Question 25
For a positive integer $n$, let $P(n)$ be the product of its digits and $S(n)$ their sum. For example, $P(29)=2\cdot9=18$ and $S(29)=2+9=11$.
$N$ is a three-digit integer with $S(N)=14$ and $S(N+1)=6$. Find the sum of all possible values of $N$.
$N$ is a three-digit integer with $S(N)=14$ and $S(N+1)=6$. Find the sum of all possible values of $N$.