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I've had organizers young as 16~ I don't think there is a hard age requirement, I think it's just a healthy amount of experience on how competitions work, I would recommend signing up for staff for several competitions before contacting a delegate about organizing one.
I'm 90% sure there is no limit, as there are some pretty young organizers I've seen from the competitions I've been to. Unless if you are a baby, then of course you can't organize one, but other than that I don't think there any limits. You obviously have to do some amount of work in the venue and getting it prepared and you might need help if you are little. Being a delegate is different, as I'm quite sure there is an age limit though.