{"status": "success", "data": {"description_md": "Ed has five identical green marbles and a large supply of identical red marbles. He arranges the green marbles and some of the red marbles in a row and finds that the number of marbles whose right hand neighbor is the same color as themselves equals the number of marbles whose right hand neighbor is the other color. An example of such an arrangement is GGRRRGGRG. Let $m$ be the maximum number of red marbles for which Ed can make such an arrangement, and let $N$ be the number of ways in which Ed can arrange the $m+5$ marbles to satisfy the requirement. 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>Ed has five identical green marbles and a large supply of identical red marbles. He arranges the green marbles and some of the red marbles in a row and finds that the number of marbles whose right hand neighbor is the same color as themselves equals the number of marbles whose right hand neighbor is the other color. An example of such an arrangement is GGRRRGGRG. Let <span class=\"katex--inline\">m</span> be the maximum number of red marbles for which Ed can make such an arrangement, and let <span class=\"katex--inline\">N</span> be the number of ways in which Ed can arrange the <span class=\"katex--inline\">m+5</span> marbles to satisfy the requirement. 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": 4, "problem_name": "2011 AIME II Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/11_aime_II_p08", "prev": "/problem/11_aime_II_p06"}}