution for each different approach. And so, the best solution awards [bonus factor exp(1/3)] goes to:
Marco Malandrone
Siddharth Tiwary (Here, the bonus is given for an attempt of looking more deeply into the distribution of currents.)
Victor Almeida Ivo
Apart from these, here is a solution by Elvinas Ribinskas which doesn't strictly satisfy the requirements as the answer is expressed as a continued fraction with computational complexity O(n). However, continued fractions are fun, too, so after delaying the decision for several weeks, I still decided to award him a full mark.

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