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I recently created a nice olympiad problem on the invariance principle, and I thought about posting it on Math Stack Exchange. However, I was unsure about it as the community guidelines have not mentioned anything about questions that we have already solved.

This has happened in many other cases, too. Whenever I've solved a really beautiful problem, I have wanted to post the problem and its solution on Math Stack Exchange for other users who might like the problem, and who may post their own solutions to it. However, since this wouldn't exactly be a question, are we allowed to post such questions?

Thanks in advance :)

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The FAQ on Meta Stack Exchange is pretty clear on this.

Yes!

There are already numerous posts that answer their own questions. There's nothing wrong with it. It's even been encouraged since the very beginning of time.

You can see there is an option to answer your own question, and in fact, the capability to write and post the answer at the same time as the question.

This is not just allowed, but encouraged by the guidance and facilitated by the system.

If the question is good enough to be asked, and your answer is good enough to resolve that, go for it!

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  • $\begingroup$ Oh, I thought those rules might not apply for Math Stack Exchange. Thanks for your answer! $\endgroup$
    – MathMinded
    Commented May 15, 2022 at 6:29
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    $\begingroup$ In Math.SE the bar has been raised. Basically because otherwise we would get a lot of crap. See the earlier discussions on this theme. Not taking a position whether the question/answer pair the OP had in mind would still be ok. We simply think this position is too sweeping to serve the site well. $\endgroup$
    – Jyrki Lahtonen
    Commented May 15, 2022 at 7:10
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    $\begingroup$ And as the links provided by Calvin Khor clarify, while this tool is perfectly valid on Math SE just like the rest of the network, it goes without saying that the question and answer both still need to be on-topic and meet the standards expected. I don't see anywhere that this is contradicted. $\endgroup$
    – Nij
    Commented May 15, 2022 at 10:13
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    $\begingroup$ As a follow up to @JyrkiLahtonen 's comment, I'll mention that I tend to not give upvotes to self-answered questions, because of that risk of people exploiting them to merely build reputation. It sounds like the OP is one of those people who would participate here even without the reputation gamification (my preferred type, honestly), but just be aware that such posts don't fit the gamification track as well as others might. $\endgroup$
    – JonathanZ
    Commented May 15, 2022 at 14:12
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    $\begingroup$ I would say that it is encouraged, but there have been a few users who almost never interacted outside of asking questions or asking and answering their own questions (i.e. never or rarely answering other's questions or otherwise interacting with others' questions), treating MSE as a de facto blog. As long as you don't go overboard with ask+answer, you'll be in good standing in the community. $\endgroup$
    – Cameron Williams
    Commented May 16, 2022 at 16:06
  • $\begingroup$ What about this: math.stackexchange.com/questions/4452042/…. Ignore the question but please read the PS at the end. $\endgroup$
    – Ruy
    Commented May 17, 2022 at 0:32
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    $\begingroup$ That PS is unhelpful and unnecessary. Flag the post (or any post) for a moderator. @Ruy. $\endgroup$
    – Nij
    Commented May 17, 2022 at 1:06
  • $\begingroup$ Alright, thanks for the suggestions. I will make sure to rarely post such questions and only if the question is 'really' that good. $\endgroup$
    – MathMinded
    Commented May 17, 2022 at 15:14
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I approve of (and have used) the approach: "I know a solution to the following question. I would be interested in seeing other solutions. If necessary, I will post my solution after enough time has passed." I am less enthusiastic about cases where the answer is posted immediately.

See Is it okay to ask mathematical puzzles and problems I have solved? for the agreement that this is OK.

Some of my examples: Evaluation of a slow continued fraction and Evaluation of a continued fraction

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Yes, you can ! I don't see why you couldn't since you have a "Answer your own question" button: Answer your own question

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Yes,

That's why there is such option, what's not allowed will not be allowed,and since you have the option, it is allowed!

It will not only be helpfull to others, but also change the reputation as the users see it and vote.
But the change depends on quality of your q.s and answer : It may be a negative or positive change!

In fact it will increase your rep. nearly double of what you get from your usual q.s if...

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