GCHQ Resistor Puzzle Help Request

I've spent the afternoon thinking about this GCHQ puzzle. In it you have to reduce a lot of resistor networks.

I haven't had to reduce resistors like this since A Level physics and I remember the rules that two or more resistors in series reduce by adding their resistances and for those in parallel you have 1/R=1/A+1/B+1/C+... for resistances A, B, C... I had assumed that these were the only rules that would be needed for any network and hadn't really paid it a second thought since 2009. As I made my way around the network starting with the first cluster that you get to from the positive side of the cell I got 4/9 and 3/4 as required by the hint. But the third network looks like this:

Drawing it out as a network I can reduce it a bit like this (I think):

This second diagram illustrates the minimum case of networks that I don't know how to solve. Presumably it reduces into some simulatanous equations and it seems to be related to something called a Wheatstone Bridge, but I need a physicist to swoop in at this point.

Update: there seems to be called something called a Δ-Y transformation which can turn a triangle into a Y shape. I'll continue to plug away.