# Answer

**The Maximum Result**

Given a network with resistors of resistances R1,…,RnR1,…,Rn, choose a path from the initial vertex to the terminal vertex, and remove all of the resistors not on the path. This does not decrease the resistance, and the resulting network is a simple series network involving *some* of the initial resistors. In particular, the resulting network has resistance at most R1+⋯+RnR1+⋯+Rn.

**The Minimum Result**

Given a network with resistors of resistances R1,…,RnR1,…,Rn, choose a minimal cut set, i.e. a minimal set of resistors whose removal disconnects the initial vertex from the terminal vertex. Replace all resistors that are not in this cut set by shorts. This does not increase the resistance, and the result network is a simple parallel network involving *some* of the initial resistors. In particular, the resulting network has resistance at least R1∥⋯∥Rn