[sdiy] A little OT, Begging a hand

[David G. Dixon]

> Sorry, I misread the original problem.  The voltages are known and the
> resistances are unknown.  In that case, the problem is underspecified, as
> Ian says.  There are six unknowns (R1, R2, R3, R4, R57 and R8) and still
> only
> four equations (current balances at four nodes).  This implies that there
> is
> no unique solution to the problem.  Two resistor values must be specified
> to
> bound the problem, but those two values cannot be R1 and R8 together, as
> this will leave only three equations for four unknowns.

... Reading further, I see that R8 = 2k2, which eliminates one unknown.
We're down to five unknowns, but we still only have four linear equations.
The fact that R1 + R2 + R3 = K doesn't help us much, because the system of
linear equations for this problem is actually written in terms of
conductances:

g = 1/R

but this condition results in a second-order equation of conductances thus:

g1*g2 + g2*g3 + g3*g1 = g1*g2*g3*K

and therefore doesn't actually eliminate any unknowns.

Specify one more resistance in addition to R8 (except R1) and the problem is
solved.