Question 19
Let $N$ be the positive integer $7777\ldots777,$ a $313$-digit number where each digit is a $7.$ Let $f(r)$ be the leading digit of the $r$th root of $N.$ What is $$
\begin{aligned} &f(2)+f(3)+f(4)\\ &\quad{}+f(5)+f(6)? \end{aligned}
$$
\begin{aligned} &f(2)+f(3)+f(4)\\ &\quad{}+f(5)+f(6)? \end{aligned}
$$