I certainly appreciate the fact that some people care about cheating in various online contests (exams, entrance tests) enough to make an announcement on meta when there is an ongoing competition. And, at the same time, that some people care about this site and do not want it to get a reputation as a "cheater's heaven" and a "homework mill".
That's the reason that there is a policy how to deal with such questions: "Contest problem" policy.
And for the same reason, many people have posted announcements here on meta with a notification when there was an ongoing contest.1
Still, I think that if we want the users of this site to monitor the site for such problems, we should at least try to make this for them as easy as possible. I'll explain which suggestions I have in mind. (This one ends tomorrow - so it is no longer relevant here. But maybe something like that could be tried in the future.)
Text of the problem. At the moment, typically the announcement about ongoing contest is posted with some link to the problems from the contest in question. (In this case not even that - the OP posted a link in the comments rather than directly in the question. Specifically, this post was about the problems from this PDF file and here is the website which contains the previous round, too.)
Not everybody will go through the effort of clicking on the link and reading the problems. If either the problems or the full texts of the problem are posted here on meta, this would make things a bit more straightforward. As far as I can tell, the texts were provided directly here only seldom.2
This doesn't even need to be in the announcement - it could be posted as a community wiki answer and created collaboratively by several users. (Certainly typing one problem is much less work than typing the whole set. Moreover, this can be made easier by some OCR software - but some manual editing will still be necessary. Of course, something like this is much easier if done directly by the organizer of the contest - they have access to the (La)TeX source used in the competition.)
One-click searches. Maybe some people would be willing not only to report the problems when they encounter them while browsing the site. Some might even actively search for those problems. Let us try to make life easier for them.
Of course, it is possible that the user posted just a screenshot of the problem - text search won't help in such cases.
If the user simply copy-pasted the problem, it should be easy to find. They might have been a bit more clever - to use an example from here, instead of "Alex and Lizzie" they might use "player A and player B". Still, it is probably that there are some keywords that are very likely to appear in such questions - even if the problem is reformulated in some way.
So we might simply include links to some searches directly here on meta - and if some users are willing to do that, they might occasionally check whether those searches return some posts which are new and haven't been noticed before.
For example, I'd imagine that it might be helpful to use built-in search and sort the results with the most recently active or newest at the top. Another option might be Google with restriction to the results in the past month or week or some custom range. (And, naturally, restricting the search to this site.) For example, in this set for the first problem, some reasonable keywords might be:
I will add that the search doesn't return locked posts - you can add
locked:1, but for the above keywords I found nothing.
I don't think that the search engines which can search for a mathematical formula will help here too much - the ones I am aware of do not index Mathematics Stack Exchange very often. And I don't think they have an option to show the most recent results.
Maybe if the post is likely to contain a picture, one could use some search engine which can search among pictures. For example, I can search in Google Images for grid numbers 25 or grid numbers shaded (restricted to this site and to relatively recent posts).
One can even search by image - but I do not know whether links like that can be shared in some reasonable way. For example, trying to search for the picture below, I finally arrived at this link. I doubt that this link will work for other users, too - and even if it does, that it will still work a few days or a few weeks later.
1To list a few examples: Cheating on USAMTS 2018-2019, USAMTS 2017-18 Round 2 Problems, There are several questions here which are basically from a current (2021-2022 round 1) USAMTS math contest
2I only found a few older announcements which actually contained the texts of the problems too: German contest “Bundeswettbewerb Mathematik 2021", German contest "Bundeswettbewerb Mathematik" 2019 and 2015-16 USAMTS Round 1 Problems.