And yeah, I am starting to think that problem-solving ability is at least somewhat intrinsic, to the extent that it has more to do with a person's temperament than anything else. It's certainly not the kind of thing I've ever seen much success in training someone to do. It seems to be the difference between initially reacting with, "Hmm, that's funny, I wonder why that happened," and "Ughh no no how do I make it stop!?"
If it were workable, I think a stellar interview question might be, "Do you find jigsaw puzzles more enjoyable with or without a picture?"