Here are four questions that work.
Select the least desirable Princess and call her A.
[1] is B older than C?
[2] does B lie less frequently than C?
[3] is B more likely to lie than you?
[4] if I were to ask, would you say that B is Princess Mischievous?
In each case, if the answer is Yes choose C; if No, choose B.
Princess Truth and Princess Lie will answer Yes if Princess C is the other of these two, and No if Princess B is.
If A is Princess Mischievous, a random B or C choice gets you a winner either way.
I see how 1 and 2 work (because they are basically the same as OP's answers.),
but I don't think 3 or 4 work.
3)
Okay, so if I ask Honest (A) if B is more likely to lie than her, she says yes. But, she says yes whether B is Mischievous or Liar, so I may end up with Mischievous, never mind the fact that I don't know that A is honest.
The case is the same with Liar. She will say yes to either one so there is no way to distinguish between them.
So basically, if you ask the question of Liar or Honest, you have a 50% chance.
4)
Okay, so I ask A if B is Mischievous. She says yes. I don't know whether A is Honest or Liar (or Misch but that point is moot since you're a winner either way if you ask her), so do I pick B or C?
So, again, my future lies on chance. Not cool.
