Some misgivings
Friends, puzzlers, PSE denizens, lend me your ears!
Despite the heading above, I am not trying to overturn the consensus
that open-ended puzzles are a bad idea. But I'm not sure we have total
clarity on exactly which puzzles are bad and and why, and in particular
one thing that earlier discussion might make one think is the key feature
seems to me not to be much of a reason to reject a puzzle.
(I shall be disagreeing with Deusovi quite a bit in what follows.
That should be taken primarily as an indication of how clearly
and unambiguously Deusovi has laid out the case.)
Specifically, consider the following remark of Deusovi's, quoted by
Brandon in this question: "puzzles should have only one solution, and
anything more than that is either a broken puzzle or not a puzzle
at all". And the following, near the start of Deusovi's answer here:
he gives a definition beginning "An open-ended question is one where
multiple answers are expected [...]" and says "Without the second
part of that sentence, it's just a question that is intentionally
too broad. These are already disallowed."
I don't think that the mere fact of having multiple acceptable
answers makes something not a puzzle, or even not a good puzzle.
The OED's definition of "puzzle" says things like "A puzzling or perplexing
question; a difficult problem" and "Something devised or made
for the purpose of testing one's ingenuity, knowledge, patience, etc."
I think these get to the heart of what a puzzle is, and having a
unique answer is not essential to it.
Consider, for instance, some of SlowMagic's recent word-transformation
puzzles. You have (for instance) two words, and you want to turn them
into two other words, by means of some repertoire of operations by which
you can move letters between the two. For instance,
this one and this one,
both currently on a well-deserved +10. The solutions aren't (so far as I
know) unique, but finding a solution at all is "a puzzling or perplexing
question", "a difficult problem", and "something devised for the purpose
of testing one's ingenuity".
For another example, consider puzzle 74 from H E Dudeney's "Canterbury
Puzzles", called "The Broken Chessboard". It presents a set of 13 pieces
and invites you to put them together to make an 8x8 chessboard. Dudeney
apparently thought his solution was unique, but later Sam Loyd found another and
Laurie Brokenshire a third; but finding any solution is enough of a
challenge that it's a perfectly reasonable puzzle even though it has
(it turns out) exactly those three solutions.
I think any definition of "puzzle" that excludes these things is a
bad definition; and any criterion of acceptability-on-PSE that excludes
them is a bad criterion.
Similarly, any definition of "solution" that would make a valid
sequence of transformations accomplishing one of SlowMagic's goals,
or a valid way to assemble a chessboard from Dudeney's pieces,
unacceptable unless accompanied by a proof that one couldn't do it
better, is a bad definition.
(Not because there's anything wrong with proofs. I'm a mathematician.
I like proofs. I like questions that demand proofs. But it's OK
not to prove everything.)
The foregoing does not constitute a rejection of the consensus
here, because "open-ended puzzles" as considered here are not simply those
that have multiple solutions. The definition near the start of Deusovi's
answer begins as quoted above, but goes on: "answers are ranked by some
sort of rule, and the answer with the best score by that ranking is the
accepted answer". And Deusovi's proposal, which seemed to attract some
measure of consensus, was that such puzzles should be forbidden here
except for three special classes; I would class the first two together
under the heading "finding optimal solutions with proof", and the third
class is of questions about puzzle design that are not themselves puzzles.
It seems to me that if a puzzle would be acceptable here although
possibly solvable in multiple ways, then adding a further criterion
by which to choose among those possibly-multiple solutions shouldn't
make it unacceptable.
(By this point, yeah, I suppose I have arrived at a definite
disagreement with that consensus. You should have expected that
ever since I started with "Friends, puzzlers, PSE denizens ...".
But when I say that Deusovi is an honourable man, I really do actually mean it.)
And yet ... Clearly something is wrong with questions like Brandon_J's
that started all this, which just invites "solvers" to construct "as many
pairs of alliterative ailments as possible". (I would apologize to Brandon
for saying this, but he's already said as much himself.) As Deusovi says,
it's more game than puzzle. But, as you can see above, I don't quite
agree with the diagnosis of how it's wrong. What, then, is the actual
disease?
One feature that SlowMagic's and Dudeney's puzzles have
(and would continue to have if we added some sort of ranking to the solutions),
and Brandon's lacks,
is that finding any solution at all is a challenge.
That element of challenge is, for me,
the most important thing that distinguishes puzzles from things that are not puzzles.
Finding phrases like "fever and flu" or "cough and cold" is not a challenge,
and that's why Brandon's puzzle is actually not a puzzle but a game.
Finding more and more and more pairs is a challenge, though.
Does "find lots of pairs",
or "find a hundred pairs",
or "find all possible pairs",
constitute a decent puzzle?
Well, "find lots of pairs" lacks another quality
that for me is near the heart of puzzle-ness
(though not quite so central
as the element of challenge): definiteness.
Not in the sense of having a unique answer,
which as I've said above doesn't bother me so much,
but in the sense of being able to tell unambiguously
whether something is an answer or not.
I think "find a hundred pairs" is a puzzle,
but it's an incredibly boring one.
And "find all pairs" is indefinite
in two slightly different ways:
first, "ailment" is a category with fuzzy edges;
second, there's no good way of checking
whether an alleged accounting of all alliterative ailments
actually achieves absolutely all.
So the position I'm coming to is that mere open-endedness as such
is no obstacle to being a puzzle, or even a good puzzle,
but that a puzzle of this kind is only any good
if it would still feel like a puzzle
without that criterion for ranking solutions,
and the ranking criterion should be seen as secondary,
as a way of choosing between multiple acceptable answers
if they should show up.
I'd like to look at some of the other objections raised to open-ended
puzzles. Deusovi lists some interesting ones.
"An answer can be invalidated by other answers." (Because if the goal
is to find not just any X but the best X, then something can cease
to be the best merely because someone else did better.) I am not convinced
that this is very bad. I have fairly often seen the following on Stack
Exchange sites (including PSE, though I think it happens more often
on others): someone asks a question; someone gives a good (and, literally,
acceptable) answer; someone else comes along and gives an even better
one -- one with clearer explanations, deeper insights, helpful illustrations.
Even questions that don't explicitly ask for "the best X" can have
better and worse answers, and sometimes an answer is good enough to get
accepted but turns out not to be the best, and another is accepted instead.
There's nothing wrong with
that.
"With these questions, you can almost never know when an answer is
correct." (Because if the goal is to find the best X, then the only
way to know whether it's been achieved is to have a proof, and proof
is hard.) Again, that's true, but if we take these questions to be
saying "find an X; best one gets the green checkmark" then this isn't
really a problem any more than the fact that any answer to any
question might turn out to be outshone by some brilliant later
answer. Deusovi says, further, that "having a clear correct answer
is a quality necessary to be a puzzle"; if that's taken to mean a
unique clear correct answer then, as I've already said, I can't
agree.
"We don't allow other questions without a single best answer."
But we do!
This one
asks for a Life configuration achieving a certain goal,
which can be achieved in multiple ways,
and the poster even says "The puzzle has been solved,
but please don't be discouraged from posting alternative solutions.
They are still very valuable,
as they seem hard to come up with."
This question, by the way, is on a mere +177 points.
"We don't allow other questions whose answers change
based on the answers that PSE members have posted --
that wouldn't be a self-contained puzzle."
True enough, but again
if we think of these questions as
"Find an X; best one gets the green checkmark"
then the answers aren't changing
based on other answers posted;
all that changes is whether an answer is worth posting,
and there's precedent for that:
we reject answers (to any question) that merely repeat
what's already in other already-posted answers.
"Open-ended questions attract many answers,
which makes them likely to land in HNQ,
which gives a bad first impression of PSE."
Bad questions with many answers are bad, for sure,
but the solution to that is to downvote them into oblivion.
I do agree that open-ended puzzles are likely
to exacerbate the problems PSE has with the HNQ algorithm,
but the real problem here is that the HNQ algorithm
doesn't understand PSE and picks unrepresentative questions,
and I don't think we should let that drive
our definition of what is and isn't
an acceptable puzzle here.
So, after all that -- and I do apologize for its length -- where
have I landed? I think most open-ended questions are bad, I think
the consensus we've arrived at is better than just allowing them all,
but I can't agree with the reasons given, and I worry that those
reasons will lead to poor decisions about other matters -- such as
what to do about answers to optimization-type questions,
a meta question about which
was what prompted me to write all this.
And I think the current consensus, while better than "anything goes",
doesn't exclude quite the right things.
If it were just up to me, I would say:
- Open-endedness as such is no crime.
- To be a puzzle, something needs to be challenging and it needs to be clear what constitutes a correct answer to it.
- Most bad open-ended puzzles fail on one or both of those criteria, and that's what makes them bad.
- There are two quite different sorts of "find the best X" puzzle, and we should try to be clear about which sort any given puzzle is.
- Sometimes it means "find any X; best one gets the green checkmark".
- These are only any good if "find any X" is a puzzle -- if it's challenging and it's clear what is and what isn't an X.
- For these, something that's demonstrably an X is a good answer, and worthy of acceptance (though a better answer might come along and dethrone it). It's not necessary to prove that no other answer could do better (though such a proof might be interesting, and make the answer a better answer as well as ensuring prompt acceptance).
- For these, the ranking criterion is just an alternative to saying "first correct answer gets accepted" or "whichever answer I happen to like best gets accepted" or whatever.
- Sometimes it really means "find the best X", and the point of the question is to show that your X is best.
- These are only any good if figuring out what X is best is a puzzle (challenging and clear).
- For these, a good answer needs to be demonstrably best, not just demonstrably X.
- All else being equal, having a unique answer is a very good feature for a puzzle to have. For many classes of puzzles (e.g., sudoku, chess puzzles) there is a firmly established convention that every puzzle's solution should be unique. But it isn't a thing that distinguishes puzzles from non-puzzles, as (I think) challenge and clarity do.
- I am entirely in favour of vigorously closing (or, as an inferior but acceptable alternative, downvoting into oblivion) puzzles that are not challenging or not clearly defined or both.
