{"status": "success", "data": {"description_md": "Let $\\clubsuit(x)$ denote the sum of the digits of the positive integer $x$. For example, $\\clubsuit(8)=8$ and $\\clubsuit(123)=1+2+3=6$. For how many two-digit values of $x$ is $\\clubsuit(\\clubsuit(x))=3$?\n\n$\\textbf{(A) } 3 \\qquad\\textbf{(B) } 4 \\qquad\\textbf{(C) } 6 \\qquad\\textbf{(D) } 9 \\qquad\\textbf{(E) } 10$", "description_html": "<p>Let  <span class=\"katex--inline\">\\clubsuit(x)</span>  denote the sum of the digits of the positive integer  <span class=\"katex--inline\">x</span> . For example,  <span class=\"katex--inline\">\\clubsuit(8)=8</span>  and  <span class=\"katex--inline\">\\clubsuit(123)=1+2+3=6</span> . For how many two-digit values of  <span class=\"katex--inline\">x</span>  is  <span class=\"katex--inline\">\\clubsuit(\\clubsuit(x))=3</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 3 \\qquad\\textbf{(B) } 4 \\qquad\\textbf{(C) } 6 \\qquad\\textbf{(D) } 9 \\qquad\\textbf{(E) } 10</span> </p>\n<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": "2003 AMC 10B Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc10B_p14", "prev": "/problem/03_amc10B_p12"}}