I sometimes post questions I already know how to answer for the purpose of sharing an interesting problem with the community. Some are well received. Some are not (this last question currently has two downvotes and no upvotes). What follows is a collection of mostly random thoughts about such questions.
There have been many complaints about problem quality over the past few weeks, so my thinking is that I can improve the average problem quality by posting interesting problems. These questions are directed at people who come here to solve interesting math problems.
I am not sure how well such questions fit in with the mission of M.SE. However, this style of sharing interesting problems is what made, for example, the Art of Problem Solving forums so great.
I'm also very tempted to post such questions with just the problem statement (because I have no work to show, as I am not seeking help). However, I try to add a little text in order to avoid them getting mistaken for homework questions. I don't think this is necessary, as a cursory look at such questions shows they are not homework. On AoPS, many questions were posted with just a problem statement, and I did not see any issues resulting from that.
Maybe such questions could be mistaken for people attempting to cheat on math olympiads. In my case, I think it's clear from my question history that I am not one of those people.
(Obviously, if you are asking for help with homework or something like that, you should include more than the problem statement...)
My question: Do you want to see more or less of this kind of question?