The smallest three-digit number $n$ such that if the three digits are $a, b$ and $c,$ then $n=a+b+c+ab+bc+ac+abc$

Evaluate $\frac{n+1}{5}$

Let the sum of the digits of the given product is written as $A 8 B 6 C.$ Find $A+B+C$.

 $\underset{2007 \text{times}}{\underbrace{\left(111111111\dots 111\right)}}\times 2007$

Let the number of distinct integers among the following numbers is $N.$ Find the sum of all digits of $N.$

$\left[\frac{1^2}{2007}\right],\left[\frac{2^2}{2007}\right],\dots ,\left[\frac{{2007}^2}{2007}\right]$, where, $\left[·\right]$ is the greatest integer function.

The square is a multiplicative magic square. That is, the product of the numbers in each row, column, and diagonal is the same. If all the entries are positive integers, what is the sum of the possible values of $g$?