Hi Jeff,
That rule does not apply here although it may be true by pure coincidence.
For example, consider a 10 megohm resistor connected directly across the
30v supply battery. It is right at the dang source and yet it will dissipate
very very little power. It is clearly not the furthest from the source.
To find out the power in each resistor you could use Thev/Norton equivalents
to reduce the network one element at a time, or you could collapse the
network one element at a timie and work backwards.
I suspect that you already used the 'collapse' method so maybe i can explain that...
Starting with R5 and R6, calculate the total resistance and then replace both
of them with one resistor that has the calculated resistance. Then, calculate
that resistance in parallel with the next resistor back which is R4. Once you have
the parallel calculation, replace those two with that one resistor. Continue in
this way until you have only two resistors in series, then calculate the voltage.
That will be the voltage for the junction of R1 and R2 and R3. From there
you can repeat the process to get the next node voltage.
Once you have all the node voltages, you can calculate the power in each
resistor and compare them.
BTW, i get 38.9 milliwatts for the power in R6 also, which is the lowest of all.