{"status": "success", "data": {"description_md": "There are $N$ permutations $(a_1,a_2,\\ldots,a_{30})$ of $1,2,\\ldots,30$ such that for $m\\in\\{2,3,5\\}$, $m$ divides $a_{n+m}-a_n$ for all integers $n$ with $1\\leq n <n+m\\leq 30$. Find the remainder when $N$ is divided by 1000.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>There are <span class=\"katex--inline\">N</span> permutations <span class=\"katex--inline\">(a_1,a_2,\\ldots,a_{30})</span> of <span class=\"katex--inline\">1,2,\\ldots,30</span> such that for <span class=\"katex--inline\">m\\in\\{2,3,5\\}</span>, <span class=\"katex--inline\">m</span> divides <span class=\"katex--inline\">a_{n+m}-a_n</span> for all integers <span class=\"katex--inline\">n</span> with <span class=\"katex--inline\">1\\leq n &lt;n+m\\leq 30</span>. Find the remainder when <span class=\"katex--inline\">N</span> is divided by 1000.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 6, "problem_name": "2011 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/11_aime_II_p15", "prev": "/problem/11_aime_II_p13"}}