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Inspired by five other puzzles, how could it be possible that in base $\pi$ adding 22 to 4 gives 26? What is the correct way to do it?

Unlike all of the other puzzles, consider these numbers in base $\pi$.

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  • $\begingroup$ Could you define base $\pi$? Or is this supposed to be a lateral thinking puzzle? $\endgroup$ – KoA May 28 '16 at 14:39
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    $\begingroup$ How would you represent $\pi$ in base 10? In a conventional sense, one can't, since $\pi$ is irrational. Same answer for your question. $\endgroup$ – Jeremy Argent May 28 '16 at 15:22
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    $\begingroup$ Um, $4$ and $26$ are not valid base $\pi$ numbers as they contain "pigits"(?) greater than $3$ $\endgroup$ – Jonathan Allan May 29 '16 at 1:47
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    $\begingroup$ You're mistaken. They're valid. They're just not in "standard form". $\endgroup$ – Jeremy Argent May 31 '16 at 14:06
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    $\begingroup$ So A is a valid base ten number and 2 is a valid binary number? How so? FYI you should have addressed your comment to me using @JonathanAllan so I would have received a notification. $\endgroup$ – Jonathan Allan Jun 2 '16 at 12:50
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Adding $2x + 2$ to $4$ gets us $2x + 6$, regardless of which base (value of $x$) we're otherwise working in. And because $\pi$ is an irrational number, this form is the simplest form you're going to get.

So straight addition definitely works.

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Perhaps:

$22_\pi + 4_\pi = 2\pi_{10} + 2_{10} + 4_{10} = 2\pi_{10} + 6_{10} = 26_{\pi} $

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  • $\begingroup$ this is the same answer that joe Z gave $\endgroup$ – Jasen May 29 '16 at 9:12
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    $\begingroup$ I posted mine before his, but his was accepted. @Jasen $\endgroup$ – KoA May 29 '16 at 9:12
  • $\begingroup$ the timing is not clear on the web site, I am not accusing you of copying. $\endgroup$ – Jasen May 29 '16 at 9:16
  • $\begingroup$ @Jasen Don't worry about it :p $\endgroup$ – KoA May 29 '16 at 9:18

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