Why is this question considered a math problem? [duplicate]

Question

I have asked this question recently. It's more likely a puzzle; because I have seen it in a puzzle quiz. Also, a math problem isn't asked in this way! It's a puzzle that challenges the IQ.

Compare it to this one. This is really like a problem. it is dealing with technical mathematical stuff like triangle's incircle.

But since the asker has stated:

Here's a small mathematical puzzle I came up with recently

the other users were convinced it is a puzzle and up-voted it; while it could and was better to be asked in math.stackexchange.com; while mine doesn't fit the math site.

So if I had stated this was in a puzzle quiz, it wouldn't be closed; right?

Answer 1

Our site policy

You can find our site policy on maths problems vs maths puzzles at Are math-textbook-style problems on topic?

So, what makes something a math puzzle rather than math problem? I think there's a few features.

• Clever or elegant solution, often an "aha" moment
• Unexpected problem statement.
• Unexpected or counterintuitive result.

^ that is a TL;DR of what distinguishes a maths puzzle (on-topic) from a maths problem (off-topic). All of the potential criteria you've mentioned for on- or off- topicness are irrelevant. None of the following (quoted from your meta question) are used in deciding our site scope:

• It's a puzzle that challenges the IQ.

  Well, IQ is a scoring system supposedly measuring intelligence, so I'm not sure what it means to challenge that. Assuming you mean something like "challenges the brain" or "requires high IQ" ... that's very subjective and hard to measure, so it wouldn't make a good scope determiner. Difficulty of puzzles, in general, is very hard to define.

• it is dealing with technical mathematical staff like triangle's incircle.

  Our scope also isn't defined by how mathematically advanced the involved concepts are. It's possible to write a completely rote problem using such concepts, or a challenging puzzle using nothing more than the natural numbers. If someone asked "what's the incircle radius of an equilateral triangle of side-length 1", that'd probably be closed.

• since the asker has stated "Here's a small mathematical puzzle I came up with recently" the other users were convinced it is a puzzle

  I don't think our users are that stupid, to believe something is a puzzle just because someone says it is. Our policy isn't based on knowing the right keywords to use in a post, either. Anyone can call something a puzzle, but that doesn't mean it is.

• if I had stated this was in a puzzle quiz, it wouldn't be closed; right?

  No, we don't care too much about the source of puzzles (at least not for the maths problem vs maths puzzle policy; maybe for others like the plagiarism policy). Someone could write a puzzle book or quiz containing questions that we wouldn't consider puzzles, or indeed a maths textbook containing things that we would consider puzzles.

Focus on what something is, not what it's called.

Look past whether the OP says something is a puzzle or not, and whether it was found in a collection of puzzles or not, and instead look at the essence of the question itself, to see whether or not it should count as a puzzle by our site's standards.

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So what about these two specific questions?

I voted to close your question (sorry! nothing personal) because it seems like a basic arithmetic problem. "If a slow clock loses 6 minutes per hour, how many ticks does it make in 6 minutes?" Looking at the accepted answer, it is indeed a basic arithmetic problem, easily answered.

I didn't vote to close the incircle question because there seems to be a "Clever or elegant solution": the problem is much easier to solve than it looks. There is a neat trick in the accepted answer which allows it to be solved without any complicated calculation.

By the way, I didn't vote on either of these questions. The incircle one isn't quite interesting enough for me to upvote, and yours isn't trivial enough for me to downvote. I don't have very strong opinions on either question, just applying the site policy to say one of them is off-topic and the other one on-topic.

Answer 2

You're really asking two questions: why was your question closed as problem-not-puzzle, and why was the other question not closed? These are largely independent questions, and in general I would recommend that if one of your questions is closed you should focus on that rather than looking for other questions that should have been closed if yours was. Sometimes questions don't get closed that should be, so the fact that some other question survived isn't evidence that yours should have.

Your clock question

I think this question would have been closed even if you'd said it was from a puzzle quiz. It doesn't matter where it's from[1], it matters what sort of question it is.

The main criterion we use is: does solving this require some sort of insight or clever idea, rather than just following a standard procedure? Your puzzle about the clock is basically a matter of arithmetic.

See e.g. Proposed policy on mathematical questions, which is the nearest thing we have to an official policy; and Are math-textbook-style problems on topic? and its top-voted answer, which offers a bit more explanation of the puzzle/problem distinction.

[1] Well, sometimes it does, because e.g. we don't accept questions that come from currently-active competitions. But that doesn't change whether something's viewed as a puzzle.

The hexagon question

It's a question that's easy to pose and not so easy to answer. There's at least one solution that involves a clever idea (using the relationship between area, perimeter and inradius).

The fact that it involves some mathematical technicalities isn't an objection to it. See e.g. the second Meta question linked above, or What tricky mathematical questions are on topic here? which specifically addresses the question of whether involving mathematical technicalities is a problem. (The votes on the various answers indicate that the community doesn't think it is.)

Having said all that, this question can also be solved pretty routinely if one is so minded (e.g., one can write down the coordinates of all the vertices of a hexagon, and then there's an ugly formula for the inradius of a triangle given the coordinates of its vertices, and then simplifying the resulting ratio surely can't be that painful; this isn't how I'd approach the question if I needed the answer but it is almost completely routine). In fact I think there exists a rather general computational procedure for solving questions in Euclidean geometry which in principle renders all questions like this one routine.

But these "routine" solutions are long and tedious and boring, and no one (no one here, at least) actually solves these questions that way. So, in practice, solving them requires some cleverness, which makes them "puzzle" rather than mere "problem" according to the standards we have here.

I think there are fairly routine solutions to the hexagon question that aren't much more painful than the clever one currently posted there. So it's a bit of a borderline case.