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Personally, I am only interested in puzzles which are "well-defined" - that is puzzles which have a clear goal and a clear set of possible options, with the assurance that there is a demonstrably correct answer. This is as opposed to riddles or enigmatic puzzles, where finding the answer generally requires more open ended thought or searching for patterns or trying to apply various interpretations to the question itself.

I think that this is a meaningful category of puzzle, and one that I would certainly like to have an explicit tag for it. The closest we have is , but this is not quite the same. For one, it includes puzzles that have riddle elements in addition to references to or usages of mathematics. Also, I've certainly seen puzzles that have a well defined nature, but are not tagged under mathematics (as they may not as directly relate to mathematics, or may relate to specific subfields - this often applies to or ). Especially since these sort of puzzles are relatively infrequent on the site, it would be nice if they were gathered into a better form.

Should we create a new tag to encompass such puzzles?

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    $\begingroup$ I think that "well-defined" is a very "hard-to-define" concept :/ $\endgroup$
    – Fabich
    Commented Jul 24, 2016 at 22:12
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    $\begingroup$ @Lordofdark Is it? I don't think I've ever had any doubt about whether a puzzle was or was not. One could define it, for instance, as a puzzle where a computer could verify an answer. Could you give an example of a puzzle that's ambiguous? $\endgroup$
    – Milo Brandt
    Commented Jul 25, 2016 at 1:15
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    $\begingroup$ @MiloBrandt Could you give a few examples of puzzles that would qualify for this tag, but aren't (and shouldn't be) tagged mathematics (or its descendants) so we could get a better idea of what you're talking about? $\endgroup$
    – Dan Russell
    Commented Jul 26, 2016 at 13:36

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Your comment outlined a pretty good definition of what well-defined which deserves emphasis, since people are wondering whether the concept of "well-defined" is itself well-defined.

A well-defined puzzle is one where:

  • the puzzle explicitly specifies is a discrete set of possible answers,
  • at least one of the possible answers is correct, and
  • you can make a computer program which can verify if an answer is correct.

This means that any well-defined puzzle can theoretically be solved by brute force on a computer, though it might take the age of the universe to do.

I think this tag is a good idea, since there are at least two people (myself included) whose are interested in this category of puzzle. Furthermore, I don't think that this qualifies as a meta-tag. The issue with meta-tags is that they don't give you a good idea of what to expect from the question, and I think on this site, there are used largely to help you find categories of questions that you are interested in or capable of answering. I think that saying a puzzle is well-defined is very descriptive, and it gives you a good idea what to expect from the puzzle since it rules out so many possibilities.

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  • $\begingroup$ Technically, a riddle or wordplay question has a set of possible answers (dictionary) of which at least one would be correct. $\endgroup$
    – David Starkey
    Commented Jul 28, 2016 at 16:18
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    $\begingroup$ @DavidStarkey But making a computer program that could verify a riddle or wordplay answer is difficult because these types of puzzles depend on interpreting the clues correctly. $\endgroup$
    – f''
    Commented Jul 31, 2016 at 7:08
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I agree with Lord of dark's comment that it seems to be (ironically) hard to define what puzzles would be tagged as "well-defined". I've read over your question a couple of times and still don't understand what a "well-defined" puzzle looks like, exactly.

To take it a step further, I feel like what you're proposing is just a meta tag, which are generally discouraged on stack exchange. I think your best bet is just to set up a set of favorite/ignored tags that mirror as closely as possible your personal preferences.

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    $\begingroup$ I think "well defined" is well defined - at least well enough. But even if it would not be, it is important to know that the author assumed it to be well defined; So it needs to be edited if it's not. $\endgroup$
    – Volker Siegel
    Commented Jul 28, 2016 at 17:30

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