Providing student choice and opportunities for independent study are recognized as viable differentiation techniques. Daily homework sets that contain more demanding problems even though not required allow the teacher to provide challenge without incurring undue stress. The modest incentive of some homework bonus points is enough to whet the appetite of students. The lightbulb problems allow dedicated students, for whom quick thinking and problem solving may not come as easily in a test situation, the chance to work on less routine problems at their own pace. If teachers want students to be able to think independently and critically, with some depth and sophistication, they have to be willing to give them some nonroutine problems without a prescribed algorithm. The aim is to strike a balance with questions that have some sophistication and yet are manageable for the most capable students in a course that is not accelerated. The spirit of the challenge problems is to nudge students in new directions from the day's lesson and to ask for creativity and thoughtfulness in new situations. In this article, the author has devised six ways to design lightbulb problems; each example is illustrated with work from his students who solved them. (Contains 6 figures.)