# Revisiting the 'math question or math puzzle' policy

There have been a lot of discussion in the past about which math questions are on-topic and which one are off-topic. But I today I found a bit old question (with amazingly net 4 upvotes) which is clearly a math problem but was re-opened. This made me think to revisit the policy discussed on meta about mathematical questions on this site. Some related discussions I found are given below:

Their summaries are (if you are not willing to read these questions):

1. O.P. asked if he can ask a math question and he was permitted to do so.
2. Few features that makes something a math puzzle rather than math problem:
• Clever or elegant solution, often an "aha" moment
• Unexpected problem statement.
• Unexpected or counterintuitive result.
4. Another meta post about the scope on this site of a math related question. The question was found to be a math problem.
5. The title of this question says it all. The given answer on this meta post was "Until a solution is posted, it's hard for us to say."

I am OK with first and fourth point here. But the other three kinda cross each-other.

If we are using advanced mathematics in a question then the probability of the solution being elegant is pretty low. (However it still is possible.) And those three features that distinguish between a math puzzle and a math problem works well with the top math questions on this site (yes, they are five different questions). But these features don't really help to distinguish when new math questions are posted because "Until a solution is posted, it's hard for us to say." And after the solution is posted, every one forgets about the question. And if it is found to be a math problem then very less number of people care to close the posts to maintain the site quality. Even if the question is closed then somehow after a month, the question can be found to be reopened by the math-lovers.

Final Question:

• Is there any improvement in the policy to get rid of math problems since last time (which was more than an year ago)?
• Is there any way to have the same opinion among different users about a question being a math problem or a math puzzle?

Side question: I couldn't really understand what he meant by "Unexpected problem statement." Can anyone please elaborate it?

• From an empirical and pragmatic point of view, I'd say "don't regulate too much" unless it becomes a real problem. If we get tons of "math textbook questions" a day and they start to "kill" the site, we need actions, but otherwise: Let the voting system take care of it. If "bad" (in the sense of "boring" or "ill-defined" or "textbook only") questions get a lot of downvotes, we have self-regulation. And for really bad examples we always have VTC. I'd rather live with a few (ignored) bad (or too expert-) maths puzzles than miss some interesting ones... – BmyGuest May 24 '16 at 13:36
• @BmyGuest For the record, I agree with this 100000000%. A lot of stuff we have these vague, negative policies toward aren't really "problems" by any stretch of the imagination, and could easily be dealt with by voting. Voting is, in fact, the only way to know what the community wants, and that's something we ostensibly care about. – question_asker May 24 '16 at 13:52
• I would be careful about what "the community" wants. Yes, it's (very) important, but our primary goal is not to heed the desires of the users, as judging by votes alone might lead us to do. Our goal is to maintain site quality. It's rare, but those two things do sometimes come into conflict (Security to the Party Part 473...). I'm not saying that's what's happening here - but it's something to keep in mind. Optimize for pearls, not sand. – Aza May 24 '16 at 23:53
• @Emrakul Yes, "site quality" is important. And literally the number one deciding factor in "site quality" is what the community wants (as a veteran of moderating sites for the last ... 18 years? 19?) – question_asker May 25 '16 at 13:40
• @question_asker I respectfully disagree. I think there are standards for quality that all users - moderators included - can fail to uphold when voting on questions. "Users can be wrong" is a pretty important thing to acknowledge, and the votes on some posts indicate that. For example, again, I don't think anyone would argue that the Security to the Party questions are of high quality, yet most of them are positively scored. – Aza May 25 '16 at 18:05
• @Emrakul What are you basing that on (re: SttP)? Because I've never heard anybody have anything negative to say about them. More to the point, things that aren't problems (and this stuff arguably isn't a problem, since nothing bad has ever happened as a result of them) don't need to be fixed. When a problem happens, let me know. (to your edit: Users can't really be wrong in that sense, no. That's all this website is, is its users. Users can disagree with you though) – question_asker May 25 '16 at 18:13
• @question_asker SttP was used colloquially as the paragon of a specific breed of poor puzzles (mass-producible puzzles) for some time on meta. At the time, they arguably were doing significant harm to the site, categorically speaking (and I'm not the only one who felt that way). A continuation of this discussion might be better in chat, though. – Aza May 25 '16 at 18:18
• @Emrakul "was used colloquially" show me. Where is this artifact of culture that I've never heard of despite it supposedly being a cornerstone of the community? I don't see where chat is going to get us. You've positioned your (and possibly a small minority of others') opinions as the "right" to which the community's opinions are opposed. As someone who has decided to discipline users by deleting their posts and comments, you're not really someone I can reason with. – question_asker May 25 '16 at 18:20
• @question_asker One, two, three, four, five, and a lengthier six, (and about a similar breed). – Aza May 25 '16 at 18:27
• @Emrakul So far that's 1) a question espousing an opinion like the one you claim is pervasive, 2) a duplicate question by a person who doesn't use the site anymore, 3) an answer about puzzle titles that namedrops the puzzle, 4) a question about a different puzzle, 5) a chat line about those puzzles from someone else who doesn't use the site anymore, and 6) a chat line from that same person. So... hardly supports your personal opinion, I guess. – question_asker May 25 '16 at 18:31

Having “math problem” as a close reason has caused demonstrable harm. I'd be skeptically interested to hear what measurably significant benefit it has actually brought, and I could philosophize about how a good math problem is inherently a good puzzle, but here are two fairly recent examples of math puzzles whose temporary closures taxed both time and good will.

### 1. The Reopened Case of   $\bf \surd{15} - \surd{7} + \surd{5} + \surd{2}$ versus $\bf 5$

Of course this reminds me of math homework. Many other puzzles I enjoy here remind me of history homework, computer programming homework, media studies homework, science homework, even spelling homework. With freedom of choice and without due dates or report cards, I don't mind at all.

This challenge was chased out of Math SE after, ironically, being branded a puzzle. What good they thought that did is another question. (Can't provide a link, the post seems to have been deleted.)

The reception here poorly reflected our quizzical spirit of curiosity. It was downright unwelcoming and produced some awkward, to put it mildly, comments.

Turns out that the numbers in question were carefully chosen by the puzzle's poser to click into place like a safe's tumblers in the hands of a skilled cracker, complete with roles for hunches and discovery, but to snowball into tedium otherwise. This puzzle is underlain by a hidden maze to be discovered and negotiated, seen here thanks to a comment:

### 2. The Reopened Case of the Relevant Primes

At first glance I thought this was a straightforward math problem simply beyond my comfort zone. Then I saw a partial, at the time, answer that disentangled the puzzle into two more-manageable pieces. Then a comment made me suspect that, once again, the puzzle had been tailored to have the mathematical pieces fall into place when viewed from an angle.

Then the puzzle got closed. After hours of disappointment, commenting and suspense, the puzzle was open again and I could complete some of the math not yet attended by others.

Part of a math puzzle/problem is, through creativity and experimentation beyond what is taught in class, to find an efficiently presentable solution, and this one had an additional hurdle at the end. One of the terms had to be rearranged like a sliding blocks puzzle before it could mince between division by 0 and conflicting incorrigible exponents. Ya had to be there.

Admittedly pointed rhetorical questions in/on closing. How much effort is required to click on “math” as a close reason? How much effort is involved in rallying a puzzle's poser and other support, such as protective nonmath-camouflage editing, to get a misapprehended puzzle reopened?

Addendum. Perhaps we could encourage math solutions to include more and more description of the puzzle-solving processes involved.

• As you know, I think there's no need to close things unless they cause a problem, and I'm not of the belief that math puzzles (or problems) cause any kind of problem except those created by our arbitrary standard of whose problems we close. However, the linked puzzles are utterly opaque to me, and I'm not convinced that they are "puzzles" in the sense of the distinction that we draw (whether or not that distinction is necessary is, of course, the conundrum) – question_asker May 25 '16 at 19:43
• Were your comment two or three separate comments, @question_asker, I would ^tick each one but comment on just this: Yes, we have difficulty judging, both objectively and consistently, just when to apply the existing distinction. I believe this is inevitable because making such a distinction at all, regardless of how well intentioned and crafted, is intrinsically flawed. – humn May 26 '16 at 1:36
• Yeah, and hence, my 'if a problem, not a problem worth trying to address' stance – question_asker May 26 '16 at 1:46