I have an idea, though I'm not sure if it's plausible. The problem with deleting a question, or just an answer to it, after it has been asked is that the person that asked it may have already seen the answer, but then no one else gets to see it. So, all this does is ensure only the person who tried to cheat first can have success. We're rewarding the first cheater.
There's also the problem that we can't possibly know all contests going on and we can't know ahead of time which questions should be avoided. We would just have to wait until someone who happens to know the contest problems stumbles upon it, and by that time there may already be an answer.
So, the best solution would be for the people organizing the contest to let us know, somehow, the questions that are in the contest. If the questions are online somewhere already, then it doesn't matter if they are online here as well. And, then the question could be immediately locked so no one can answer. This serves the purpose that we now can see all contest problems here, instead of having to search elsewhere. So, if someone else tries to ask the same question later, there's a much higher probability that it will be noticed quickly and stopped.
But, I'm not sure how that would actually work. Could the contest people add a question on here that includes all the problems from the contest, and flag it for being closed immediately? Then, after the contest is over, people could provide answers for the various questions. This isn't ideal with several questions in one post, but people also have a problem with having many different questions asked quickly and flooding the front screen, so there has to be a compromise somewhere.