Based on current revision of the tag-wiki and tag-excerpt, the tag contest-math seems to be a meta tag. In short, the usage guidance says that it should be added if a questions is from a mathematical contest, which means that it is actually not determined by the content of the question, but by other factors.
Admittedly, the tag-info has not been updated for some time. (It mentions homework tag, which no longer exists.) I will copy the current revision here in full.
Suitable questions that would have this tag are of the following sort:
- Actual problems from mathematics competitions
- Inquires about alternative proofs for a particular problem that is from a math contest.
- Questions that have been explicitly inspired by a contest problem.
- Soft questions requesting advice on competing in contests or those inquiring into the general utility of such things in terms of encouraging the further pursuit of mathematics.
See here for a list of mathematics competitions from which you can ask questions. This tag cannot go along with the homework tag.
Moreover, question having this tag are often treated differently from other questions, especially as far adding context is concerned. Here are two quotes from past meta discussions.
Both of them are taken from an answers to Why a question without showing any work is getting upvoted?
I am somewhat in favor of various subcommunities, say, those forming around selected tags, within Math.SE developing their own norms. Enforcing such norms will mostly be up to the subcommunities themselves. It is good to have some common standards (enforced for example via our common review queues), but IMO the keen followers of a tag are best placed to judge many cases.
It has never been the tradition in the contest problem community to provide more than the question, and a source for the problem/solution where known.
Considering the fact that the tag might change attitude towards the question, I would suggest to be careful when adding the tag to questions where the OP did not mention a contest, preparation for a contest or the OP did not use the tag themselves.
If the tag is supposed to be used otherwise, we should discuss how and clarify the tag-info. (Personally I would stick with the current version, perhaps I would consider worth adding problems from contest-related books, such as IMO compendium and other books which are intended as a preparation for math contests.)
I consider it difficult task to decide what is contest math based on contents of the question. Especially since there are many university-level competitions (Putnam, Miklós Schweitzer, IMC, Vojtěch Jarník and many others), plenty of questions from various undergraduate topics might have appeared in such contest. (And if I remember correctly, I have seen comments and answers saying that some of them indeed did appear in such contests.)
Despite the fact that meta tags should be avoided if possible, due to the popularity of this particuar tag, complete removal of contest-math tag does not seem to be a reasonable option.
For example, we have a few questions almost disjoint families of cardinality $\mathfrak c$. Such as Countable set having uncountably many infinite subsets (and many posts linked there) or Partitioning an infinite set (and many posts linked there).
I do not thing that such question should be tagged contest-math simply because it appeared on a mathematical contest. (Unless the question was asked in a connection with a contest.)