When I was a first year undergrad, we organised a mathematical Call My Bluff evening. A game master prepares questions in the vein of "What is a happy number?", "State one interesting theorem from Ramsey theory", and so on, questions whose answers a first year undergraduate is unlikely to know but likely to understand. Then, several teams have to invent credible answers and quietly submit them on a piece of paper. The game master reads them all out, along with the correct answer and the teams have to guess which answer is right. There are some points for identifying the right answer, but even more points for every team that fell for yours.
It's great fun, and actually quite demanding: when you invent a definition, you must take care not to define the empty set and not to define something that you already know under a different name. Accordingly, when you are evaluating the answers, you are trying to rule out those that seem to define/state something boring or something well-known under a different name. Of course, inventing answers is also very creative and makes you realise how difficult it is to ask interesting questions or introduce interesting concepts.
