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:
Yet another 2018 puzzle
Can we just solve all "make this number out of 2,0,1 and 8" once and for all?
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!
