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Concerning question 18,
Doesn't your prior work for 22 show that P doesn't need to be included within the years 89-91? What rule makes it necessary for P to be included within those first three years?

It is NOT necessary for P to be hired in one of those years. The question has asked for a complete list of professors who COULD have been hired then; our prior work shows that P could have been hired in those years, so she must be on any complete list of possibilities (you may also find this advice helpful).
Clearer?

Haha no i totally thought that was clear, i also was considering C. I guess it would have been better for me to ask why A was incorrect. You eliminated A because P wasn't present, but i don't exactly see why its wrong. i basically had a 50/50 shot between the two

Well, our prior work shows that P could have been hired in those years, so she must be on any complete list of possibilities. (A) doesn't have P, and is therefore incomplete.

Hi Dave. Based on the rules, in addition to O, R, and M, I had placeholders of N in '89, S in '92, and T in '95 because from what I could tell it was the only place they could go. Is there a reason you didn't have them as placeholders, or did I read the rules incorrectly?

You're exactly correct.
I purposely left those off because I wanted to drive home the fact that even if you don't see a valid deduction when you're working up your diagram, that does NOT mean that you have to struggle with the game!