AMC 12 2012b Problem 14

Bernardo and Silvia play the following game. An integer between $0$ and $999$ inclusive is selected and given to Bernardo. Whenever Bernardo receives a number, he doubles it and passes the result to Silvia. Whenever Silvia receives a number, she adds $50$ to it and passes the result to Bernardo. The winner is the last person who produces a number less than $1000$. Let $N$ be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of $N$?

\textbf{(A)}\ 7 \textbf{(B)}\ 8 \textbf{(C)}\ 9 \textbf{(D)}\ 10 \textbf{(E)}\ 11