Difference between revisions of "2012 AMC 10B Problems/Problem 20"
| Line 4: | Line 4: | ||
<math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 11 </math> | <math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 11 </math> | ||
| + | |||
| + | ==Solution== | ||
| + | |||
| + | Let's test each solution, for our first case <math>7</math>, we start out with <math>7</math> and the number is then given to Bernardo. He will double the given number so in this case <math>7\times 2\equals 14</math> | ||
Revision as of 21:07, 28 February 2012
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 $7\times 2\equals 14$ (Error compiling LaTeX. Unknown error_msg)
