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I sometimes post questions I already know how to answer for the purpose of sharing an interesting problem with the community. Some are well received. Some are not (this last question currently has two downvotes and no upvotes). What follows is a collection of mostly random thoughts about such questions.

There have been many complaints about problem quality over the past few weeks, so my thinking is that I can improve the average problem quality by posting interesting problems. These questions are directed at people who come here to solve interesting math problems.

I am not sure how well such questions fit in with the mission of M.SE. However, this style of sharing interesting problems is what made, for example, the Art of Problem Solving forums so great.

I'm also very tempted to post such questions with just the problem statement (because I have no work to show, as I am not seeking help). However, I try to add a little text in order to avoid them getting mistaken for homework questions. I don't think this is necessary, as a cursory look at such questions shows they are not homework. On AoPS, many questions were posted with just a problem statement, and I did not see any issues resulting from that.

Maybe such questions could be mistaken for people attempting to cheat on math olympiads. In my case, I think it's clear from my question history that I am not one of those people.

(Obviously, if you are asking for help with homework or something like that, you should include more than the problem statement...)

My question: Do you want to see more or less of this kind of question?

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    $\begingroup$ If you want to post a question, post it. No need for the politics ("[I] am posting this to raise the question quality on this site"). $\endgroup$ – Andrés E. Caicedo May 4 '13 at 23:07
  • $\begingroup$ @AndresCaicedo Ok. I added that mainly so it would not be mistaken for homework or cheating. Thanks for the input. $\endgroup$ – Potato May 4 '13 at 23:08
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    $\begingroup$ Politics is bad $\endgroup$ – Tim May 4 '13 at 23:27
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    $\begingroup$ There has been some concern in the past about people using MSE as a means to publish, rather than as a means to get answers to questions, but IIRC it was never settled. Such concerns are unlikely to amount to anything unless you are prolific with your questions. (or do other things concurrently that trip peoples' sense that something's not right) $\endgroup$ – Hurkyl May 4 '13 at 23:43
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    $\begingroup$ Nearly every concern I'm aware of about questions like this are obviated if you both make the origin and intent of the question clear, and post your own answer along with the question. $\endgroup$ – Hurkyl May 4 '13 at 23:43
  • $\begingroup$ @Hurkyl Well, that takes the fun out of it for others who want to solve the question, doesn't it? It's very tempting to scroll down and immediately get the answer, even if you initially intend to solve it yourself. $\endgroup$ – Potato May 4 '13 at 23:46
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    $\begingroup$ @Potato: Of course, the intent of withholding the answer gets thwarted the moment somebody else posts an answer. :) So while I understand the motivation, I'm not sure the intent can actually be achieved except for a short while. $\endgroup$ – Hurkyl May 4 '13 at 23:48
  • $\begingroup$ And FYI, I don't think anyone who has expressed concerns about question quality has been talking about the level of the questions are at or how interesting they are. (but I could be wrong) $\endgroup$ – Hurkyl May 4 '13 at 23:53
  • $\begingroup$ I'm sure there has already been a discussion here of posting questions to which you already know the answer, but how to find it? $\endgroup$ – Gerry Myerson May 4 '13 at 23:55
  • $\begingroup$ @GerryMyerson I tried search. I recall being linked to a such a question a while ago, but it was focused on people who immediately answer their own questions, instead of the practice I am describing above. $\endgroup$ – Potato May 4 '13 at 23:58
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    $\begingroup$ @Tim, one of the silliest things we can say is that politics is bad. Bad politics is bad, but you simply cannot live without politics: you may not enjoy it, but probably you do not have much pleasure brushing your teeth, either. $\endgroup$ – Mariano Suárez-Álvarez May 5 '13 at 0:06
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    $\begingroup$ @Mariano, if you do not have much pleasure brushing your teeth, you're doing it wrong. $\endgroup$ – Gerry Myerson May 5 '13 at 0:13
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    $\begingroup$ Or maybe this one: meta.math.stackexchange.com/questions/1839/… or this one: meta.math.stackexchange.com/questions/265/… $\endgroup$ – Gerry Myerson May 5 '13 at 0:18
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    $\begingroup$ Alan S Blinder, The Economics of Brushing Teeth, The Journal of Political Economy 82 (1974) 887-891, theunbrokenwindow.com/wp-content/uploads/2008/04/… $\endgroup$ – Gerry Myerson May 5 '13 at 0:28
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    $\begingroup$ @Gerry: Wow! $\textbf{}$ $\endgroup$ – Pete L. Clark May 5 '13 at 2:21
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There is a substantial difference between two problems cited in the question.

  • The successful one is a natural statement about $0,1$-matrices. Matrices filled with zeroes and ones come up all the time, and their spectral properties are of substantial interest. My first reaction to that problem was "This is really neat! I have to know why this is true."

  • The unsuccessful problem is some unmotivated statement about algebraic identities or inequalities with year number (1997) in them. Honestly, who cares? It almost has too localized written over it. These things are produced routinely for math contests every year. I saw enough of them already that I don't feel the need to look for more (and if I did, I know where to find them).

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  • $\begingroup$ Thanks for your input. So to be clear, you appreciate problems that are posed as a sort of "community service," as long as those problems are interesting enough? $\endgroup$ – Potato May 5 '13 at 2:32
  • $\begingroup$ @Potato I think people are unlikely to object to a question they personally find interesting, whatever the source of the question. Of course, "interesting" is in the brain of beholder. I made an attempt to explain why I reacted to the first one with wow and to the second one with yawn. And it's the second reaction that provokes one to ask "why is this here?" $\endgroup$ – 75064 May 5 '13 at 2:37
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    $\begingroup$ I agree with this answer completely. $\endgroup$ – Pete L. Clark May 5 '13 at 3:03
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One thing I notice about the question you linked to as not being successful was that you said you know how to solve it but did not post a solution. (And just now I noticed that, conversely, the other question you linked to which was much better received does include a hint sufficient to reveal the solution you have in mind.) I think that could have something to do with how the question was received. Could you perhaps explain your motivation for not leaving your own answer and/or say a little more about why you want to post old contest problems like this for others to solve?


Reply to Potato: Thanks for commenting. In your successful question, you posted a hint in hidden mouse-over text (or whatever it's called). That seems to be ideal for information that some users will want to see and others won't. I think that posting a hint to this type of problem makes a big difference in convincing people that you've done enough due diligence in asking the question. Otherwise anyone could post infinitely many old contest problems: are those good questions that deserve upvotes?

Really though I'd like to explore more deeply the issue of whether posting (former) contest problems is a positive contribution to a site like this, especially given that there are already other sites squarely devoted to this purpose. But it's not how I want to spend my Saturday evening, so let me get back to you on this.

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    $\begingroup$ I did not leave a solution or hint because it is my understanding that many people do not want solutions or hints unless asked. I noted that I already knew how to solve it so that people would not leave comments about me not showing my work. I'm posting old contest problems because people here complain about not seeing enough good problems on this site, and many people come here looking for interesting questions to solve. Admittedly, the poorly received question I linked is not actually that interesting... $\endgroup$ – Potato May 5 '13 at 2:13
  • $\begingroup$ Perhaps if I was more careful in my problem selection, and stayed away from contests whose solutions are easily available online already, people would like the questions more? $\endgroup$ – Potato May 5 '13 at 2:15
  • $\begingroup$ @Potato: Probably. I should say that I myself don't care for math-contest type problems of almost any level, so I tend not to read those questions here, let alone upvote/downvote/vote to close them. To me math contest questions are somehow a little boring (which is not at all to say that I am very good at solving them: I haven't tried since I was 18 years old, and back then I was -- for a serious student of mathematics -- pretty bad). If you really want to ask good questions I think that's great and you should try harder and ask better questions. Which is easy for me to say, of course... $\endgroup$ – Pete L. Clark May 5 '13 at 2:25
  • $\begingroup$ Substitute 'contest problem' for 'tricky elementary problem in ring theory', then. Do you appreciate questions that are asked only to give others (those who are looking for them) interesting and creative problems to do? I do, but I get the feeling others do not. I think the reason people complain about decreased problem quality is that answering questions becomes less fun. I think using the site would be more fun if there were more interesting questions to answer. $\endgroup$ – Potato May 5 '13 at 2:29
  • $\begingroup$ @Potato: I am all for more interesting questions to answer. My opinion though is that a really interesting question is one which is new (or at least, new to all the people involved in discussing it). I also think it's not prohibitively difficult to ask actually novel questions, mathematics being vast and rich as it is. Actually, motivated by this discussion I have posted a question on the main site which has been troubling me for a while. $\endgroup$ – Pete L. Clark May 5 '13 at 2:50
  • $\begingroup$ Addendum: a question is also interesting if, while not new, someone has something new to say about it. This is part of my attitude to these pre-solved questions: I think it's nice to post one of these if you think you have a new solution or are looking for a different solution from the standard, known ones. $\endgroup$ – Pete L. Clark May 5 '13 at 2:54
  • $\begingroup$ Thanks. I will do my best to ask novel questions! $\endgroup$ – Potato May 5 '13 at 3:22
  • $\begingroup$ Pete, it's called "spoiler tag" because it can be used to write down spoilers for books/murder cases/lottery draws/movies/etc. $\endgroup$ – Asaf Karagila May 5 '13 at 7:05
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There is a new user who has been posting questions to which it already knows answers, and is pretty snotty when people give part answers. At this point I don't read the questions, I just vote to close, for example https://math.stackexchange.com/questions/436873/right-triangles-whose-areas-minus-their-in-radius-is-a-square-number

Note that Andre left a comment about the closing at The existence of a certain class of triangle using Secant squared expressing mystification.

Maybe people do not care; I dislike the motives of the OP. There was also the part where the first profile picture by this person was of a girl's rear end, wearing a bikini. Not sure what that was about.

There was a case on MO that had some similarities, although that one had some entertainment value: https://mathoverflow.net/questions/29534/the-product-of-n-radii-in-an-ellipse

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  • $\begingroup$ I expressed mystification at the stated reason for closing, which was lack of clarity. The question was not particularly interesting, since it turned out that the obvious approach worked. But that criterion would close most questions on this site. Closing because OP knows the answer, so need not ask the question, seems not unreasonable. It even fits one sense of "not a real question." The problem is how to determine whether OP knows the answer. $\endgroup$ – André Nicolas Jul 5 '13 at 19:31
  • $\begingroup$ @AndréNicolas, hi. It was the earlier questions about 6000 primes and 8000 primes that showed that this OP was quite happy wasting the time of other people. If you just look at the comments by this OP when people do give answers...the comment on your answer was fairly benign, in comparison. As I recall, I did not find a choice saying "Not a Real Question" which is available on MO. $\endgroup$ – Will Jagy Jul 5 '13 at 19:41
  • $\begingroup$ One of the primes questions seems to have attracted some interest. Perhaps the evident rough edges will get smoothed, or at least covered. $\endgroup$ – André Nicolas Jul 5 '13 at 19:54

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