Rather than me setting exercises for others to do, I'd like people to give me some challenging questions It's a thread where people can share nice problems, but I'd like the benefit of seeing if I can get to the result myself too.

By challenging questions I mean ones which require insight and clever tricks, or ones with nice results, rather than something that requires a lot of knowledge and can be done by appyling heavy theorems. 

Content-wise they can contain anything that doesn't assume too much university-level knowledge, although I would like to learn some things along the way so don't hold back.

I'm mainly looking at people like Jane, mathsy and Ricky, but anyone else is of course welcome

Thank you.