Total resistance of a complex circuit when neither series or parallel rules can be applied.?

Someone is asking for my help, and it's been way to many years since I've been in school for this.

Here is the problem. I have 5 resistors in a network such that no two are either in series or parallel, so those rules won't work. I'm looking for the total resistance between points A and B.

Here is the circuit.

http://img.photobucket.com/albums/v74/puppy_raiser...

What I know.

If the 400 ohm resistor were an open R total would be 900 ohms and if a short, 600 ohms, so with 400 ohms (or any other value), the answer must be between 600 and 900.

What I think I remember.

It seems to me, you have to assume a voltage or current someplace, then using ohms law calculate other values, finally coming up with 3 equations and 3 unknowns. Solving for the 3 unknowns with basic algebra skills gives a quick path to the answer, but coming up with the 3 equations or even what the 3 unknowns are escapes me. Any help out there (with how you did it) would be much appreciated.