Sangar Number

Here, I just want to give some clues (not the complete solution) so you can still get the enjoyment of problem solving if you haven't got the answer yet : $\boxed{630}$ :)

• Let $D(x)$ be the function returning the number of digits of integer $x$ .
• The first step is to find all possible values of $C$ . There are $17$ possible values of $C$ which can be achieved with bruteforce with the help of function $D(x)$ and modulo.
• Because there only $17$ possible values of $C$ , we can brute them all.
• Next, how about $A$ and $B$ ? We can brute only one of them! Let's say we brute the value of $A$ . Because we have known $N, A, C$ , we can find the value of $B$ (of course you have to check whether $B$ is an integer or not).
• The value of $A$ can be up to $10^9$ (which is still too slow if we bruteforce until this number). Luckily, there is a smaller upperbound to brute the value of $A$ . Hint : Let $A \leq B$ .
• Again, the function $D(x)$ plays a role to check if $N$ is a Sangar Number or not.

With these algorithm, I can get the answer in ~ $20$ seconds.

Alright then, happy solving guys! :D