Significance of American Mathematical Monthly Problems in Math Grad School Admissions I have started solving problems from the American Mathematical Monthly. While I will definitely continue this, I am not sure how much this will help for math graduate school admissions (assuming I submit my solutions and they are recognized by the Monthly). How significant would multiple solutions to Monthly problems be in admissions? What about having the published solution to a problem? One issue is that I don't know how difficult the problems are presumed to be: all I know is that I personally have solved at least one of them!
It probably depends on the committee members, but I wouldn't expect it to help much.

If you get a really clever solution published, or they publish a problem you submit, that could make a difference.  It certainly wouldn't mean as much as a research paper, but it could be viewed as the same sort of thing on a smaller scale.

Otherwise, the potential impact is not large.  Solving Monthly problems would be viewed favorably, as evidence of talent and effort, but it's not likely to mean the difference between admission and rejection.  (Still, it's worth listing on your CV.)