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Today I posted the question below:

Challenge: find the order of an element in a Finite Abelian Group with a given presentation

I was surprised to find that there is no such thing as a challenge tag and took the liberty to tag the question as such anyway. It is meant to indicate that the answer is known to the OP, and that the problem is interesting to solve, or has a beautiful or unexpected answer.

In order to prevent abuse of this tag (such as "this is definitely not homework, it's a great challenge, haha"), it could be required that the OP does post an answer and then deletes it, which would make it readable by moderators.

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    $\begingroup$ I think this came in the past, should we have puzzles. The answer was pretty much no. $\endgroup$ – Asaf Karagila Jul 31 at 14:48
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    $\begingroup$ math.meta.stackexchange.com/questions/29043/… is highly relevant $\endgroup$ – YuiTo Cheng Jul 31 at 14:49
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    $\begingroup$ In addition, there have been failed suggestions on Area51 for a math-challenge exchange. $\endgroup$ – davidlowryduda Jul 31 at 14:50
  • $\begingroup$ @AsafKaragila Thank you for the related questions. I noticed on Puzzling.SE that questions whose statement and answer only involve mathematics are systematically deleted nowadays. $\endgroup$ – Arnaud Mortier Jul 31 at 15:05
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    $\begingroup$ That is something to consider, and is worth bringing up for discussion with the community at large. But for the case of the tag, which is the focus of this question, this is a meta-tag, which are highly discouraged, and I'd think that even if there is a support for allowing puzzles to be posted (I'd like to register that I'm not a big fan of the idea), they should be marked differently, e.g. by a "Challenge" at the start of the title. If nothing else, I'd say that a chatroom is probably the best option. $\endgroup$ – Asaf Karagila Jul 31 at 15:08
  • $\begingroup$ @AsafKaragila Thanks. I take it that in the end, such questions do not belong in SE at all because they are not proper Q&A spirit. $\endgroup$ – Arnaud Mortier Jul 31 at 15:12
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    $\begingroup$ They'd also get closed due to lack of context, and confused with contest math questions, which people don't seem to use the tag for, in order to get around rules. There's Also a puzzle tag already. $\endgroup$ – Roddy MacPhee Jul 31 at 15:39
  • $\begingroup$ @RoddyMacPhee That's why I was suggesting a rule that the OP has to include a hidden answer to their question, visible by moderators, to make sure that they do have the answer. $\endgroup$ – Arnaud Mortier Jul 31 at 15:41
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    $\begingroup$ The tag with this name was created and removed once in the past: math.stackexchange.com/posts/1365280/revisions Such tag is also mentioned in Mark Bennet's answer here: Using Math.SE for contests. I left a few aadditional comments in the Tagging chatroom. $\endgroup$ – Martin Sleziak Jul 31 at 19:13
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Here are a few of my own thoughts on this issue:

I think the reason is that Math SE is fundamentally a question-and answer-site (tour). While learning and problem-solving are promoted here, questions created solely to encourage problem-solving are not on-topic here.

In these types of sites, there would be a lot of discussion, and lots of different ideas would emerge as people gradually discover the solution. In other words, there would be a lot of chit-chat as expected from a forum-like site. As a consequence, this would disrupt the flow of 'ask questions, get answers' with no distractions, which would not be a good fit on an SE site.

In the comments, it has been mentioned that there have been previous proposals to create an exclusive site for problem-solving on Area 51. However, a rigorous process is needed to ensure that the site will be useful as its own site, as well be able to sustain a community around the site. A future 'challenge-problems' site is too close to Math SE to be its own site, and seeing that questions focusing on alternative answers to a question already are on-topic on this site, there really should be no need for a separate site.

So where should challenge-type questions be asked? From my personal opinion, I think Brilliant would be a much better site to ask. The difference with Brilliant is that it is fundamentally a site about improving problem-solving.

As such, there are many features such as the daily questions, and the community tab where there are hundreds of user-submitted questions created every day. There is also a discussion page where users can post an interesting questions and users can discuss freely. The site would be more suited for a 'challenge-type' question because it is not so focused on asking and answering.

All in all, Math SE is primarily a question-and-answer site, and although there will always be a need for problem-solving, I believe this site just isn't the place to ask these types of questions.

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    $\begingroup$ Thank you for sharing. That's what I understood from the comments. I will still leave this particular challenge-question open though because it has a huge teaching/learning value. $\endgroup$ – Arnaud Mortier Aug 17 at 13:21

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