# Simple Arithmetic Puzzle 2. Or is it?

A second maths puzzle!

\begin{align}0+0&=0\\1+1&=1\\2+2&=2\\12.2+6&=20\\12.3+6&=21\\9+(-3.2)&=-10\\7+(-1.1)&=-3\\0.95+(-0.95)&=-1\\e^\pi+(-\pi)&=\quad?\end{align}

Can you find the value of the question mark?

HINT 1:

GIF

HINT 2:

SQRT

HINT 3:

X

HINT 4:

ANS = ☐

Not very simple this time I suppose :)

• You could still title it "e to the pi minus pi" and submit it to the FTC (albeit late) :P xkcd.com/217 Jun 13, 2018 at 19:42
• e^π+(−π) = 19.9990999792 Jun 22, 2018 at 4:26

The rule is

$a$ + $b := \lfloor \sqrt{a} * b \rfloor$

And so the answer is

$e^\pi$ + $(-\pi) := \lfloor \sqrt{e^\pi} * (-\pi) \rfloor = \lfloor -15.11256\ldots \rfloor = -16$

Examples

$12.2 + 6$

$\lfloor \sqrt{12.2} * 6 \rfloor = \lfloor 3.4928\ldots * 6 \rfloor = \lfloor 20.957\ldots \rfloor = 20$

$12.3 + 6$

$\lfloor \sqrt{12.3} * 6 \rfloor = \lfloor 3.5071\ldots * 6 \rfloor = \lfloor 21.042\ldots \rfloor = 21$

$7 + (-1.1)$

$\lfloor \sqrt{7} * (-1.1) \rfloor = \lfloor 2.6457\ldots * (-1.1) \rfloor = \lfloor -2.9103\ldots \rfloor = -3$

Hints

Hints 2,3 and 4 pretty much spell out the procedure. Hint 1 is the acronym GIF which, in this particular case, stands for Greatest Integer Function. I have used the floor function notation which is equivalent.