{"status": "success", "data": {"description_md": "There is a unique positive integer $n$ such that$$\\log_2{(\\log_{16}{n})} = \\log_4{(\\log_4{n})}.$$What is the sum of the digits of $n?$\n\n$\\textbf{(A) } 4 \\qquad \\textbf{(B) } 7 \\qquad \\textbf{(C) } 8 \\qquad \\textbf{(D) } 11 \\qquad \\textbf{(E) } 13$\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>There is a unique positive integer  <span class=\"katex--inline\">n</span>  such that <span class=\"katex--display\">\\log_2{(\\log_{16}{n})} = \\log_4{(\\log_4{n})}.</span> What is the sum of the digits of  <span class=\"katex--inline\">n?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 4 \\qquad \\textbf{(B) } 7 \\qquad \\textbf{(C) } 8 \\qquad \\textbf{(D) } 11 \\qquad \\textbf{(E) } 13</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": 2, "problem_name": "2020 AMC 12A Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12A_p11", "prev": "/problem/20_amc12A_p09"}}