# Handling underspecified “Make <this number> from <these digits>” questions

### The problem:

We get a lot of questions like this one:

## How to use the numbers 3, 5, 6, and 7 to get 100?

Any mathematics symbols and processes to use the numbers 3, 5, 6, and 7 once each to get 100.

That's the whole thing, as of its original posting.

This is way too underspecified. Among other things, allowing any math operators often leaves things open to some clever but surely unintended techniques for getting to any arbitrary number; if not disallowed by the problem statement, nesting logs or using the successor function to reach particular numbers makes for unsatisfying but valid boilerplate solutions. It's also not clear if the numbers given can be used more than once each, nor if all of them must be used. This puzzle needs some help.

We've discussed these types of puzzles recently:

Those questions were principally concerned with the genre fatigue that inevitably happens when we get several similar looking puzzles in a short period of time (which often feel hastily produced and, like the example above, are often not well specified). The answers to both those meta questions, written by @Rand al'Thor, basically say to vote on the quality of the puzzle — that is, downvote the question if it is poorly specified or uninteresting — and close as duplicate when possible. We're also reminded that a close-vote is not a super-downvote.

Having said that, the general consensus has been that puzzles that don't limit the available operations are too broad and should be closed as such, as there are simply way too many ways to solve them otherwise and no criteria given for then selecting a "best" answer amongst the solutions.

That's not to say that all puzzles of these types are categorically too broad or off topic—in fact we've had some good examples of puzzles with well specified rules for what is allowed, including some whose rules are very simple. And, of course, a puzzle that gives criteria for a "best answer" can still work well even when it would otherwise have too many solutions. And then there's this gem which shows us that a clever poser can still bring novelty to a sometimes tired-feeling type of question.

But compare those examples with the likes of this or this or this or this, or (sigh) this which HNQed and got piles of upvotes for both question and answers.... in one case the OP actually said they "would like to see creative ways to make this work" which is not the kind of thinking that lends itself to creating a puzzle with a single, or at worst a very few, correct and interesting solutions, but it's definitely a good first step to creating something that's going to wind up rightly closed for being too broad.

### What to do, what to do ...

Personally, I think that taking a particular list of allowable operations and a particular set of digits and asking for them to be assembled into a sequence to create a particular number is a cookie-cutter approach to churning out a puzzle that shows no creativity in its creation and will admit no novelty in its solution. We've seen these done to death, and I'd be happy not to see them any more; if they were all closed as duplicative of some early example(s) of the genre, I'd lose no sleep over it.

(Note that most of the good examples I listed earlier go beyond this: one is actually looking for help completing a challenge where they were only missing one number, which seems fair game here; many were not just finding any solution, but a contest to find a shortest or longest sequence; and some added a decidedly new element to the trope, either in their construction or in their intended solution.)

So let's consider questions whose formulation is nothing more than a set of allowable operations, a set of allowable digits, optionally an ordering rule for use of those digits and/or operations, and optionally specifying if using each digit and/or operation more than once is allowed; and where the requirement is to create expressions that evaluate to a particular value, or to every integer value in some specified range. These types of puzzles are mechanical in their formulation and in their solutions, with no variety in them beyond the specification of values and operations to use. If your opinion of how to handle such questions is different when the set of allowable operations is narrowly confined (say, to at most the basic arithmetic operations $$+, -, \times, \div$$ and $$( ... )$$ parentheses for grouping, or perhaps extended to include exponentiation, square roots, and factorials), please indicate that as well.

### Question 1: Should cookie-cutter puzzles like this be closed as duplicates? (And if so, what question(s) should be the dup target(s)?)

If the community consensus is that these puzzles should be considered independently on their own merits, rather than closed as duplicates, then the kind of underspecified questions that are a problem—specifically including, but by no means limited to, puzzles that do not restrict which operations can be used—should be closed as Too Broad until they are fixed. (No, that isn't a question; it's a statement.) But we should have a stock comment that tells the poster what is wrong with their question and how they can fix it, ideally with pointers to some good examples of the genre. So ...

### Question 2: What comment text should we use to help posters salvage puzzles of this type that are closed for being Too Broad?

I'd really like to hear the Community's input on these questions!

Personally, I think that taking a particular list of allowable operations and a particular set of digits and asking for them to be assembled into a sequence to create a particular number is a cookie-cutter approach to churning out a puzzle that shows no creativity in its creation and will admit no novelty in its solution.

Agreed. But so far at least, being a cookie-cutter has never been a reason to close. This is an issue that many SE sites have faced: the problem of mass-producible questions isn't one limited to a site where questions are often original content rather than requests for help. Here on Puzzling, it's not just but also, for example, (several "What is a [...] Word(TM)" puzzles have had solutions involving "shares letters with such-and-such a word", which could of course be done for any word) and other tags too.

In my experience, though, it's usually only a hypothetical problem. Yes, one could post a million slight variations of the same question, but in reality this never happens, and if it did it would probably be grounds for mod action against the user rather than community action against site scope.

More importantly, on Puzzling we've historically done well at judging such questions by voting. When a puzzle genre gets overdone, votes on new questions in that genre will drop rapidly as people get sick and tired of them. That's what put paid to the spaghetti craze of 2014, the rebus craze of 2015, and many others since then - and even smaller things that couldn't count as crazes, like my Mysterious Email puzzles with monotonically decreasing scores. I've already discussed this here.

## Question 1

Should cookie-cutter puzzles of this type be closed as duplicate? (And if so, what question(s) should be the dup target(s)?)

This is a possibility I raised here. Creating a canonical Q&A pair and closing a bunch of other things as dupes of it is an appealing idea - and it's worked well here with water-pouring puzzles, for example - but in this particular case, I don't think it's workable. Different techniques are needed to solve different puzzles, and there's so much variety that it can't all be covered in one puzzle: anything broad enough to be a dupe target for all of them would be far too broad.

The main issue is in the lists of operations. Varying the set of allowable operations can drastically change what the solution of such a puzzle will look like. Varying the numbers used to form a given number, or the different numbers which can be formed from the same numbers and operations, is unlikely to make much of a difference to the underlying structure of the puzzle and its solution.

That's not to say some of them can't still be closed as dupes, of course. If someone wants to know how to form $N$ from $a,b,c,d$ and we already have a question about how to form all natural numbers from $a,b,c,d$, then dupehammer away. Maaaaybe, if the same list of operations is coming up over and over again, we could create a "how to form a general $N$ using a general $a,b,c,d$ and THESE operations" Q&A and close a bunch of others as dupes.

But I don't think it's possible to create one post broad enough to cover all the puzzles. As the SE blog puts it: Having one “perfect” form of a question that contains every possible answer to every slight variation of that question is a myth at best and actively harmful at worst.

## Question 2

What comment text should we use to help posters salvage puzzles of this type that are closed for being Too Broad?

Without actually writing up a template, I have the following suggestions for such a comment.

• Explain exactly what's wrong and how to fix it. Don't just close the question, but point out why phrasing like "any mathematical symbols and operations" is too vague. List examples of possible operations, including some weird and abstruse ones that they probably won't want to allow, to show them why they need to narrow the possibilities.
• Be nice and encouraging. Not just Be Nice, but also be positive. Even if you think someone's question is really bad, word the comment in terms of how they could make it a good question, rather than what's wrong with it.
• Point to good examples of the same type of question. "Good" not necessarily meaning highly-voted, of course. Find some examples of really well-specified (not even necessarily imaginative, but clearly on-topic and not too broad) puzzles of the same type, so that the OP can see what they should be doing.
• I never said, or even suggested, that being “cookie-cutter” is a reason to close. You’ve now responded to that imaginary suggestion twice, and I’m not sure why. My suggestion was that they be closed as duplicates because they are often, in some cases literally, copying an existing puzzle but changing the specific values. We close as dup when that happens in water jug puzzles, as you note: even though the particular numbers lead to different particular steps, the broad puzzle and its solution path is essentially the same. It’s not about quality, or site scope - but about being duplicate. – Rubio Feb 18 '18 at 15:22
• @Rubio I just wanted to get that out of the way - even if you didn't suggest it, I've seen others do so. Wasn't intended as a rebuttal towards you; I just wanted this to be said clearly on meta :-) – Rand al'Thor Feb 18 '18 at 15:25
• Fair enough. That said, rather than repeat what you said in the earlier metas I already referenced, it might be nice if you addressed the specific question of this type of puzzle. There are indeed different formation-of-numbers puzzles which need a variety of techniques to solve, but here we’re talking about the generic template of: use \${OPERATOR-LIST} and \${DIGITS} to make \\${TARGET-VALUE}, where the only thing to “solve” is finding which operations in what order will mechanically evaluate to the desired number. My question was, are THOSE dups; could you answer the question I asked? – Rubio Feb 18 '18 at 15:38
• (More to the point - if water pouring puzzles are sufficiently similar to close as duplicates, why would puzzles that fit the template I described not be? I contend they are, and am curious what the community thinks. Specifically, where there is disagreement, I’m interested to know why.) – Rubio Feb 18 '18 at 15:40
• @Rubio I've edited to expand on my answer to Question 1. Not sure whether or not I'm imagining the tone of crankiness in your comments, but I'm not trying to be argumentative here. This is a useful discussion, and I'm open to being proven wrong. – Rand al'Thor Feb 18 '18 at 15:48
• Not cranky, just pushing a bit for a targeted answer to a targeted question because I agree it’s a useful discussion to have. I don’t want to get lost in the weeds talking about cookie-cutter-as-close-reason, or with answers that try to cover the entire formation-of-numbers territory when that’s not at all what I’m asking about. I gave examples of puzzles that I explicitly said were NOT template questions to show this genre CAN offer questions that admit a Puzzling element. Too many of these don’t, though (many are just arithmetic grinds); if we can decide that a class of them are dups, great! – Rubio Feb 18 '18 at 16:01
• @Rubio I'll admit that I didn't actually follow all of your links to example questions (there were a lot of them!) Reckon it would help if I spent some time doing that? I've tried to be quite general in this answer, because I think there are a lot of general principles to be stated here, but if you think it'd be more useful with examples ... – Rand al'Thor Feb 18 '18 at 16:09