Say we have $n$ resistors, with unknown resistances $r_1,\ldots,r_n$. We build a network using these, along with any finite number of other resistors of known resistance. We then measure the resistance $R$ of our network between two points, which we think of as a function of $n$ variables $R(r_1,\ldots,r_n)$.
The question: which functions can arise this way?
It can be checked that $R$ must be a rational function whose numerator and denominator have degree at most $1$ in each variable separately, and that all of the coefficients should be non-negative. These conditions are not sufficient: a recent question on puzzling.SE concluded that the function $R(r_1,r_2)=r_1r_2$ could not occur.