{"status": "success", "data": {"description_md": "Let $f(x) = 10^{10x}, g(x) = \\log_{10}\\left(\\frac{x}{10}\\right), h_1(x) = g(f(x))$, and $h_n(x) = h_1(h_{n-1}(x))$ for integers $n \\geq 2$. What is the sum of the digits of $h_{2011}(1)$?\n\n$\\textbf{(A)}\\ 16081 \\qquad \\textbf{(B)}\\ 16089 \\qquad \\textbf{(C)}\\ 18089 \\qquad \\textbf{(D)}\\ 18098 \\qquad \\textbf{(E)}\\ 18099$\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>Let  <span class=\"katex--inline\">f(x) = 10^{10x}, g(x) = \\log_{10}\\left(\\frac{x}{10}\\right), h_1(x) = g(f(x))</span> , and  <span class=\"katex--inline\">h_n(x) = h_1(h_{n-1}(x))</span>  for integers  <span class=\"katex--inline\">n \\geq 2</span> . What is the sum of the digits of  <span class=\"katex--inline\">h_{2011}(1)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 16081 \\qquad \\textbf{(B)}\\ 16089 \\qquad \\textbf{(C)}\\ 18089 \\qquad \\textbf{(D)}\\ 18098 \\qquad \\textbf{(E)}\\ 18099</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": "2011 AMC 12B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc12B_p18", "prev": "/problem/11_amc12B_p16"}}