Unknown resistor solving

I'd just redraw it:

Vr | [R1] | +----+-----+--o Va | | | | | [?R4] [R3] [?R6] | | | +--o Vm | | | | | [?R5] +----+-----+--o Vb | [R2] | Vs

So the current through the whole thing is (Vr - Va)/R1, which should be equal to (Vb - Vs)/R2, or at least it had better be, and that current also goes through the parallel combination of R3 || R6 || (R4 + R5). You know R3, so the best you can solve for is the current through the parallel combination of R6 || (R4 + R5); which voltage drop is, of course, Va - Vb.

You're right. There are too many unknowns, unless somebody knows something that they haven't revealed yet.

Maybe it's just that a page full of arithmetic is enough to baffle the teacher. ;-)

Cheers! Rich