Sometimes, questions are posted that turn out to be part of a problem from an ongoing contest. We've discussed this on meta in the past (here, here, and here), but we never settled on an explicit policy. In absence of such a policy, the moderation team has internally decided how to deal with these questions consistently. This has worked well so far, but I think it is better to have an explicit written policy. Such a policy would make it clear what people who report these questions can expect from us and allows for community input even if there is no consensus.
I have drafted the policy that the moderation team is more or less following right now in an answer below. Please discuss changes to a proposed policy in the comments, or suggest alternative policies or other thoughts in another answer. Note that since this answer describes the status quo, the moderation team will follow that policy unless the community clearly prefers a different policy.
For a bit more background, I looked around what some other sites on Stackexchange do. On Stackoverflow, contest questions are allowed if they are otherwise good questions, while on Mathematics.SE contest questions are locked until the contest ends. What we currently do here is somewhere in the middle of Stackoverflow and Mathematics.SE. On Physics.SE, contest questions are seen as a special case of "academic dishonesty" and are locked/closed if the contest rules do not allow outside help.