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Sometimes when I see a question out of a textbook or competitive exam, I want to post a generalization of the specs of the question. I think my situation is (probably?) similar to this.

Should I post it in a Q-A form (Answer you own question - share your knowledge, Q&A-style) or not because the problem (with its specific numerical values) has already been answered at that place? The first question I had in mind to post a general solution of was this one.

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  • $\begingroup$ This seems similar to what Coping with abstract duplicate questions. is trying to help deal with. I added a link there to my own question on the main site of Proving that among any $2n - 1$ integers, there's always a subset of $n$ which sum to a multiple of $n$ where I describe various aspects of those types of questions, and also included links to $15$ previous questions which demonstrate these aspects, although I know there are actually quite a few more related questions on this site. $\endgroup$ – John Omielan Feb 9 at 0:13
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    $\begingroup$ Mast, one way to provide generalizations is to download Latex on your home computer, then post expository writeups on some sort of web page. Then you may call someone's attention to a relevant piece with no more clutter than a comment explaining the relevance and giving the link. $\endgroup$ – Will Jagy Feb 9 at 0:37
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    $\begingroup$ @JohnOmielan I appreciate your effort on the $2n-1$ problem, but I think that it handles the issue in the wrong direction. You have created a post from which links flow out. Ideally, we should have a canonical post, and links should flow into it, i.e. related questions should be closed as duplicates of the canonical Q&A. From the point of view of making the repository of questions and answers accessible and searchable, a target node is far more useful than a source node. $\endgroup$ – Xander Henderson♦ Feb 9 at 3:01
  • $\begingroup$ @XanderHenderson Note I posted the wrong meta question link. It should have been List of Generalizations of Common Questions instead, with my link being in the "Number Theory" section. As for there being a "canonical post", my answer lists several posts which solve the general situation. However, I believe where the question is for a small $n$ (e.g., $3$ or $4$, so $2n - 1$ is $5$ or $7$), it can be more useful to use one of the questions specifically for that $n$, such as one of the posts I list in ... $\endgroup$ – John Omielan Feb 9 at 21:28
  • $\begingroup$ @XanderHenderson (cont.) this answer, with other answers handling different cases. I also believe my posts can be helpful to anybody who is interested in learning more re: question variations and techniques used to solve these types of problems. As for the general "usefulness" of what I've done compared to having a specific "target" node, I'll leave that to anybody who wishes to check my post to determine for themselves. This includes updating a post or writing their own as a "target" one to use, with them being welcome to add a link in an answer. $\endgroup$ – John Omielan Feb 9 at 21:29
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In my opinion, one of the biggest problems facing Math SE right now is the proliferation of nearly identical questions which are essentially the same problem, asked over and over again, but with different numerical values. One way to help alleviate this problem is for folk to write general questions which give "canonical" answers to those questions—indeed, every question which I have posted on Math SE has been in order to address commonly duplicated questions. Thus, in general, I am in favor of posting questions which generalize, and which can serve as duplication targets for, other questions.

That being said, if you are posting such a generalization, please ensure that it really is a generalization, and that it could (potentially) answer a larger range of potential questions (or, indeed, your generalization could immediately serve as a dupe-target for more than one already extant post). On the other hand, if your new answer is only a minor generalization, or if you can't see it addressing a larger range of questions in the future, please consider posting that answer in reply to the question which you are seeking to generalize.

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    $\begingroup$ I think many of our existing canonical questions (aka abstract duplicates) were created by taking an existing Question and supplying a generalized Answer. It's been my practice to lightly edit the body of the Question as necessary to highlight the fact it has been so adapted. $\endgroup$ – hardmath Feb 8 at 18:50
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    $\begingroup$ @hardmath That is another strategy, so long as it falls within the Guidelines for Context Editing and Rewrites. Personally, I think that I would prefer to see a new question asked-and-answered, and some flags for dupllicates. $\endgroup$ – Xander Henderson♦ Feb 8 at 19:35
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    $\begingroup$ It may be convenient to have a tag to identify such generalized answers (created on purpose or not), and to present them first in lookups for duplicates in review. Generally speaking, we have ways to identify branches of mathematics and fine-grained subjects, but not much for the quality of questions (upvotes are hardly usable for this purpose), or the 'level' (as in approximate years of curriculum). On the long run, I fell there is too much material and to few ways to filter. $\endgroup$ – Jean-Claude Arbaut Feb 9 at 12:13
  • $\begingroup$ @Jean-ClaudeArbaut I think that is a reasonable a idea, and worth some discussion. This isn't really the right place for it---we have a meta thread for tagging. I have copied your comment to the tagging chatroom, where we might be able to discuss this in a more on-topic forum. $\endgroup$ – Xander Henderson♦ Feb 9 at 12:15

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