Question 21
Shawn starts with a positive integer $n$. Each next number is obtained by subtracting the largest square not exceeding the current number, until 0 is reached. For example, $60-7^2=11$, $11-3^2=2$, $2-1^2=1$, $1-1^2=0$, giving the sequence $60,11,2,1,0$. Let $N$ be the smallest starting number whose sequence contains 8 numbers, including the starting number and 0. What is the sum of the digits of $N$?
Enter the number only (an exact fraction is allowed).
Enter the number only (an exact fraction is allowed).