How would you solve this resistive network?
This is a really easy circuit to solve.  The reason it appears difficult is because the schematic is obfuscated by deliberately using unintuitive layout.  First, this is a good lesson on why logical schematic layout matters.  Second, you'll see this circuit is actually very simply once you draw it logically.

In general, draw schematics with power and ground voltages being horizontal lines sorted by ascending voltage bottom to top.  Then show the rest of the circuit with logical flow (nothing to do with current flow) left to right.

In your case, draw the battery at left with the positive node going up from the top, then across the sheet to the right.  Similarly, the negative node should go down from the battery, then across the sheet left to right.  Now fill in the resistors vertically between the two horizontal power lines that run across the top and bottom of the sheet.

Once you do this, the circuit will be obvious and you'll wonder how you didn't see it before.

Hint: Look at how many nodes this circuit actually has.  Yes, it really is that simple.