Interesting. Fact - We've played the most non-conference games against Minnesota, trailing the series 20-29-2. They were a good rival for a long time, but we haven't played them in 20 years, and they pretty much suck these days anyway.
I could go with a lot of traditional powers: Miami, FSU, Penn State, USC even Alabama. I voted "other" but maybe it is Penn State. We've played them 13 times, we're 6-7 all time and we've played them within the last 10 years. That would be a good series to play again, even for several years. How about a "neutral" game against them someplace like Chicago? chuckleshuffle