{"status": "success", "data": {"description_md": "For each positive integer $n$, let $S(n)$ be the number of sequences of length $n$ consisting solely of the letters $A$ and $B$, with no more than three $A$s in a row and no more than three $B$s in a row. What is the remainder when $S(2015)$ is divided by 12?\n\n$\\textbf{(A)}\\ 0 \\qquad\\textbf{(B)}\\ 4 \\qquad\\textbf{(C)}\\ 6 \\qquad\\textbf{(D)}\\ 8 \\qquad\\textbf{(E)}\\ 10$\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>For each positive integer  <span class=\"katex--inline\">n</span> , let  <span class=\"katex--inline\">S(n)</span>  be the number of sequences of length  <span class=\"katex--inline\">n</span>  consisting solely of the letters  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span> , with no more than three  <span class=\"katex--inline\">A</span> s in a row and no more than three  <span class=\"katex--inline\">B</span> s in a row. What is the remainder when  <span class=\"katex--inline\">S(2015)</span>  is divided by 12?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 0 \\qquad\\textbf{(B)}\\ 4 \\qquad\\textbf{(C)}\\ 6 \\qquad\\textbf{(D)}\\ 8 \\qquad\\textbf{(E)}\\ 10</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": 5, "problem_name": "2015 AMC 12A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc12A_p23", "prev": "/problem/15_amc12A_p21"}}