Difference between revisions of "2012 AMC 10B Problems/Problem 20"
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Bernardo and Silvia play the following game. An integer between <math>0</math> and <math>999</math>, 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 <math>50</math> to it and passes the result to Bernardo. The winner is the last person who produces a number less than <math>1000</math>. Let <math>N</math> be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of <math>N</math>? | Bernardo and Silvia play the following game. An integer between <math>0</math> and <math>999</math>, 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 <math>50</math> to it and passes the result to Bernardo. The winner is the last person who produces a number less than <math>1000</math>. Let <math>N</math> be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of <math>N</math>? | ||
| − | <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> |
Revision as of 21:02, 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 ?
