{"status": "success", "data": {"description_md": "Let $x_1\\leq x_2\\leq \\cdots\\leq x_{100}$ be real numbers such that $|x_1| + |x_2| + \\cdots + |x_{100}| = 1$ and $x_1 + x_2 + \\cdots + x_{100} = 0$. Among all such $100$-tuples of numbers, the greatest value that $x_{76} - x_{16}$ can achieve is $\\tfrac mn$, where $m$ and $n$ are relatively prime positive 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>Let <span class=\"katex--inline\">x_1\\leq x_2\\leq \\cdots\\leq x_{100}</span> be real numbers such that <span class=\"katex--inline\">|x_1| + |x_2| + \\cdots + |x_{100}| = 1</span> and <span class=\"katex--inline\">x_1 + x_2 + \\cdots + x_{100} = 0</span>. Among all such <span class=\"katex--inline\">100</span>-tuples of numbers, the greatest value that <span class=\"katex--inline\">x_{76} - x_{16}</span> can achieve is <span class=\"katex--inline\">\\tfrac mn</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive 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": 4, "problem_name": "2022 AIME II Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/22_aime_II_p07", "prev": "/problem/22_aime_II_p05"}}