Here you go — you did this type of problems as a kid/teenager. 1) you likely have a talent for it 2) you have some training.

I did participate in math/informatics olympiads as a teenager and even taught it a little and from my experience, some type of people just _like_ that sort of problems naturally, they tickle their minds, and given time this people would develop to insane levels at it.

'Normal people', in my experience, even in math departments, don't like that type of problems, and would not fare well with them.