Please let me know if this question does not belong here.
I have always wondered how the problem-setters for contests like the IMO come up with the problems. The creation of problems like those set at university, or found in textbooks, seem natural -- a mathematician uses their years of experience in mathematics to fashion questions from known problems, theorems, and their proofs.
But competition maths seems a bit different. Often it is not as clearly tied with a particularly useful result, or sometimes it comes across as purely for the sake of a competition (I am thinking of those long geometry problems in particular in that case). Yet many of them are really neat, interesting standalone questions, and usually quite tough as well.
I was wondering whether anyone who has taken part in the creation of such questions could share a bit about what the process is like? Does one often operate 'in reverse' (for instance with the hard IMO geometry questions: starting with a construction, mildly arbitrary, and 'erasing' the steps)? Or perhaps asking oneself a question, trying to answer it, and if it is an appropriate amount of difficult, shape it as a question? Would love to hear from anyone with experience in the area.