Is there a mathematical way to know the answer? (or you can do it only by trial and error)
Could you prove that it is possible or impossible mathematically?
Electronic – How to arrange six 6-ohm resistors to have a total resistance of 6-ohm
resistors
Related Solutions
I'd use a transformer like this: -
simulate this circuit – Schematic created using CircuitLab
The transformer turns ratio would convert the 3 ohms of the inter-wired 6x 2 ohms speakers to 1.5 ohm seen on the primary. This, being in series with 2x parallel 1ohm speakers makes a total impedance of 2 ohms seen by the voltage source.
The turns ratio is 1:\$\sqrt2\$ by the way
I think you can try Y-Δ transform, transform half of the upside or downside 3 resistors to "Y", then it'll be easier to analyze.
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Best Answer
simulate this circuit – Schematic created using CircuitLab
here R5//R1 series to R3 => 3 + 6 = 9 in one branch
R4 + R6 + R2 => 6 + 6 + 6 = 18 in 2nd branch
18 // 9 gives 6