We address the problem of motivating students in Data Structures and Algorithms courses by presenting two simple problems that each have a series of improvements to a basic algorithm, leading to spectacular decreases in runtimes. Coining a new term, we refer to such sequences as being "thrills of algorithms". Seeing runtimes drop from an estimate of days (or even years) to just a few seconds has a visceral impact which conveys the importance of efficient algorithms in a way unlikely to be forgotten. The demonstrations are particularly compelling because they can be performed live in class on the lecturer's laptop. To assist staff teaching such courses we provide detailed pseudocode descriptions and complexity analyses for the various methods, and can supply implementations on request.