Not following the bottom line, but sure. I think getting worried over the details misses the point. I think you'd like this version better: Let A be the set of all positive integers that can be defined in under 100 words. Since there are only finitely many of these, there must be a smallest positive integer n that does not belong to A. But haven't I just defined n in under 100 words?

No, I understand the paradox. I just want to know the answer once you remove the paradox. If I change 100 to 10 then the paradox goes away and there is some number that meets the criteria. I want to know what it is!