Is it OK to ask and answer my own question, with the intent of showing the community how to do something useful? In this situation I would not be seeking answers to the question (unless someone has a better solution). I can't find guidelines here, though this seems to suggest not accepting my own answer in this situation.
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I say go for it. I would say write the question and then immediately post the answer as an answer. I would hold off on accepting your answer until other people have a chance to chime in with what they think might be best.
Try it with a few questions, see how you do. If your questions are good and interesting, then you will likely get multiple answers or up votes to the question. If your questions are not interesting, then you will not get any other answers or up votes (up votes to the answer say little about the question). If you are not getting answers/votes, then it is probably an indication that you should stop.
Asking questions and then immediately answering them is one of the very first things that this resource was used for. If it's good enough for Doug Hull, then it's good enough for me.
That said, we have not worked out how we would like to incorporate such postings. I started a discussion of this recently but it hasn't gone very far.
I have no objection to the creation of "how-to" postings. The overview says that the resource is "collaborative environment for finding the best answers to your questions about MATLAB, Simulink, and related products". If that involves people putting together canonical answers to problem patterns, then in my opinion that would be a worthwhile use of the resource.
If you ask a question, and none of the answers is satisfactory, and then you, through other means such as yourself or via a friend, come up with a different and better solution then I have no problem with you posting it as an answer to your question.
If you just have a nifty way of doing something, then you might consider uploading it to the File Exchange or adding it to the FAQ ( http://matlab.wikia.com/wiki/FAQ#toc) if you consider it to be universally useful and not just some niche application. If it's really something universally useful, enough to be tagged a tutorial, then you could post it in Answers, but make sure it's not something better suited for the File Exchange or FAQ. For example a tutorial on how to ask questions on the Answers forum would be good but demo code for how to do a Monte Carlo Simulation might be better on the File Exchange or FAQ.
I've done this repeatedly: I had some ideas for a specific problem and wanted to know, how others solve it. Then I'm waiting for a week and add all I know about the topic. Example: Answers: rare examples of confusing error messages, or Answers: license files from the FEX. Sometimes I add my personal answers in form of comments to the answers of others. Until today, nobody told me that he or she was bothered by this.
I assume Richard's comment concerns threads like:
Question: "I have a problem ABC and cannot solve it..." Accepted Answer from the same author: "Ah well, I've done it with e LOOP".
Such threads are a waste of the time of all readers. The increase of the reputation by the accepted answer has not relation to the bad quality of the question.
If it really is about something cool, then I'm in agreement with the others. Go for it... People could still add their own answers if they had a useful point of view.
But if it's something mundane that shows up again and again (proving that a lot of people would rather ask a question than use the search facility / or that the search facility is not powerful enough), it'd be a pointless self-gratifying exercise.