# Why are numerical puzzles disliked?

I posted a puzzle about getting numbers from 0 to 9 with the digits of 2022 and it got downvoted. Fine. But then I noticed that another similar puzzle was downvoted even more, so it seems there is some generic issue about them.

I remember that at the beginning of puzzling.SE such puzzles were welcomed, and besides I do not think that they are in scope for mathematics.SE (they are far too easy). What changed?

• That other one was downvoted partially because it wasn't defined well - if the "shortest" answer wins, what does that mean? Nov 1 '21 at 17:40
• @bobble: so a reason could be that there isn't a single answer to the puzzle?
– mau
Nov 1 '21 at 17:53
• Well, for these questions it's always important to be very specific about the rules to prevent disagreements, so if the rules aren't clear it's not a good puzzle Nov 1 '21 at 17:53
• There's several meta posts from people who dislike these types of puzzles, sometimes even calling for them to be declared off-topic: 2017, Jan 2018, Feb 2018. Reading those older metas might give you an idea of why people dislike them, although we never had enough such people to make a policy banning them outright. Nov 3 '21 at 5:45
• These questions aren't in scope for mathematics.SE for similar reasons : they are (often, not in your case) poorly phrased, they can have multiple answers which means that one is never in a position to choose the "best" answer at any time, and (this is applies in your case) they can be too broad, asking for solutions to multiple questions , however linked they are. What changed on MSE? The enforcement of the guidelines, if anything. They are not good questions in general, that's the problem. You can probably use a chatroom to refine them, if there is any consolation. Nov 5 '21 at 7:33

I can't speak for others, but here are the reasons I strongly dislike them:

They're low-effort. You can ask the same question for any numbers, any sources, and any set of allowed operators. What makes any individual puzzle of this type special?

They're often ill-defined. Many of these questions allow "any standard operator" without specifying what exactly counts -- there are a whole lot of possible operators. Are trig functions allowed? What about hyperbolic trig functions? Double factorial? Is the "$$F_\bullet$$" function, giving the Fibonacci sequence (e.g. $$F_7 = 13$$), allowed?

One frequent ambiguity is in concatenation - are you allowed to concatenate the starting digits, or any results along the way? Another is if the puzzle is defined in terms of characters - many forms of mathematical notation reuse the same symbols for different meanings. If you allow parentheses and fractions, is the Legendre symbol allowed? Without any explicit rules, there's no way to tell for certain what an expression means. Mathematical writing, like all writing, is context-dependent.

They're not single puzzles. A single one of these would be answered in minutes, so questions often instead ask for you to create a whole range of numbers. This doesn't make the puzzle any more interesting, it just makes it take longer to answer -- and it often means that the end result will be split among multiple people.

Puzzles should have a definitive solution that "puts the puzzle to rest" - both in general, and specifically because of this site's format.

They aren't "narrow" enough to be good puzzles. The best puzzles are ones where there is a particular clever solution that the setter has in mind, and the puzzle will require you to find that one to solve it. In questions, the OP often doesn't really have any particular solution in mind (or even know if it's solvable!).

And all of these problems are only compounded when the question is posed as an optimization problem. If you say "find the solution with the least number of operators", or something to that effect, then...

• any ambiguities in the problem statement are extremely harmful, because it's impossible to tell whether a solution is the best answer or invalid.
• you'll get a bunch of different answerers not only filling in the gaps, but also incrementally improving on other answers.
• it's more likely that you don't actually have a clever solution in mind, and so the solution won't be interesting.
• well, I can say something just for my own puzzle. I specified the operators which could be used; I know it was low-effort, but it was meant to be used on a specific date (new year's eve).
– mau
Nov 2 '21 at 9:20