{"status": "success", "data": {"description_md": "There are two distinguishable flagpoles, and there are $19$ flags, of which $10$ are identical blue flags, and $9$ are identical green flags. Let $N$ be the number of distinguishable arrangements using all of the flags in which each flagpole has at least one flag and no two green flags on either pole are adjacent. 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 two distinguishable flagpoles, and there are <span class=\"katex--inline\">19</span> flags, of which <span class=\"katex--inline\">10</span> are identical blue flags, and <span class=\"katex--inline\">9</span> are identical green flags. Let <span class=\"katex--inline\">N</span> be the number of distinguishable arrangements using all of the flags in which each flagpole has at least one flag and no two green flags on either pole are adjacent. Find the remainder when <span class=\"katex--inline\">N</span> is divided by <span class=\"katex--inline\">1000</span>.</p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2008 AIME II Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/08_aime_II_p13", "prev": "/problem/08_aime_II_p11"}}