The 'definitive' "How Many Games & Which Game Will We Win The League At?"
Yes, I'm sticking my neck on the line here, but here goes.
First, this is based on no games being re-arranged (Arse v City could be if we draw against Wigan).
Second, this is based on us retaining a goal difference advantage.
Third, this is based on United being our closest rivals.
Fourth, this is based on us winning the derby (This bit is important).
Looking at United's fixtures between now and the derby, giving them the benefit of the doubt; Huddersfield(W), Newcastle(W), Palace(W), West Ham(W), Swansea(W) and then give them 4 points from their home games with Liverpool & Chelsea, This is 72 points by the time they play us (A game which I'm assuming they lose and we win). After the derby there will be 6 games left, 18 points available, giving a possible (but highly unlikely) 90 points for United.
So, City need 90 points by end of play at the derby (IMHO).
Looking at our fixtures and possible results (pessimistically), we have Burnley(A) 1, Leicester(H) 3, Arse(A) 1, Chelsea(H) 3, Stoke(A) 3, Brighton(H) 3, Everton(A) 1, giving us 83 points, plus 3 from the derby = 86 points. Yes, we could beat Burnley this weekend, just as we could lose to Arsenal, but as a slightly pessimistic view, this seems a balanced forecast for the next 7 PL games.
So, before the end of the derby we need a 4 point swing based on the above forecasts; Either United drop 4 or more, we get 4 or more, or any combination of United dropping and City gaining that amounts to 4 points in our favor.
Winning the title mathematically before the derby seems a bit unlikely (Would need a 7 point swing based on the above forecasts), but still possible.
Winning the derby as a result of beating United (as this is their loss and our win) is DEFINITELY POSSIBLE :D
Disclaimer : I think I have my math correct ;)