Question

Determine all three digit numbers $N$, such that $N$ is divisible by $11$ and $\frac{N}{11}$ is equal to the sum of the squares of the digits of $N$.

Answer 1

Given that $n$ is a three digit number divisible by $11$

and $\frac{N}{11}$ = sum of squares of digits

Therefore, only two such numbers are possible which are $550$ and $803$.