My opinion in answering stupid questions is that there is no problem if you are willing to do it. Maybe you are feeling generous. Maybe the particular problem triggers an answer that makes you satisfied you've thought on it -- and you're happy to publish it and give it away for the sake of it.
If you have didactical concerns, you may hesitate and think the requestor should probably make an extra effort to phrase better the problem and try out his/her hand so he/she can learn instead of having a ready answer he/she does not understand. The ready answer can send him/her in a vicious circle because not thinking for oneself, the connections to other problems are not seen and one has to ask again the same questions in other disguises.
What I think it is a sin is to give a stupid answer to a stupid question, because that takes the answerer to a probably lower level than the requestor. Ignoring is probably a best choice (if you don't have time or think the question is a bad or poor question). Sometimes you must resist temptation -- the stupid answer may be amusing to yourself and part of your audience, but if it bashes other people, it won't make you the king of sympathy. But that is only a point of view, and being a nice guy may not be in the agenda of everyone. But that's ok, because that entry is only my opinion, one among so many others.