I was wondering about the following question -- what do you think about puzzles of this type (that are looking for an answer which is obtained by what I would describe as 'non-mathematical trickery' [though that's subjective])?

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    $\begingroup$ I'd rather we close questions like those, unless they have something redeeming... $\endgroup$ – J. M. is a poor mathematician Dec 27 '10 at 11:30
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    $\begingroup$ That is not a mathematical puzzle. It is a semantics puzzle: the question hinges on the meaning of the symbol $=$. Obviously if $=$ is taken to have its usual mathematical meaning, the expressions in the title is non-sense. As such it does not belong on this website. $\endgroup$ – Willie Wong Dec 27 '10 at 12:59
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    $\begingroup$ @InterestedQuest: if you harbor doubts about whether the question is appropriate, perhaps you shouldn't have taken the bait and given an answer? Also, for future reference, please include a bit more identifying information about the question in the title of the meta posts. It makes it a bit easier to identify threads. Thanks! $\endgroup$ – Willie Wong Dec 27 '10 at 13:01
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    $\begingroup$ I agree with the closure -- this is not a math question, and therefore is off-topic for the site. Just because it has a consistent mathematical interpretation -- e.g. interpreting $=$ in any ring in which $4 = 0$ -- doesn't make it a math question. In mathematics, equality is a symmetric relation, so asking if $1 =5$, then some other stuff, then what does $5$ equal, doesn't fly as a sincere question. Rather, the OP clearly intended to pose a puzzle, c.f. e.g. the injunction against reading others' answers. This is against the spirit of a Q&A site. $\endgroup$ – Pete L. Clark Dec 27 '10 at 16:42
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    $\begingroup$ Completely agree with Pete. Being open minded involves also rejecting bad content, and not letting every bit of crap through. Besides, OP always has the option of editing the question and flagging the moderator, who can then reopen the question with the same binding vote. $\endgroup$ – Aryabhata Dec 27 '10 at 17:52
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    $\begingroup$ @Willie Wong, I have observed people provide answers to heavily down-voted questions in the past (like the one about kalle-numbers), so I wasn't sure if we shouldn't answer them just because they could be inappropriate. $\endgroup$ – InterestedGuest Dec 27 '10 at 20:11
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    $\begingroup$ To add to InterestedQuest's observation, there is even the (golden) Reversal badge that is awarded for highly upvoted answers to downvoted questions... Elliott got one because of that downvoted question. $\endgroup$ – J. M. is a poor mathematician Dec 27 '10 at 21:50

The question certainly does have a valid mathematical interpretation. Namely, in any ring $1 = 5\ \Rightarrow\ 4 = 0 \ \Rightarrow\ 2 = 10\ \Rightarrow \ 3 = 15\ \Rightarrow\ 4 = 20\:.\ $ So $\rm\ 5 = 1 + 4\ \mathbb Z\ $ is the best one can say generally (note that the ring could possibly have smaller characteristic $2$ or $1$).

I think it was ill-advised for the question to be closed so quickly (in $20$ minutes!) by a binding moderator vote - without any community feedback whatsoever and without giving the OP a chance to clarify the question. It would be better to let the community make these decisions.

This remark is based on general principles - not the specifics of this question. Even if the community later deems the post to be off-topic, the answers and discussion will help readers to realize what the community considers to be on-topic - which helps keep future posts on-topic. But rapidly closing the post prohibits such valuable discourse. While such rapid closure makes sense for spam etc, I think it was a bit extreme here.

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    $\begingroup$ This is not even close to the interpretation intended by the OP; just because the OP uses the equality symbol in a way which can be meaningfully interpreted does not mean that that interpretation was in any way intended by the act of communication. If you believe that this new question is worth posting, you are free to post it yourself; I closed the question because it was clear that the intentions of the OP were not aligned with the point of posting questions on this site. In any case, whatever valuable community feedback can come out of this situation can occur now. It is simply too... $\endgroup$ – Qiaochu Yuan Dec 28 '10 at 11:32
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    $\begingroup$ ...inefficient to let the community make all of these types of decisions. I agree that there are boundary cases, but this is not one of them. I expect questions on this site to be asked in good faith, and this question wasn't (if it was, the meaning of the symbol = would have been explicitly stated). $\endgroup$ – Qiaochu Yuan Dec 28 '10 at 11:34
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    $\begingroup$ @Qiaochu: The decision as to what is or is not valid content for this site should not be made by a single person (and certainly not by rash 20 minute decisions). Please refrain from doing so in the future lest it lead to alienating valued contributors. $\endgroup$ – Bill Dubuque Dec 28 '10 at 17:52

It reminds me of: "one plus one equals window" vs. "one plus one equals two".

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    $\begingroup$ I have no idea what "one plus one equals window" means and I am fighting not to ask, because I am pretty sure I will not be thrilled with the answer. Ah, I think I did it -- please don't tell me! $\endgroup$ – Pete L. Clark Dec 27 '10 at 13:05
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    $\begingroup$ @Pete the 1 s represent the vertical sides, the = represent the horizontal sides, and the + represents the middle of the window. Next time, don't tell me not to tell you. :) $\endgroup$ – Mateen Ulhaq Jan 15 '11 at 6:36

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