# Correct way to add 22 to 4 to get 26

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 $\pi$.

• Could you define base $\pi$? Or is this supposed to be a lateral thinking puzzle? – KoA May 28 '16 at 14:39
• How would you represent $\pi$ in base 10? In a conventional sense, one can't, since $\pi$ is irrational. Same answer for your question. – Jeremy Argent May 28 '16 at 15:22
• Um, $4$ and $26$ are not valid base $\pi$ numbers as they contain "pigits"(?) greater than $3$ – Jonathan Allan May 29 '16 at 1:47
• You're mistaken. They're valid. They're just not in "standard form". – Jeremy Argent May 31 '16 at 14:06
• 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. – Jonathan Allan Jun 2 '16 at 12:50

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