I'm having major trouble with this circuit, I can get the series resistors easy, but the rest is puzzling.

 

show your work:

do the series resistors, then redraw the circuit. if that is not clearing the picture up, we'll help

 

The problem is that some of the relationships are not obvious because they are draw in a screwy way (which was the intent).

You can always apply a test voltage and determine the current that would flow and take the ratio to find the equivalent resistance.

But in this case you can just redraw the circuit an a more usual way, preferably with no lines crossing. Once you do that (and you may have to redraw it a couple of times since each redrawing will reveal some more of the traditional structure to you) you will be able to get the equivalent resistance by hand.

As a check, assuming I haven't done anything wrong, the result should be between 35Ω and 40Ω and is much closer to one end of the range than the other.

 

label the nodes when redrawing, so that you do not make mistakes

 

we can numarete all current values for junction (rule) in points that accrossed. (conversation of electric charge etc.) and that helps us to make the loop rule (which it's an electrostatic force is conservative.) Suppose we go around a loop, measuring the potential differences across successive circuits elements as we go. (the head-bang is about the direction of loops that you choose to get signs) Rest part is just about the Kirchhoff Rule's Applications.