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Why was my question closed here? Probability every team successfully presents a solution

At a summer math program a contest is held for $n$ teams. Each team, composed of $n$ individuals, is given the same $n$ problems to work on. Suppose that on each team, there is one person who knows how to solve all $n$ problems, another who knows how to solve $n-1$ of the problems, and so on down to one member who only knows how to solve a single problem. One person is chosen from each team at random. These selected individuals are randomly ordered and asked one at a time to select a problem that has not already been taken. What is the probability that every team successfully presents a solution?

I had asked my professor and other graduate students in the department, and they all did not know how to do this problem. I know MO has had some debates recently (over the last year or two) on whether or not it is welcoming to graduate students. Clearly MO is not welcoming if this question was downvoted to oblivion, even when a tenured faculty member and fellow graduate students did not know how to solve it. MO wants to intimidate graduate students into thinking their questions are too trivial by deeming them offtopic.

For all the inanity and Red Guards posturing of math graduate students (and even faculty) on Twitter, this is nonetheless a real problem that they've highlighted about MO's unfriendliness.

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    $\begingroup$ Rather than how difficult a question is, a criterion for a question to be on-topic on MathOverflow is whether it is interesting for mathematicians. On the one hand, very many questions graduate students may ask are interesting for mathematicians, and on-topic on MO -- but on the other, it is possible to ask arbitrarily difficult questions which are not interesting for mathematicians. -- "Difficult = interesting" is a common misunderstanding. $\endgroup$
    – Stefan Kohl Mod
    Commented Aug 16, 2021 at 17:14
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    $\begingroup$ It is probably reasonable to ask why a question was deleted, though more likely to be useful to ask how you can improve future questions to avoid deletion; but the editorialising at the end of your post is not likely to contribute to a useful discussion. $\endgroup$
    – LSpice
    Commented Aug 16, 2021 at 21:42
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    $\begingroup$ "asked one at a time to select a problem that has not already been taken". What exactly does that mean? The success or failure depends on the strategies the team members use in their choices in general. Also, there is no information on how the subsets of problems the members of different teams solved are related to each other and that influences the outcome too. The problem is not well-posed as you wrote it in the sense that the probability space is not unambiguously defined by the provided information. No wonder there was no solution offered. $\endgroup$
    – fedja
    Commented Aug 17, 2021 at 3:39
  • $\begingroup$ It is not even clear to me from what you wrote whether the two chosen team members have to present just one problem each or they should go all the way until all $n$ problems are discussed taking turns, but that may be due to my poor understanding of English grammar... $\endgroup$
    – fedja
    Commented Aug 17, 2021 at 3:43
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    $\begingroup$ A problem such as this may be on-topic in math.se ... However you would have to add your own attempted solution to avoid being closed there. You may ( instead of solutions) get hints, like "Can to you do the cases $n=1, n=2, n=3$?" $\endgroup$
    – Gerald Edgar
    Commented Aug 17, 2021 at 11:39
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    $\begingroup$ I was one of the people who voted to close it; I also commented that it was not research-level, and so can offer my reasoning. As fedja has said, the question was ambiguous, and therefore difficult to answer; I think that once the ambiguity is resolved (so that the process in the question happens algorithmically), the probabilities can be calculated for each $n$ by simply applying the process. As such, I did not (and do not) see there being much chance of the question being interesting on the level of research. $\endgroup$
    – user44191
    Commented Aug 17, 2021 at 12:58

2 Answers 2

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I said what I think of the problem itself in the comments (1 2). So yeah, the posts of this sort (randomly created puzzles that aren't even well-posed as written) will not be enthusiastically welcomed here. If you get curious about something "just because" (which, by itself, IMHO is perfectly normal for a mathematician), then make sure that you know yourself what you are talking about before posting and take some effort to make the problem statement crystal clear to everyone.

On the other hand, I have already said many times that (again, IMHO) any clearly stated question that is neither trivial, nor well-known to be totally hopeless should pass. It is certainly none of my business why people ask their mathematical questions. My part of the game is to see if I can figure them out, period. Of course, no matter how clearly the question is posed, I can always declare that something is "not interesting" for me, but deciding that it is also of no interest to other members of the community is a bit outside of my area of competence, so I prefer just to do nothing in such cases rather than to vote to close. Doing otherwise looks impolite to me not only toward the posters, but also (and even more so) toward other community members who might be willing to think about the question.

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Two comments beyond what fedja said.

The first is about the general phenomenon of closure of questions. A lot of posted questions are reasonable but unclear or otherwise flawed. One approach to these questions is to vote to close, citing the flaw, ask the poster to fix the flaw, and thus reopen. The second approach is to ask the poster to fix the flaw first, and only close later if they refuse to do so. I think the first is very unwelcoming but the second is necessary.

I don't fully understand the timeline in your case but it looks closer to the second. In particular, Anthony Quas gave a comment pointing out what needed to be clarified, and the question wasn't deleted until days later (after, according to other comments, you deleted and then undeleted it instead of changing anything).

The second is about presentation. Your question was presented in word problem format, without an associated purely mathematical formulation. This led to confusion as the word problem was ambiguous, but it also led people to mistrust your question as what a math researcher, absolutely including a grad student, would typically do is give formulas in addition to (or instead of) the word-problem motivation. You can find many examples of questions on MO that do this.

I expect if you had posted a formal statement you would have gotten a dramatically better response.

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  • $\begingroup$ The second "the first" should be "the second"? $\endgroup$
    – Gerry Myerson
    Commented Aug 20, 2021 at 21:59
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    $\begingroup$ @GerryMyerson Yeah. I'm trying to come up with an ironic explanation to justify that but I've got nothing. $\endgroup$
    – Will Sawin
    Commented Aug 20, 2021 at 22:41

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