{"status": "success", "data": {"description_md": "Tetrahedron $ABCD$ has $AD=BC=28$, $AC=BD=44$, and $AB=CD=52$. For any point $X$ in space, define $f(X)=AX+BX+CX+DX$. The least possible value of $f(X)$ can be expressed as $m\\sqrt{n}$, where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. 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>Tetrahedron <span class=\"katex--inline\">ABCD</span> has <span class=\"katex--inline\">AD=BC=28</span>, <span class=\"katex--inline\">AC=BD=44</span>, and <span class=\"katex--inline\">AB=CD=52</span>. For any point <span class=\"katex--inline\">X</span> in space, define <span class=\"katex--inline\">f(X)=AX+BX+CX+DX</span>. The least possible value of <span class=\"katex--inline\">f(X)</span> can be expressed as <span class=\"katex--inline\">m\\sqrt{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are positive integers, and <span class=\"katex--inline\">n</span> is not divisible by the square of any prime. 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": 6, "problem_name": "2017 AIME II Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/17_aime_II_p14"}}