{"status": "success", "data": {"description_md": "Let $(a_1,a_2, \\ldots ,a_{10})$ be a list of the first $10$ positive integers such that for each $2 \\le i \\le 10$ either $a_i+1$ or $a_i-1$ or both appear somewhere before $a_i$ in the list. How many such lists are there?\n\n$\\textbf{(A)}\\ 120\\qquad\\textbf{(B)}\\ 512\\qquad\\textbf{(C)}\\ 1024\\qquad\\textbf{(D)}\\ 181,440\\qquad\\textbf{(E)}\\ 362,880$\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\">(a_1,a_2, \\ldots ,a_{10})</span>  be a list of the first  <span class=\"katex--inline\">10</span>  positive integers such that for each  <span class=\"katex--inline\">2 \\le i \\le 10</span>  either  <span class=\"katex--inline\">a_i+1</span>  or  <span class=\"katex--inline\">a_i-1</span>  or both appear somewhere before  <span class=\"katex--inline\">a_i</span>  in the list. How many such lists are there?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 120\\qquad\\textbf{(B)}\\ 512\\qquad\\textbf{(C)}\\ 1024\\qquad\\textbf{(D)}\\ 181,440\\qquad\\textbf{(E)}\\ 362,880</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": "2012 AMC 12B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc12B_p19", "prev": "/problem/12_amc12B_p17"}}