{"status": "success", "data": {"description_md": "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 $N$?\n\n$\\textbf{(A)}\\ 7\\qquad\\textbf{(B)}\\ 8\\qquad\\textbf{(C)}\\ 9\\qquad\\textbf{(D)}\\ 10\\qquad\\textbf{(E)}\\ 11$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Bernardo and Silvia play the following game. An integer between  <span class=\"katex--inline\">0</span>  and  <span class=\"katex--inline\">999</span>  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  <span class=\"katex--inline\">50</span>  to it and passes the result to Bernardo. The winner is the last person who produces a number less than  <span class=\"katex--inline\">1000</span> . Let  <span class=\"katex--inline\">N</span>  be the smallest initial number that results in a win for Bernardo. What is the sum of the digits of  <span class=\"katex--inline\">N</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 7\\qquad\\textbf{(B)}\\ 8\\qquad\\textbf{(C)}\\ 9\\qquad\\textbf{(D)}\\ 10\\qquad\\textbf{(E)}\\ 11</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2012 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc12B_p15", "prev": "/problem/12_amc12B_p13"}}