I didn't mean (at least, I think I didn't, and I certainly shouldn't have) to imply that challenge alone suffices to make something a reasonable puzzle; I agree that it doesn't. I think (but would need to meditate further on it to be sure) I agree that the possibility of a fully satisfying Final Solution (it's most unfortunate that those words have the other meaning they do) is a necessary component.

But, and here I think we may disagree, I don't think this means that the only meaningful question is "did they get The Solution or not?". ... And, actually, thinking about it more, I think I do in fact disagree about the necessity of a maximally-excellent Final Solution.

I think what matters is not the existence of One True Solution, but the ability to identify, more or less unambiguously, certain things that count as solutions. To take your examples: Tetris isn't a puzzle because there's no such thing as a "solution to Tetris", but if I specified the order in which a large finite number of pieces were going to drop then "find a way to survive all the way through" would be a puzzle, though probably a very bad one.

Fermi estimation isn't generally a puzzle because its approximate nature means that there's no clear way of deciding whether something is a solution or not; but I claim "find a way of estimating X given the available information" could count as a puzzle.

I know we at-least-kinda-partially-agree on this because you've already said that something can be a puzzle despite having multiple solutions.

(But you might still hold that to be a puzzle something has to have an optimal or final or complete solution, even if there are things that count as solutions despite falling short of that. I don't think I think that's the case, except in the content-free sense that if something has a well-defined set of solutions then "find and understand all the solutions" is a version of it that has One True Solution and you might reasonably consider that a best-possible solution to the original.)

Let's have a couple of concrete examples. 1. That puzzle of Dudeney's. "Combine such-and-such pieces to form a properly coloured 8x8 chessboard". It turns out to have exactly three solutions, none obviously better than the others. I say that the original question is a puzzle; it's an intellectually challenging task for which one can clearly identify whether a given thing is a solution or not.

(My working definition of "puzzle": an intellectually challenging task, whose goal is to produce an abstract artefact meeting certain well-specified conditions. "Abstract artefact" means e.g. a word, or a diagram, or a sequence of 100 positive integers, or a specification of how to move something around, as opposed to an actual physical thing.)

2. The (not very good) puzzle that spawned this discussion. "Make the number 2019 using at most ten 8s and such-and-such a set of arithmetical operations". It has lots of solutions, but we can identify clearly whether any given thing is a solution, and doing it with <= ten 8s is nontrivial. So this too is a puzzle.

In case 2 (but not case 1) what makes the puzzle challenging is the restriction on the number of 8s. I claim that this gives us an obvious criterion for what makes a solution better or worse: how much it outdoes this specific restriction. (If it had said "at most ten 8s and at most ten arithmetic operations" then there would be multiple ways of measuring how far beyond the requirements a given solution goes, though of course one could always come up with a specific metric.)

In either case, any solution gives closure in the following sense: we wondered whether the thing could be done, and now we see that it can and how it can.

In either case it's possible to wonder whether there are other solutions, or (in the second case but not the first) whether there are better solutions.

If you're going to say that the second is not truly a puzzle (unless recast as "find, with proof, the optimal solution") because one can "solve" it without bringing closure, then I think you have to do the same for the first. For me, that wouldn't be an acceptable outcome: I think Dudeney's puzzle is obviously a puzzle, despite its multiple solutions.

An alternative would be to say: no, finding any solution to either of these does bring closure, because you've done all that you were asked to, and that's all there is to it.

That doesn't work for me either, though this feels like a more subjective thing: I don't feel that closure has been entirely achieved merely because I've found a way to do something. I wonder whether there are others. I wonder whether there are others that are simpler, more symmetrical, more obviously correct, etc.

So: I say that a puzzle needs to have a well defined class of solutions; in many but not all cases it has just one, and all else being equal it's best when there's just one; in cases where there's more than one, there is sometimes (but not always) an obvious metric on which to compare solutions, and one can distinguish between better and worse solutions; "find, with proof, the best solution" is then a further puzzle, and a solution to it is a fortiori a solution to the original; but

... that puzzle is in general much harder than the original, and may be unreasonably hard, and the original puzzle is still a perfectly reasonable puzzle in its own right.

I think the key point on which we disagree is this: For something to be a puzzle, is it necessary that finding a solution is the same thing as definitively bringing it closure?.

I say no, because e.g. "find a way to put these together to make a chessboard" is a puzzle, and finding any way to do it solves the puzzle, but closure is only achieved when one establishes that there are no other ways, and doing that is extra-hard, and in general "find a way to do this tricky thing" puzzles are considered solved as soon as someone has found a way to do it.

@GarethMcCaughan Yes, that is the claim I make. I do feel the same way as you do - often, I think finding one way to do something doesn't feel like enough! I think it's good to explore multiple facets of a puzzle even after it's been solved, and there's value in having those as answers even after a Solution™ has been posted. But that deeper exploration is a bonus to the solution.

But doesn't that mean that sometimes giving a solution to a puzzle (i.e., something that counts as solving it) doesn't provide final closure to it?

I say that the Dudeney chessboard problem is a puzzle. "Here's one of the possible dissections" is a Solution™: anyone can look at it and say "yes, this puzzle has been solved". Maybe we'd like to explore it more, but the puzzle is solved: the task has been successfully completed.

Sure. Maybe the solution won't satisfy everyone's curiosity about closely related problems (such as "how many ways are there to do this? what's the best way to do this?"). But the original question has been answered.

OK, so we are in agreement that something can be a Solution™ without finally and completely knocking the thing on the head. In which case -- tell me again why these optimization puzzles don't have a Solution™? Specifically, suppose the question is "Find a way to do this with at most ten 8s; fewest 8s gets the green checkmark". Someone finds a way with eight 8s. Done. But if someone finds one with seven 8s they've found a better solution. This is (I am aware I'm repeating myself here) ...

... no different from any other puzzle where an answer may be accepted because it provides a Solution™, but then un-accepted because someone else found a better one.

So it seems like it's very specifically making that explicit that bothers you. Maybe?

There's a difference between a "better answer" and a "better solution". In the Dudeney puzzle case, "here's all of the possible dissections" is a more complete answer: a solution, and a more thorough exploration of the problem. I have no problem with saying "that's a better answer, so I'll switch acceptance to that". But it's better because of its detail, not because it has more solutions in it (or because it's more 'optimal' - it optimizes the size of the set of solutions given, no?)

Can you give an example of a different type of puzzle where "an answer may be accepted because it provides a Solution™, but unaccepted because someone else found a better one"?

On the Dudeney one: suppose one person posts "I found a solution; here it is" and another posts "I found two solutions; here they are". I claim the second person has a better answer (though not yet a maximally-good one) precisely because they found more solutions. Do you disagree?

Unaccepting for a better solution: e.g., some of our puzzles are mathematical ones asking for proofs of things. Solver A finds an ugly proof with a lot of brute-force calculation in it. OP accepts this since it's a valid solution. Solver B finds a three-line proof straight out of the Book. OP un-accepts A's proof and accepts B's because it's much nicer.

(Perhaps you wouldn't ever do that, but one principle around these parts is that within reason OP is entitled to accept whichever answer they find most satisfactory.)

Yes, I do think that those are better answers (and would happily change my acceptance in the second case). But they're better because they're more complete answers, not because the individual solution is 'better'.

I don't understand the distinction you're making, at least not in the mathematical case.

Incidentally, here's a concrete example that isn't of quite that form. puzzling.stackexchange.com/questions/55950/…

(I would also accept a horribly messy proof explained well, over a clean 3-line proof that's full of incomprehensible symbols. The quality of the answer is in its explanation, not how direct the proof is. And while those may be fairly intertwined in the case of mathematical proofs, they're not the same thing.)

(It may be the case that one answer is inherently more easily clearly explainable than another. So maybe that solution has an advantage in the explanation department - but it's still better because of its clearer explanation, not just because of any inherent superiority.)

I wasn't claiming that directness is the only thing that matters in a proof. Only that if you have two answers consisting of proofs then you may reasonably prefer the better proof, whatever it is about it that makes it better.

(well if an answer is completely maths then the question itself is probably off-topic)

(Adam: no, some questions are mathematical but entirely on topic here)

(Clarity of explanation is indeed a merit in a proof and might well be what makes one proof better than another.)

(Yeah but a "3-line proof full of incomprehensible symbols" says a lot about the question)

(or about the answerer)

((((()))))

(((()))((())))

I didn't think you were claiming directness was the only relevant thing. But I still don't think any solution is inherently better than any other given the same quality of explanation. (Your example above is more clearly explained than the balanced binary tree one, and more thorough (because it mentions more possibilities: namely, other trees). So it's a better answer. The quality of the solution is the same, though - it solves the puzzle completely, just like the other answer.)

In the case of a proof, "quality of explanation" is an aspect of the solution, not some thing that can be separated from it.

Ah right, so you're using "proof" in the sense of "convincing, rigorous[-ish] explanation", not just in the formal sense. (My bad for misinterpreting that.) I'm not sure this is analogous though. It would be like if someone asked the question "explain how to solve this Sudoku" rather than "solve this Sudoku".

The fact that quality of explanation is important has been emphasized. But it still seems that the real puzzle is the latter, and convincingness of explanation is an important part of an answer, but not a solution.

I'd say the solution is the proof method; the answer is the proof and explanation around it. (You'd say two proofs are the same proof if one just justified its statements more thoroughly, no? The one with more justification is better as an explanation, but the underlying proofs are "the same proof".)

(I admit I'm not 100% sure of this, though. There may very well be a problem with this point of view that I haven't noticed yet.)

Interesting suggestion.

Even if I do agree to that, though, I'm not sure we can really draw any conclusions here, because you could say "you change the acceptance because the solution is better" and I could respond "you change the acceptance because the explanation [and therefore the answer] is better".

Indeed.

And it still feels as if most of the discussion at this point consists of the two of us restating our different positions and getting annoyed that the other guy Just Doesn't Get It :-).

(not very annoyed, for the avoidance of doubt)

but it does feel like "one solution can't be better than another" is an axiom for you and you're then picking your positions on everything else to make sure that axiom remains true; whereas for me it isn't an axiom and I don't see any reason to believe it, and to me it seems like the positions I'm adopting are more natural ones.

Yeah, it felt like "he Just Doesn't Get It" to me too, and I imagined you felt the same way. To me, a puzzle is a question, and once someone has given a definitive answer to the question, the puzzle is solved. Maybe it opens new, related questions, but the original puzzle is done.

It being possible to say "yes, this puzzle is solved, there is no more work to do on the original question" is a core component of what a puzzle is to me. It's why we close and delete questions with subjectively correct answers: because it makes it not possible to definitively say "this question has been solved".

(And this is part of how the SE format works, too: an accepted answer brings closure to a question. Even if there are more, similar questions that spawn from an answer, they're separate questions.)

Keep in mind that the general goal of SE sites is to have the best answer possible so that we have a collection of high quality answers. It is for this reason that I agree with Gareth

Well, we've established that sometimes someone can give an answer sufficient for the puzzle to be solved, and then someone can come along and give a better one that justifies un-accepting the old one and accepting the new one even though it was already true in some sense that "the original puzzle is done".

The "best" answer in what sense, though? We want clearly explained answers, not "the answer that optimizes some arbitrary criterion among the answers people have currently found".

And, considering once again those "prove X" mathematical questions, I claim that there are lots of ways in which one proof can be better than another, they don't all come down to clarity, and any of them can be sufficient reason to pick a new answer to accept.

So I just can't get on board with this alleged principle that for something that's really a puzzle there's no difference between "this really truly solves the puzzle" and "this is definitive and it makes no sense to ask for something better".

If you're judging answers by any other metric than "does it solve the puzzle, and how well does it explain its solution?", that seems to me to be turning it into a game. It's no longer "find a solution, and explain it as best you can"; it's "try to compete against other answers and win". "Winning" a puzzle seems nonsensical to me. On SO, if someone asks "is it possible to do this in less than 10 lines of code", that doesn't mean a one-line answer is better than a 3-line answer.

If I asked such a question on SO (though I doubt I would), and if one person posted a 3-line answer that I accepted and someone else came along with a(n otherwise equally good) 1-line answer, I absolutely would switch to the new answer.

This business about games doesn't make any sense to me. You can call these things "games" if you like, but there's nothing bad about something being a game. What matters is "is it a puzzle?" not "is it also something else?". They aren't usually posed in terms of "winning" and that feels like terminology you've made up in order to make these things seem less puzzle-like. (Again, I'm sure it doesn't feel that way from your end.)

(I need to be AFK for a bit now. Apologies for resulting slow responses.)

I'm not saying "it makes no sense to ask for anything better [by some metric]". I'm saying that if the question is "Can you do it in under 10 eights?", then the answer "Yes - for example, here's a way to do it in 7" may lead to the new question "Can you do it in under 7 eights?". But that's not a part of the original question.

And no, that's not terminology I made up - the puzzle/game distinction, and the phrasing in terms of "winning", were originally given by Rubio.

I think the line between "a puzzle being a game" and "the inner workings of SE turning a puzzle into a game" has been slightly blurred

I've made that distinction before. There's inherent gamification of question-answering in the SE model. But that doesn't mean that the questions themselves should be games.

If the underlying question is "Can you do it in under 10 eights?", then "Yes, here's a way to do it in 7" is a solution. "Yes, here's a way to do it in 6" is also a solution, but no more thorough than the previous one. OP might accept it on a whim (not like we can stop that), but I don't think that should be the point of the question.

Questions should not be "the answer with the best [criterion] gets the tick", any more than an SO question should be "the answer with the fewest loops / function calls gets the tick". That changes it from a question to answer (with any competition being incidental, coming from the format of SE), into a game to win (with competition between answers baked into the question). The winner is no longer the most thorough answer, but the one that "beats" the others.

And this is why I argue that in that case, the true underlying question is "What's the best [X] that the PSE community can come up with?". (And that's where the problems with answers invalidating other answers come in.)

That's not a thing that you can definitively give a solution to, unless someone happens to answer with the true optimum (with proof).

"Can you do it in under 10 eights?" is clearly off-topic if it is possible for conflicting solutions. However "Optimise the number of eights" is what I thought we were discussing?

Huh? What do you mean? It's perfectly on-topic: "Yes, you can: here's one way to do it" is a fine answer.

It's too broad due to phrasing

"Can it be done in under 10 eights", then? The "you" there is meant as the general "you", not "you in particular".

What I mean is that "Optimise the number of eights" is only a search for the most optimised answer. "Can it be done in under 10 eights?" is a free-for-all where every answer under 10 eights is an alternative solution

The solution is "Yes, here's why" or "No, here's why". You can use different reasons why, but I thought we were in agreement that a puzzle could have multiple solutions, with none of them being inherently better or worse.

Yes a puzzle can have multiple solutions but an uncountable number of solutions is too-broad

"Can it be done in under 10 eights" is nowhere as restrictive as "Optimise the number of eights"

How is it too broad? There's a clear answer: "yes, it can be done" (or "no, it cannot be done"). That there are multiple ways of doing it doesn't matter, because the question is whether it can be done. Just like "prisoner strategy" questions may have infinitely many valid strategies, but finding any one of them would solve the problem.

This is confusing me a lot because using the same reasoning "Can you solve the riddle - what is black and white and red all over?" isn't too-broad

If the question is truly meant to be "can it be done?", then that's a bad puzzle (and arguably not a puzzle at all?), but not too broad if the answer is just "yes" or "no".

It might be "subjectively correct answers", though.

If we use this model we can resurrect any too-broad question by slapping a "Can it be done?" on it

And this is why it doesn't make sense to me

What questions in particular do you have in mind? Because most of those would still fall under "subjectively correct answers".

My point was that "Can it be done?" doesn't only require a yes or no answer. Its practically an extension of another question. In this case it could be an extension of "Do it in under 10 eights"

Sure, just a yes or no answer without any reasoning isn't going to be a good answer. But just because the reasoning can be different in different answers also doesn't make a question too broad. (Is a Sokoban puzzle too broad because there are infinitely many sequences of moves that can solve the puzzle?)

So then you agree that I can ask "Can you solve the riddle - what is black and white and red all over?"

You can ask that. And then it will be closed as "subjectively correct answers".

This cannot be the case since "because the reasoning can be different in different answers also doesn't make a question too broad". Apparently we should only inspect whether the answer is "yes" or "no"

I never said that that's the only thing you should look at. But even if it was, whether the answer is yes or no is still subjective.

"Can you solve the riddle - what is black and white and red all over?" is an example. Ok, I'll look for a question which has multiple indisputable correct answers which has been closed for being too-broad to give a better example

(I'd replace "can you" with "is it possible to". I agree that "can you, personally, do X" is unacceptable.)

New question. "Is it possible to find a solution to this?"

So that would be an acceptable question to ask?

"Is there an object that is fine if dropped off of a building but is destroyed if put in water?" is probably not too broad in particular. It's not a puzzle, though, and not an appropriate question for this site.

but the answer to my question would only be "Yes" or "No" right? So just because the answers will contain "Yes," at the start makes this question on-topic?

No. "Too broad" is not the only reason a question can be off-topic.

I would still say that is not a puzzle, and still "subjectively correct".

What makes "Can you do it in under 10 eights?" any different?

It's not subjective?

You can clearly demonstrate a way to complete the task in under 10 eights using the allowed operations, and that is not subjective.

I'm not saying you can 'revive' any bad question by just adding "is there a solution" to the front of it. But if the fundamental question being asked is "is it at all possible to do better than 10 eights?", then that is an acceptable question, and an acceptable solution is "yes, it is possible: here's one way to do it". (Just like "is it possible for the prisoners to escape this situation" can be answered "yes, here's a strategy that works", even if there are infinitely many others.)

For my above question you can clearly show that at least one valid answer is possible which doesn't make it any different than "Can you do it in under 10 eights?"

Whether an answer to the original riddle is valid is still subjective, and "identify an object that fits this set of criteria" isn't a puzzle IMO.

And you're ignoring the examples I keep giving. Do you disallow questions like the classic prisoners and lightbulbs problem, because there are infinitely many valid solutions? Or a Sokoban problem, which also has infinitely many valid solutions? (You can just keep pushing a block back and forth halfway through a solution.)

Well requesting a strategy (referring to the prisoners problem) is broad however considering only reasonable strategies, I doubt there are a vast number of them. Any answer would almost certainly be deserving of praise and they are all alternative solutions. I think it is unfair to compare a question like this to a "Is there a solution to [insert too-broad question here]" type question

~ which is exactly what "Can you do it in under 10 eights?" is

Another issue is that I can scale it to "Can you do it in under 1000000 eights?" and by your definition it still wouldn't be too-broad because only "Yes," or "No," is what we consider

There are infinitely many of them - you can, after all, just wait as many days as you like before declaring victory (if you're the last prisoner).

And yes, that's not too broad - but it's still a bad question, and should be downvoted. "Too broad" is not the only reason a puzzle can be worthy of downvotes and/or closure.

@Adam Which too-broad question do you propose fits here?

@Deusovi "Do it in under 10 eights"

That's not a question, though.

And I'm not sure that's too broad. (I'm not quite sure that "too broad" as a close reason even fits Puzzling anymore, after the change a while back.)

(I'm not saying it's not. I'm saying I'm not sure.)

What happened to the solution™?

Hold on, am I even talking to Deusovi right now?

What?

I said it didn't have to be unique.

What happened?!?!

"guess what I am thinking" -> "game" which is what you've been arguing against this whole time

I think a better criterion than "exactly one answer" is "there must exist at least one definitive solution". A puzzle must have a solution that conclusively answers the question. Vague riddles do not satisfy that criterion. (And neither do questions asking about vague riddles, for the most part.)

So this is why I'm fine with "Is it possible to make this number with under ten 8s?", but not with "Make this number with as few 8s as you can". The former is possible to give a conclusive answer to; the latter is not (at least, not without mathematical proof).

(obviously "Make this number with as few 8s as you can" should be "Make this number with as few 8s as possible")

Then in that case, it requires proof of optimality, as I've been arguing the entire time.

Aaaaannnnd the cycle continues again :P

What is your stance on this? chat.stackexchange.com/transcript/message/51757626#51757626

I think that sounds reasonable, and I'm happy to have answers with at least the beginning of a proof of optimality as partial answers.

(But I disagree with what you said in the comments leading up to that - the "answer invalidation" is a real issue, for questions that I denoted as type (b) here: chat.stackexchange.com/transcript/message/51764066#51764066 )

(...but I think that type of question shouldn't exist anyway, and optimization questions should be type (a). The problem is that the ones we have now are (b) pretending to be (a).)

@Deusovi I agree with this

I geared it towards only (a)

Right, that's why I decided to make that distinction.

So in your opinion, what does the original question class as?

(also I've just noticed that the two original questions that caused this debate have had their lock removed by Community)

(Well I accidentally shared the link to my answer and not the question and I cannot edit it but you get the picture)

It's phrased as either (a) or (d) ["is it possible to do better than this specific amount?"], but a lot of questions phrased as (a) are "actually" (b) (in how answers are posted and accepted), especially when the original question's phrasing is unclear.

Has it ever been discussed somewhere what counts as an on-topic optimisation question or could that be something to ask on meta? I think a clear understanding of a valid question could help define a valid answer

That's what the original "open-ended" meta question was for (or at least, that's what my response to it was for).

Fair enough. Expansion might be needed though because I think that once the others come back into this chat they might debate the questions further. In that case I think a meta should be created

Yeah, I was planning on creating another with my thoughts on this when I had time. Wasn't sure whether it should go to an existing question or whether it should be its own question, though.