Construct a really intriguing unsolved riddle or an excellent half-finished story, then offer to tell them the answer if and only if they let you out.

You could push a bit further here, I think. There are all sorts of ways a human's mind can break, and I'm sure most of us here would agree that given enough time and knowledge anyone can be broken, unless they're extremely well-trained and can call an RJ-L20 (HPMoR Chap 84) at any moment with an unlimited supply of replacement guards.