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I was thinking of a proof of impossibility for a long-running unanswered question on this site. By a proof of impossibility, what I mean is a proof that no possible answer can solve the challenge. When I polled chat for other interested fellows, one response was this:

unfortunately, I don't think that would fit as an answer, since the question asks about solutions to the challenge, but about a proof that it's impossible

So I came here to ask: if I could prove that a challenge had no valid solutions, could I post it as an answer?

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    \$\begingroup\$ Although in this particular case your proof is only for one language... the situation is quite different. \$\endgroup\$
    – DELETE_ME
    Apr 10, 2018 at 6:29

4 Answers 4

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This is my opinion:

  • If the proof of impossibility is trivial, offer it as a comment and hope the OP revises their question or deletes it. If they don't, it should be closed as "unclear what you're asking."

  • If the proof of impossibility is nontrivial - which I think must be the case here, since you said the question is a long-standing one - then offer it as an answer.

In the latter case I would say there is no need to make it "Wiki Answer" as suggested by Dennis. If the proof is nontrivial then you put work into it and it is helpful for the community (so that others don't keep trying to solve it), so you should credit - and rep - for it.

This is basically how it would work on sites such as Math or Physics - if the question is "how can I do X" it's quite acceptable to give an answer "you can't do X, for nontrivial reason Y." I think it should be the same here.

[Added later: it turns out that you can have a "Wiki Answer" question without the answer being Community Wiki. In that case the person who posted the answer does still get the rep, so in that case applying it wouldn't cause a problem. (Note that +20 votes on this answer are from before this text was added.)]

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  • \$\begingroup\$ It's worth noting that the wiki answer lock applies only to the question—you can still vote on all the answers. \$\endgroup\$
    – Nissa
    Apr 11, 2018 at 13:03
  • \$\begingroup\$ @StephenLeppik you can vote on the answer, but the person who wrote it doesn't get any rep. (It's owned by "community wiki" not by the author.) \$\endgroup\$
    – N. Virgo
    Apr 11, 2018 at 13:46
  • \$\begingroup\$ (This is because its purpose is to allow many people to collaborate on one answer, so it wouldn't make sense for the rep to go to just one of them. That's not what's needed here though, so it doesn't feel like the right solution to me.) \$\endgroup\$
    – N. Virgo
    Apr 11, 2018 at 13:49
  • \$\begingroup\$ I agree that it doesn't make sense for the answer to be community wiki. If a proof on impossibility is worth an answer as opposed to a comment in the first place, then the person who gives the proof deserves rep just as much as any other answer. \$\endgroup\$
    – dylnan
    Apr 11, 2018 at 17:11
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    \$\begingroup\$ @Nathaniel The Wiki Answer lock doesn't actually require the answer to be CW. All it does is prevent the addition of further answers and it adds the notice that further additions should be made by editing the existing answer. It's perfectly possible to have a Wiki Answer lock with an answer that still gets reputation. (And it's a bit unfortunate that now all the voting on this matter happened based on a false assumption.) \$\endgroup\$
    – Martin Ender
    Apr 16, 2018 at 11:32
  • \$\begingroup\$ @MartinEnder I agree that is unfortunate. (Also unfortunate that the feature is called "wiki answer" if the answer doesn't have to be wiki. Really quite strange actually.) I think my assumption was a reasonable one, even if incorrect. \$\endgroup\$
    – N. Virgo
    Apr 16, 2018 at 11:38
  • \$\begingroup\$ @Nathaniel Yeah, I'm not blaming you, I had to test it to be sure. \$\endgroup\$
    – Martin Ender
    Apr 16, 2018 at 11:39
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    \$\begingroup\$ The good news is that our answers are compatible now. I can get behind a Wiki Answer without a Community Wiki. \$\endgroup\$
    – Dennis
    Apr 16, 2018 at 13:19
  • \$\begingroup\$ @Dennis me to, I have no objection to Wiki Answer if the answer isn't CW. \$\endgroup\$
    – N. Virgo
    Apr 16, 2018 at 13:22
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Yes, if the question is locked as Wiki Answer

Note This is a point of view, not an authoritative answer.

If you have a proof of impossibility, the challenge cannot be properly solved. It should get one answer (the proof of impossibility), but no other answers.

Fortunately, Stack Exchange supports this. Mods can lock questions with the reason Wiki Answer, which is described as follows.

This question's answers are a collaborative effort: if you see something that can be improved, just edit the answer to improve it! No additional answers can be added here

I think this is a perfect fit: it effectively closes the challenge, but it also provides a space to detail why the challenge had to be closed.

Example of a question locked as Wiki Answer: The Definitive C++ Book Guide and List

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    \$\begingroup\$ What if the proof wasn't fully exhaustive, and a valid solution was written later? \$\endgroup\$
    – DJMcMayhem
    Apr 9, 2018 at 20:46
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    \$\begingroup\$ That would require moderator attention to unlock the post. As always, invalid PPCG answers should be deleted. \$\endgroup\$
    – Dennis
    Apr 9, 2018 at 20:54
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    \$\begingroup\$ The only downside is that a proof of impossibility (on this site) likely requires quite a bit of work, but the poster isn't going to get any rep. It'd be great if we could bounty them or something. \$\endgroup\$
    – Nathan Merrill
    Apr 9, 2018 at 22:51
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    \$\begingroup\$ @NathanMerrill While I'm OK with providing a space for these proofs, I don't think we should actively encourage any part of this process. That said, I'm not sure if a wiki lock would even prevent a bounty. \$\endgroup\$
    – Dennis
    Apr 9, 2018 at 22:58
  • \$\begingroup\$ @Dennis a wiki lock stops bounties—I just checked here. That said, why should this be discouraged? \$\endgroup\$
    – Nissa
    Apr 10, 2018 at 2:34
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    \$\begingroup\$ @StephenLeppik Because non-solutions to unsolvable challenges aren't really on topic right now, so they should remain an exception. \$\endgroup\$
    – Dennis
    Apr 10, 2018 at 3:05
  • \$\begingroup\$ @NathanMerrill Bounty on different answer? (or whatever way we often do to bounty challengers) \$\endgroup\$
    – DELETE_ME
    Apr 10, 2018 at 6:31
  • \$\begingroup\$ @user202729 We don't bounty challengers. We bounty the challenge they wrote. This resulted in a 500 bounty on the question, awarded to the best answer. \$\endgroup\$
    – Stewie Griffin
    Apr 10, 2018 at 9:05
  • \$\begingroup\$ @StewieGriffin What about this? \$\endgroup\$
    – DELETE_ME
    Apr 10, 2018 at 9:13
  • \$\begingroup\$ That's the exact same thing as the link I posted (but the year before). The bounty is posted on the challenge. The author doesn't get any rep, only more attention. We don't give bounties on unrelated challenges... \$\endgroup\$
    – Stewie Griffin
    Apr 10, 2018 at 9:14
  • \$\begingroup\$ @StewieGriffin No bounty? \$\endgroup\$
    – DELETE_ME
    Apr 10, 2018 at 9:15
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    \$\begingroup\$ @Dennis Doesn't this answer make them on-topic? \$\endgroup\$
    – Nathan Merrill
    Apr 10, 2018 at 12:04
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    \$\begingroup\$ @NathanMerrill It makes an exception for them. Wiki answer is used to provide a space for content that would normally have to be deleted, but is too valuable to delete. For example, it is used for old book recommendation questions on SO. \$\endgroup\$
    – Dennis
    Apr 10, 2018 at 13:27
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    \$\begingroup\$ @Pavel Historical significance prevents edits, comments, and votes. Wiki Answer is closer to a permanent close vote than a lock for historical significance. \$\endgroup\$
    – Dennis
    Apr 10, 2018 at 14:39
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    \$\begingroup\$ Is it possible to post an answer without CW-ing it and then lock the question as "Wiki Answer", or would it automatically CW the answer? \$\endgroup\$
    – Erik the Outgolfer
    Apr 12, 2018 at 13:47
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Vote to close

(Or whatever the closest available option is based on reputation)

A challenge with no solutions is not capable of generating new answers in a valuable way, and other types of challenges incapable of being answered well are often closed. I would lean towards "Unclear what you are asking", alongside a comment that links to the proof of impossibility, which would allow the poster or some other community member the chance to tweak the challenge constraints into one that does have solutions in case there is something interesting in the core of the challenge even if other parts make it inaccessible. In this way challenges which are impossible for abstract reasons that are difficult to prove get treated the same as a challenge which says both "Answers must do X" and "Answers must not do X": both are impossible as defined, and clarification is requested to resolve the impossibility. Then, if no improvement is/can be made, the challenge stays closed.

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    \$\begingroup\$ I disagree - a proof of impossibility is just as valuable as a solution in many cases, if for nothing more than to provide a target for later dupes. \$\endgroup\$
    – user45941
    Apr 9, 2018 at 23:22
  • \$\begingroup\$ @Mego I feel all those who downvoted on this answer feel the same. \$\endgroup\$
    – ReinstateMonica3167040
    Apr 15, 2018 at 0:30
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Answer it with a stronger model language

Some questions can't be solved on Turing machine, then you can try a stronger model to solve it. A proof is welcomed. No strong model abusing, though

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  • \$\begingroup\$ This opens a can of worms: Can I answer any other question with a stronger model? What's the syntax for this stronger model? What's "strong model abusing"? \$\endgroup\$
    – Nathan Merrill
    Apr 10, 2018 at 18:01
  • \$\begingroup\$ 1.No strong model abusing. If no valid usual model solution, stronger is allowed. 2. There are alreasy some syntax designed for such @NathanMerrill \$\endgroup\$
    – l4m2
    Apr 10, 2018 at 18:48
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    \$\begingroup\$ 1. So, you are saying that if an answer is impossible, you'll need to provide that proof that it is impossible and then also answer it in a stronger model? 2. The reason I ask about syntax is because we define a language by its implementation: We require an interpreter for that source code. If none exists, then it's an invalid answer. \$\endgroup\$
    – Nathan Merrill
    Apr 10, 2018 at 19:38
  • \$\begingroup\$ (I suppose you already know that downvotes on meta indicates disagreement) | There are some languages implementing such "stronger model" (e.g., Brainhype, Scheme-1), but those languages are not allowed on PPCG becaues they don't have any implementation. \$\endgroup\$
    – DELETE_ME
    Apr 11, 2018 at 12:16
  • \$\begingroup\$ True. Just leave it there to show it's commonly disagreed \$\endgroup\$
    – l4m2
    Apr 11, 2018 at 13:44

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