Looking at the other comments, it seems like most people really like the cheat. I admit it's very cute, and you're absolutely right that this sort of thinking can be helpful in artificial situations like exams and games --- I've used it myself.

That artificiality is why I don't really like that approach, though. It's a brand of thinking that generally works only on artificial problems, because the key component ("you wouldn't be asking me this if it didn't have a well-defined answer") doesn't exist on most problems. Proving that it's constant and then using the r -> 0 trick to calculate the constant is much more satisfactory to me.