About NON-open-ended puzzles with multiple answers working towards an optimum

Question

A while ago, consensus was reached that open-ended puzzles are no longer welcome on our site. That means, if a question has no absolute "best possible" answer, so that any answer could conceivably be outdone in the future, then we're supposed to close it as too open-ended to work well here: there's no way to know when/whether an answer is optimal, and there could conceivably be arbitrarily many different answers.

We still have an optimization tag, though, and not every "find the least/most/largest/smallest" puzzle is off-topic. Quite often such puzzles have an answer which is provably correct. Hence why I posted an answer on that previous meta thread to clarify exactly what "open-ended" means. I also said:

If an absolute best answer exists and seems likely to be provable, then it's not open-ended: even if some answers are posted with successively better but non-optimal solutions, those are partial answers with increasing progress towards an upper/lower bound, not just iterations in an open-ended answer stream.

Nowhere on that meta thread was anything said about deleting answers. (You can check by searching "delet" on the whole page.) However, a few hours ago one of our moderators deleted all answers to this question except the one which brute-forced all possibilities with a computer - including the optimal answer which Bass skilfully found, as well as other answers which were optimal at the time of posting. The deletions were justified by the following comments:

Based on the rules established by this meta post and the consensus around it, an answer must have justification for why the solution is optimal. Without that, this is a comment, not an answer.

Apparently the "rules" he was thinking of was the following quote from that previous meta:

Optimization questions should have a provably best answer (ideally, not one that needs heavy programming or mathematics to prove, in the same way that we currently don't want puzzles that require heavy programming or mathematics to solve). Answers should come with justification of why they are optimal; an answer without this is not a full answer, but more of a comment.

But since the main discussion was about closing open-ended questions, it's arguable whether there's a clear consensus on deleting certain answers to non-open-ended questions as well. Neither the quote just above from Deusovi's answer, nor the other one from my answer, received any disagreement from the community ... however, they weren't really integral parts of the discussion, which was primarily about the handling of certain questions rather than certain answers to different questions. So here's a new meta to get consensus on this point.

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If an optimisation-type puzzle is NOT open-ended, and answers are posted which give bounds on the solution WITHOUT proving optimality, should those answers be deleted?

For example:

• Q: Find the smallest possible number of X needed to satisfy Y.
• A1: Here's a way of getting Y with seven X.
• A2: Here's a trick that enables Y with six X.
• A3: Here's a proof that it can't be done with four X.
• A4: Here's a proof that six X is the least possible.

After (or even before?) A4 is posted, should any or all of the other answers be deleted? A4 is the only one that proves optimality, but the others all establish bounds, A2 is the actual optimal solution (only without proof), and A1 was the best solution found at the time of posting.

Answer 1

Having written a lengthy meta post on this same subject myself, I took a deep breath, rethought the matter, erased my post, and here's my final policy suggestion:

Let's not have a policy on this.

Let's face it: the problem here was not that we didn't have a policy for this particular situation. Instead, the trouble was entirely caused by the fact that we had one policy too many, which led to a misunderstanding in the enforcement step. I'm pretty certain that no-one would have even suggested squashing an entire boatload of decent answers, unless there was a written policy somewhere that seemed to prescribe that the mods must do so.

At the very core of the Stack Exchange network we already have a mechanic for judging whether an answer is useful for the site: the user votes. Since everything we do should be for the good of the main site users, there cannot be a more direct indication for what's good and what's not.

If there's ever a reason to go against the user votes by mod action, it should be something quite extraordinary, like demonstrated plagiarism, or hidden personal attacks on other users, or something on that order of seriousness. If there seems to be a policy in force that suggests deleting a 10+ upvote post, it's more likely that we should review (and possibly abolish) the policy, rather than the well received post.

Deleting useless posts that usually stand at zero votes or under, like late dupes and such, is of course a perfectly common task, and should go on as usual.

TL;DR

Let's not solve the problem of too much legislation by adding even more legislation.

Answer 2

First of all, I'd like to apologize: I vastly misinterpreted the community consensus on this issue, and I didn't realize that I had inadequately communicated my "open-ended" proposal's intended effect on this type of question. I should not have deleted the posts there, and I fully acknowledge and apologize for my mistake.

That being said, I would like to make an argument that calling these types of answers "Answers" (even partial ones) doesn't make sense, and we should reconsider how we deal with them.

I think single answers to optimization questions, without proof of optimality, should be compiled in a single Community Wiki post rather than as their own individual answers.

I think this is especially true for formation-of-numbers questions, but a lot of my thoughts here apply more generally.

Answers invalidating other answers

This was one of my core arguments against allowing open-ended questions: it didn't make sense to have a question where answers became retroactively invalid. That's one of the reasons we don't like people making major changes to their puzzles after they have been posted. As Rubio says in his stock comment mentioned in this post about changing questions,

Changing your question after you've received answers is inappropriate, as it invalidates the answers you've received. It can even make those answers wrong, and adversely affect the reputation of those who answered. If you now have a new or additional question, create a new post and ask it there; you can link back to this one if needed for reference.

[emphasis mine]

The major problem here is that answers do invalidate other answers. In Rand's helpful example, once A2 is posted, A1 is no longer a valid Answer. If the question itself said "I can do Y with six X - what's the least number of X possible?" then A1 would not be an Answer at all. (And these answers are posted for the express purpose of collaboration: they're not hidden information, so it's not analogous to a full answer to a different type of puzzle 'invalidating' a partial answer.)

So now we have a state where later answers to questions can change whether other answers are An Answer or Not-An-Answer. This seems to be a problem with how we determine Answer-hood - the status of an answer shouldn't change based on a separate answer.

Analogy to Partial Answers

Adam draws an analogy to partial answers in his answer above. I don't think this is entirely analogous, though: the word "progress" seems to be used for two different things.

The progress of a partial answer must be extendable into a full answer. As I argue in the recent discussion on partial answers with 'list-of-clues' questions, a partial answer that is not demonstrably extendable into a full Answer is a comment, not an Answer. Even if it happens to be the correct path, if it's not shown to be the correct path it's not a Partial Answer.

For instance, say someone gives a simple puzzle where eight crossword clues each give a word with a double letter, and those letters spell out the answer. Someone else gives an answer to the question that gives a guess at one of the clues and guesses that all the answers have a double letter (maybe based on the title). This is still just a comment rather than a Partial Answer, even if it happens to be entirely correct: it's not known (or even thought very likely) to be extendable to a full solution, so it's a 'fragmentary thought' rather than a (Partial) Answer.

The same applies here: the nature of these optimization problems is that a single solution does not necessarily lead to any better ones. Giving an answer with 6 Xs might be the right one, but it also might be entirely useless for finding the way to make Y with 5 Xs. There's no way to tell whether a solution happens to be the correct one without that proof.

Overall impact on quality of answers

It also seems to me that these types of questions encouraging partial answers may give the mistaken impression that more "gamelike" open-ended questions, where a bunch of people each give their own maybe-valid answer -- the exact type we decided were bad in the other 'open-ended' meta post -- are encouraged as high-quality questions. This is not necessarily a problem with the question itself (as Rand said, these types of questions are not off-topic according to the previous meta post, because they are not necessarily open-ended). But it may be good reason to reconsider how we organize answers to them. At time of posting, the two relevant questions have 16 and 13 answers, respectively. That means the first must have at least 6 invalidated answers, and the second must have at least 12 -- most of which have nothing even attempting to show optimality (which is the actual hard part of the question).

These questions are not off-topic, but they seem to encourage lots of low-effort answers. I'm definitely not saying that all answers there are low-effort -- even the ones that don't try to show optimality can still be difficult to find if they're optimized well! But there are several answers that don't particularly try to be optimal (and even some that intentionally break the rules of the question by adding new operations).

Community Wiki: the best solution to the problem

So, we have a lot of answers that are not Answers, but still could hold some value. They often either give a good bound for the problem, or (as Adam helpfully points out in his answer above) a strategy that may lead forward. These answers are explicitly meant to be built upon by other users.

This sounds like the exact type of thing that Community Wiki answers are meant for. They have a much lower reputation barrier for edits, so people can more easily contribute to improving them. And using a CW answer has some other benefits too: less answer clutter in general, and an easy-to-find list of so-far-optimal answers. TheSimpliFire's answer on one of the two relevant questions is a good example of how this might look.

So, I think that when a question of this type is posted, there should be a CW answer made (ideally by the asker, but if they don't anyone else could make one). Answers that solely consist of "here's how you can do Y with only n Xs" should be edited into the CW answer with credit rather than posted separately. Answers that have (part of) a proof that a certain number is optimal can be posted separately as (Partial) Answers.

Answer 3

Optimisation answers without absolute proof = partial answers

*within reason

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An answer to a typical optimisation question that doesn't prove with 100% certainty that better cannot be done is exactly the same as a partial answer to a non-optimisation puzzle.

Here are the similarities between these types of answer

• They are both incomplete
• Both may not have reached the stage which can invalidate them (i.e may not lead to the final answer)
• They both exhibit direction which may lead to the final answer
• Both are somewhat useful to other puzzlers
• They are a display of progress and current knowledge

Due to these similarities, I propose that we treat them as equal so all queries should be resolved by referring to the discussion on partial answers here.

Admittedly though, this creates the rather difficult question - how do you quantify the specific value of an optimisation answer? Its not as if there is a clear "List-of-Clues" to value answers with.

Short answer: we do this on a case-by-case basis, there is no general rule which can 'calculate' the importance of an optimisation answer, however...

Long answer: an optimisation answer which doesn't show any indication of progress is not even partial. If it isn't possible to build upon the existing answer to lead to full proof and the answer in itself does not profoundly pave the way for another answer (e.g find restrictive bounds) then it is not even partial. Answers which meet the requirements for being an "alternative answer" are, however, exempt from this. The answer requires at the bare minimum some proof to even be considered as a partial answer. An answer must standout on it's own for it to at least be partial. Anything that these general rules cannot be applied to will require special consideration (e.g an answer which offers a radical new technique).

A small reminder to solvers: if you do not feel like your answer could standout on it's own in some regard then it should be posted as a comment

Enforcement

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I propose that all optimisation answers which aren't at least partial should be deleted. Many optimisation questions tend to attract a lot of attention so I also propose that the question should be protected if it is likely to attract a lot of non-partial unfinished answers in order to protect the integrity of the question and current answers. If a question is packed with partial optimisation answers then the bar to qualify for a partial answer should be raised and all further additions under the bar should only be comments. As a preventative measure to stop a question from ever reaching the stage of getting packed with partial answers, the bar should be set in some way prior to answers, preferably by the original poster.