In the early '90s, I heard a noncommercial FM DJ say she was going to give away concert tickets. "But first," she said, "I have to think of a suitably distressing question for you to get (them.)"
I suppose that makes the caller's win feel more earned. Given a choice, however, I probably would have just said, "Concert tickets will go to the first (or other designated) caller..."
If I'd been awarding a box set of CDs, however, I probably would have followed her lead--and asked more than one not-easy-to-answer question.