The mother problem:
Find the sum of all $3$ digit numbers which are equal to $25$ times the sum of their digits.
So we can write: $\begin{align} 100x+10y+z &= 25 \times (x+y+z) \\ &= 25x + 25y+25z \end{align}$
$\Rightarrow 25x= 5y+8z \quad ---(1)$
Thus the question reduces to finding all possible solution of $(1)$ with the constraints of $x,y,z \in [0,9]$,now it may not be too hard using a brute force aproach (but however tedious) to find that only $3$ pairs of $(x,y,z)$ will be the required solution but I am looking for a smarter approach for this computation,any ideas?
Also if somebody knows any alternative but efficient solution for the actual problem, I will appreciate it as an answer.