{"status": "success", "data": {"description_md": "Let $(a_1,a_2,a_3,...,a_{12})$ be a permutation of $(1,2,3,...,12)$ for which $$ a_1>a_2>a_3>a_4>a_5>a_6 \\text{ and } a_6<a_7<a_8<a_9<a_{10}<a_{11}<a_{12}. $$ An example of such a permutation is $(6,5,4,3,2,1,7,8,9,10,11,12)$. Find the number of such permutations.\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>Let <span class=\"katex--inline\">(a_1,a_2,a_3,...,a_{12})</span> be a permutation of <span class=\"katex--inline\">(1,2,3,...,12)</span> for which <span class=\"katex--display\"> a_1&gt;a_2&gt;a_3&gt;a_4&gt;a_5&gt;a_6 \\text{ and } a_6&lt;a_7&lt;a_8&lt;a_9&lt;a_{10}&lt;a_{11}&lt;a_{12}. </span><br/>An example of such a permutation is <span class=\"katex--inline\">(6,5,4,3,2,1,7,8,9,10,11,12)</span>. Find the number of such permutations.</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": 3, "problem_name": "2006 AIME II Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/06_aime_II_p05", "prev": "/problem/06_aime_II_p03"}}