1. The problem statement, all variables and given/known data http://sudokupuzzles.net/IMG_0033g.gif [Broken] 2. Relevant equations Flow into a node=flow out of a node. Turned relative flows through each node (A,B,C,D,E,F) into system of equations; and entered system of equations into augmented matrix as shown. Reduced matrix to REF. 3. The attempt at a solution http://sudokupuzzles.net/IMG_0034.jpg [Broken] I am not certain if I can be more exact with part a f_5 and f_6. I entered all the pertinent equations into the system possible for each node. (Is there another eautaion that could be entered (to help reduce answer)?) Part b, I have no visual explanation, as per the diagram, to why f_1=f_6.