Is the number constant or does it change as the reputation of a user grows?
I've been there, myself, in the beginning, I had my privileges revoked. I don't want to repeat such a thing.
Can we list factors that contribute to it, then?
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There's too many factors to even come up with an average number of questions, although the number of questions you've asked is taken into consideration. Basically, everything surrounding the questions you've asked is taken into consideration.
You could have 5, 10 or even 15 questions before it kicked in depending on how the questions were voted on, how many were deleted, and a whole lot of other things. We deliberately do not disclose the mechanics of the algorithm because we don't want people doing the least amount needed to squeak by instead of just trying to write decent questions.
The same goes for our quality filters that rejects questions not due to a block, but for poor formatting, capitalization, etc. We don't want to tell folks exactly what that looks for or we'll end up with a poor question that barely squeaked by, when the system is deliberately trying to get a better question altogether.
Just put effort into your questions and you should not have to worry about it. A neat trick is to read them out loud to yourself before you post them to make sure that they read well, and include everything you meant to say.
The rest is, well, seekrit.