Sometimes proving a statement takes careful step-by-step reasoning. But other times, all you need is a single well-chosen example.
Indeed: many problems don’t ask you to prove that something always works. Instead, they ask whether something is possible at all: can an object exist, or can a situation happen, even if it sounds unlikely? In those cases, finding just one example that works is enough to solve the problem.
In this sheet, we’ll practise building examples and constructions. The goal is not to try lots of random cases and hope one works, but to think smartly and strategically about what an example should look like.
By the end of the session, you should feel more confident spotting when an example is enough, and how to construct one that does exactly what the problem asks for.