2012 AMC 10B Problems/Problem 20
Problem
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
?
Solution
Let's test each solution, for our first case , we start out with
and the number is then given to Bernardo. He will double the given number so in this case $7\times 2\equal 14$ (Error compiling LaTeX. Unknown error_msg)