{"status": "success", "data": {"description_md": "A cube with side length 10 is suspended above a plane. The vertex closest to the plane is labelled $A$. The three vertices adjacent to vertex $A$ are at heights 10, 11, and 12 above the plane. The distance from vertex $A$ to the plane can be expressed as $\\tfrac{r-\\sqrt{s}}{t}$, where $r$, $s$, and $t$ are positive integers, and $r+s+t<1000$. Find $r+s+t$.\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>A cube with side length 10 is suspended above a plane. The vertex closest to the plane is labelled <span class=\"katex--inline\">A</span>. The three vertices adjacent to vertex <span class=\"katex--inline\">A</span> are at heights 10, 11, and 12 above the plane. The distance from vertex <span class=\"katex--inline\">A</span> to the plane can be expressed as <span class=\"katex--inline\">\\tfrac{r-\\sqrt{s}}{t}</span>, where <span class=\"katex--inline\">r</span>, <span class=\"katex--inline\">s</span>, and <span class=\"katex--inline\">t</span> are positive integers, and <span class=\"katex--inline\">r+s+t&lt;1000</span>. Find <span class=\"katex--inline\">r+s+t</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": 6, "problem_name": "2011 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/11_aime_I_p14", "prev": "/problem/11_aime_I_p12"}}