Inverting Op-Amp Configurations

You are provided with an ideal op amp and three 10-kOhm resistors. Using series and parallel resistor combinations, how many different inverting-amplifier circuit topologies are possible?

I think there are five, but I'm not sure. I have one with series on the input, one with series on feedback, one with parallel on input, one with parallel on output, and one where I just said screw the third resistor and didn't use it. Are there any other possibilities I've left out?