How do people create difficult, recreational problems (e.g. like those found in competitions such as the IMO)? 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.

For Euclidean geometry, it is usually by "playing with GeoGebra". Sometimes, when playing around you create a new configuration with some unexpected properties like concyclic points. Then you try to 'hide' information (by for eg. redefining the points in some other way) to make it difficult.
Evan Chen has also written an article about creating problems here 
