# Simple Arithmetic Puzzle 6. Or is it?

Here's a sixth one! (with a twist)

\begin{align}16&=\boxed9\times18\\5&=13\times\boxed3\\?&=9\times20\end{align}

Can you find the value of the question mark?

HINT 1:

Z+

• Yay, finally! $(+1)$ :D – Mr Pie Sep 11 '18 at 10:55

$17$

Reasoning

Each equation represents a well know physics formula.

To decipher each one, let $A=1$, $B=2$, $\ldots$. Then, whenever a number is surrounded by a square, interpret that as the variable to be squared.

So, for example, the first equation is $$P = I^2R$$ or Power is current squared times resistance.

The second equation is $$E = mc^2$$ or Energy is mass times the speed of light squared.

The third equation is $$? = It$$ which I've interpreted as current times time which is charge usually represented as $Q$ ($=17$).

• (+1) Yes. Can you read my mind? You seem to be able to answer quite a few of these :) – TheSimpliFire Sep 11 '18 at 17:42

I am completely certain the answer is... drum rolls-

$\frac{143187}{2898}$

Whenever I see such questions, I just do this:

Since we are clearly upgrading mathematics, not following all those "boring" rules. Let's define some things for our superior representation:

$a×b$ in our superior notation will be equivalent of $\frac{a}{\alpha} + b*\beta$ in the lame maths
Since there are only 2 data points, 2 variables are enough for our awesome "knowledge" puzzle. Let's just write the given information in the lame maths:
$16=\frac{9}{\alpha}+18*\beta$
$5=\frac{13}{\alpha}+3*\beta$

As we are the royals who don't dirty their hands with such utter useless things, let's call the neighbor's child who is a failure at everything... He takes a whopping 10 minutes and gives us this:

$\alpha=\frac{69}{14},\space\space \beta=\frac{163}{207}$

Now we just plug these into out search for knowledge to solve this awesome enigmatic-puzzle as follows:

$9×20$ is $9*\frac{69}{14} + 20*\frac{163}{207} = \frac{(9*69*207)+(20*163*14)}{14*207} = \frac{128547+14640}{2898} = \frac{143187}{2898}$

Now, let's take care of the box too, shall we? In the new world, the following rules will be followed for giving boxes to numbers:

We treat whole numbers as a common species, so when there are only whole numbers present, the lowest (class) of them will be given the work to hold the box.
While if there are any lowly fractions, which are clearly worse than whole numbers, then they will have to carry the box for everyone no matter what!

Hence, our question mark gets the box! tada

P.S.: Although yes, the answer is written to show that such type of questions, inherently, are worthless. But this answer is equally valid to any other answer that OP has. This answer follows all the proper logical rules that would be valid in actually solving such question.

• This is cheating... but in a very clever way. $(+1)$ :P – Mr Pie Sep 11 '18 at 10:56
• Nice approach, but (of course you know) this isn't the answer I was expecting. How would you deal with the box around the numbers? :) – TheSimpliFire Sep 11 '18 at 11:09
• ... it does have significant meaning other than inferiority ranking – TheSimpliFire Sep 11 '18 at 11:16
• @TheSimpliFire Well, I wrote the answer in this way because you tagged the question with "mathematics" but in my opinion, this just has some symbols thrown around and is not actually a mathematical question. The person making such questions can think of infinite different rules and come with something that looks exactly like what you asked. So, any answer is equally valid in my opinion. Although I will stick around to see what was the original thinking behind this question and the box! :) – lucifer Sep 11 '18 at 13:11