Magic 7

Answer: 8


7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 = 99 = sum of all 3 rows
$\therefore$ sum of each row is 33


Writing the numbers in terms of $n$
               
    
   $\begin{align}26-2n\ \ +\ \ 19-n\ \ +\ \ 12\ \ &=33\\ 
26+19 + 12-33&=3n\\
24&=3n\\
8&=n\end{align}$




Writing the numbers in terms of $x$
 7 + 14 = 21, 12 is missing to make 33


Say $n$ + 12 + $x$ + 12 = 33,

then $n$ + 14 + ($x-$2) = 33




Same idea gives $x-$4 at the bottom

$\therefore$ 3$x$-6=33, so $x$ = 13



And $n$ + $x$ + 12 = 33 $\Rightarrow n$ + 13 + 12 = 33 $\Rightarrow n$ = 8


Using reasoning and not algebra
 7 + 14 = 21, 12 is missing to make 33

33 $-$ 14 = 19
19 = 7 + 12
19 = 8 + 11
19 = 9 + 10
no more options so these 4 numbers are 8, 9, 10, 11 


$n$ + middle + 14 = bottom + middle + 12

difference between $n$ and bottom = difference between 12 and 14



This gives 2 options: