So I recently read The Mysterious Benedict Society, which was good fun, and I'd recommend it if you like kid lit. In it there is an exam whose structure I admired.
It begins, of course, with the instruction to read all the questions before you answer any. It's multiple choice, fairly long, and opens with complex questions involving arcane knowledge. When you reach question 21, however, some of the arcane terms sound familiar . . . and if you look back at question 1, that question provides the information you need to answer 21, and vice versa.
Sadistically brilliant, I thought; or maybe brilliantly sadistic. I supposed it would not be fair to use such a structure (even reduced in length) for anything but a course on children's literature in which The Mysterious Benedict Society was required reading. But I was tempted.
Tempted or not, I think my students are safe. I wanted to post some sample questions of inspired sadism, and after an hour of trying to invent a suitable pair, I'm giving up. I think the trick is to have fairly long questions, more along the line of reading comprehension passages than simple multiple-choice questions, and likewise, fairly long answers, so that information can hide in them. Feel free to try your hand at this.
Considering all the complaints I've had about quizzes, ambiguous questions, being unreasonable about expecting people to retain obscure details, and so on, I'm rather relieved about my inability to devise a good set of inside-out (so to speak) questions and answers. I may be given to ambiguity, but I'm not naturally sadistic.