AMC 10B 2012 Problem 20

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 ?

Answer Choices
A. 7
B. 8
C. 9
D. 10
E. 11