What is the minimum number of doctors that could be at Souderton?

I diagrammed the entire chain both ways for the set up. I then picked the preferable chain, which gave an answer of two, which is correct. My question is, is there anything wrong with this method, for a two group question like this? Chains for reference: Ls-->Nr&Pr-->Ks&Os-->Ns ==========(Ks-->Jr-->Os) I put this section underneath that loops back in) Nr-->Or-->Js-->Kr[or Or]-->Ps-->Lr I noticed in the second chain, there were only Js and Ps, so I picked this. Is this a valid method? Thank you!