{"status": "success", "data": {"description_md": "Given that $O$ is a regular octahedron, that $C$ is the cube whose vertices are the centers of the faces of $O$, and that the ratio of the volume of $O$ to that of $C$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers, find $m+n$.\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>Given that <span class=\"katex--inline\">O</span> is a regular octahedron, that <span class=\"katex--inline\">C</span> is the cube whose vertices are the centers of the faces of <span class=\"katex--inline\">O</span>, and that the ratio of the volume of <span class=\"katex--inline\">O</span> to that of <span class=\"katex--inline\">C</span> is <span class=\"katex--inline\">\\frac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime integers, find <span class=\"katex--inline\">m+n</span>.</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": 5, "problem_name": "2005 AIME II Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/05_aime_II_p11", "prev": "/problem/05_aime_II_p09"}}