Ok, here's my take. To me, the logic goes as follows:
We know that the voltage is a constant. Let's call it V.
Lets call the power dissipated by 4 resistors P4, and the power dissipated by 3 resistors P3.
P4=V^2/(4*R)=20
P3=V^2/(3*R)
therefore,
P3/P4=4/3
P3=P4*(4/3)
Ok, now let's look at North's solution:
P3=P4/3 + P4
simplifying,
P3=P4*(4/3)
Same answer (which I think we already knew).
I probably just repeated whan Len (and maybe several others) said.
I have the same problem as Len. I don't understand how you would come up with North's solution unless you knew the answer and juggled numbers until you got there.