{"status": "success", "data": {"description_md": "How many sequences of $0$s and $1$s of length $19$ are there that begin with a $0$, end with a $0$, contain no two consecutive $0$s, and contain no three consecutive $1$s?\n\n$\\textbf{(A) }55\\qquad\\textbf{(B) }60\\qquad\\textbf{(C) }65\\qquad\\textbf{(D) }70\\qquad\\textbf{(E) }75$", "description_html": "<p>How many sequences of  <span class=\"katex--inline\">0</span> s and  <span class=\"katex--inline\">1</span> s of length  <span class=\"katex--inline\">19</span>  are there that begin with a  <span class=\"katex--inline\">0</span> , end with a  <span class=\"katex--inline\">0</span> , contain no two consecutive  <span class=\"katex--inline\">0</span> s, and contain no three consecutive  <span class=\"katex--inline\">1</span> s?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }55\\qquad\\textbf{(B) }60\\qquad\\textbf{(C) }65\\qquad\\textbf{(D) }70\\qquad\\textbf{(E) }75</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": 4, "problem_name": "2019 AMC 10B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/19_amc10B_p24"}}