In a previous article in this series, it was suggested that it is part of our responsibility as teachers to attempt to induce "perturbations" in our students' mathematical thinking. Especially when teaching seniors and capable students at any level, it is important that we unsettle them, shake their perceptions and attempt, wherever possible, to ensure that they regularly question those things that they take for granted. In this article we consider some more favourite problems: borrowed from a variety of sources, classroom-tested over many years, and always guaranteed to induce discussion, questions and even flashes of inspiration.