There has been a recent spate of related "22+4" questions that can all be answered by using different cyclic numbering systems. The OP's always say "use base 10," perhaps not realizing that that requirement doesn't make the answer much more difficult. If I say, "add 22 and 4 to give $x$," then $x$ can always be acquired by using a rule that the numbers you are using have a maximum, after which further additions take the numbers back to $0$, and then start counting up again. The maximum number is $x-27$, which then sends $x-26$ to equal $0$, $x-25=1, \dots, x=26$. This numbering system is called the integers modulo $n$, where $n$ is $1$ plus that maximum number.

As you can see from my answers to all these questions, here, here, here and here, I have simply changed the numbers I have used to answer these questions.

The purpose of this meta post is to a) educate users about the integers modulo $n$, as a distinct concept from "base something", and b) to raise the point that the repeated use of this question is unoriginal (and the questions should perhaps be marked as duplicates).

I'm aware that some people spend their time finding creative answers to these questions, but aren't there better ways to spend one's time? I apologise if you enjoy answering questions on this site for the sake of it.

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    $\begingroup$ The questions should be down voted, not held as off topic or closed. Lost creativity and or originality are grounds for down voting, not closing. As long as the puzzles have a degree of variance then they should remain on topic. I'm responding explicitly to your point of should they be closed as duplicates. $\endgroup$
    – Insane
    May 29, 2016 at 7:23
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    $\begingroup$ It's just a mini version of the "copy-cat wave" I describe in this answer. Downvote, wait it out and it'll be gone soon. $\endgroup$
    – Alconja
    May 29, 2016 at 22:29
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    $\begingroup$ @Alconja So should this meta question be marked as duplicate? THE IRONY. $\endgroup$
    – paste
    Jun 6, 2016 at 14:03
  • $\begingroup$ I don't think that the answers which you linked to really correctly answered the questions. I mean, its easy to say that your using modulo 44 so therefore 22+4 = 26 = 44+26 = 70 (and just change the 44), whereas I feel like each of these questions has a different, more challenging answer, such as 4 feet + 22 yards = 70 feet. (The question I'm quoting from is your first "here" link). Personally, I think that its quite cool that all of these different numbers can be made from 22 + 4 WITHOUT using modulo, and have been rather enjoying the puzzles. $\endgroup$ Jun 9, 2016 at 19:10
  • $\begingroup$ @Toastrackenigma I agree that most of the questions linked have interesting intended answers; that is why I only down voted the =9999 one because that one didn't seem to have an intended answer. However, it is important for the OP to tell us not to use modular arithmetic - otherwise the question can too easily be answered through a reworking of the numbers in one of my answers. All the questions stressed beautifully that base 10 must be used, but that is of hardly any consequence in relation to the use of modular arithmetic. $\endgroup$
    – ahorn
    Jun 9, 2016 at 20:16


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