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Even though I have not asked any questions or answered any questions here, I have been reading the Puzzling SE site for more than one year.

So, I have this question.

How do you know a question is answerable? Because some people may ask questions that are not answerable. I mean questions which have not any correct answer... Or fake questions..

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There are a few different kinds of non-answerability.

  • Some questions are unclear: it seems like they don't provide enough information to tell whether any given thing is or isn't a solution. These usually get closed for being unclear. (Some questions are deliberately unclear because part of the puzzle is figuring out how to interpret them. There's a special tag for those.)

  • Some questions are too broad: it's reasonably clear what it would mean to solve them, but there seem to be lots of equally-good solutions. These usually get closed too.

  • Some questions are just nonsense, usually because someone is trying to make trouble. These usually get deleted outright.

In these cases, it's possible to be mistaken about the question's failings, but when that happens the author of the question can always push back and maybe provide some evidence that the question is better than it seems. (This is very rare, as it happens. We're generally careful, and give the author of the question opportunity to defend its merits.)

  • Some questions are ambiguous: there's a well-defined puzzle there but it needs some clarification before it's quite clear what it is. In these cases, usually the comments to the question have requests for clarification, or answers begin by saying "I'll assume you mean X", or answers say "If you mean X, the answer is A; if you mean Y, the answer is B". Puzzle authors are usually cooperative about clearing up their meaning.

  • Some questions are, on the face of it, perfectly reasonable puzzles of the sort that ought to have clear solutions, but through error or malice they turn out not to have solutions, or to have multiple solutions. This hardly ever happens. When it does, the commonest outcome is that someone writes an answer saying "this question doesn't have a solution because ..." and it gets accepted. Very occasionally it will become apparent that a puzzle is deliberately broken because someone's trying to cause trouble; those get deleted.

  • At any given time, there are quite a lot of old puzzles that are sitting unanswered. Perhaps some of those are actually unanswerable. If so, they don't do much harm; I don't think a lot of time is spent by PSE members agonizing over old puzzles that have gone unsolved for months.

I'm not sure I've yet exactly answered the question. If something seems on the face of it to be a "normal" puzzle, how do you tell it's insoluble? By trying to solve it, and seeing what happens. You may make a series of logical inferences and arrive at a contradiction. You may find that there's a place where it seems like you can make a choice, and try both ways and find solutions on each path. You may find a mathematical characterization of all the solutions and be able to prove that there are exactly 196883 of them or something. If a puzzle isn't found to be insoluble that way (maybe it's a riddle or something) then the more likely outcome is that it just stays unsolved, drops off the bottom of the recent-questions page, and is largely forgotten thereafter.

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How do you know a question is answerable? Because some people may ask questions that are not answerable. I mean questions which have not any correct answer... Or fake questions..

In general, we assume a question is answerable unless there's evidence to the contrary.

  • Some questions are posted by an OP who doesn't know the answer - according to policy, this should be stated in the question if it's not clear, precisely because people should know beforehand if there's a possibility they'll be wasting their time on something unsolvable.
  • It's also happened that people have posted troll questions which have no answer. This is severely frowned upon - again, precisely because they could waste a lot of people's time by doing so.

The vast majority of questions are answerable, naturally, but there's always a small risk when you start working on a question that the OP may have made a mistake in the setup of the problem, or forgotten to mention that they don't know if it's answerable, or simply be a troll. A small risk.

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    $\begingroup$ Especially with Gareth's questions. Those are always unanswerable troll posts :-P $\endgroup$ – Rand al'Thor Nov 29 '17 at 12:10
  • $\begingroup$ Especially with Bejoscha's questions. These regularly have a mistake 8c). But there are unanswered open as well... ;-) $\endgroup$ – BmyGuest Dec 3 '17 at 11:52

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