2012 AMC 10B Problems/Problem 20
20. Bernardo and Silvia play the following game. An integer between and , 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 to it and passes the result to Bernardo. The winner is the last person who produces a number less than . Let be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of ?