{"status": "success", "data": {"description_md": "Let $x_1,x_2,\\ldots ,x_6$ be nonnegative real numbers such that $x_1+x_2+x_3+x_4+x_5+x_6=1$, and $x_1x_3x_5+x_2x_4x_6 \\geq \\frac{1}{540}$. Let $p$ and $q$ be positive relatively prime integers such that $\\frac{p}{q}$ is the maximum possible value of $x_1x_2x_3+x_2x_3x_4 + x_3x_4x_5 + x_4x_5x_6 + x_5x_6x_1 + x_6x_1x_2$. Find $p+q$.\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": "

Let x_1,x_2,\\ldots ,x_6 be nonnegative real numbers such that x_1+x_2+x_3+x_4+x_5+x_6=1, and x_1x_3x_5+x_2x_4x_6 \\geq \\frac{1}{540}. Let p and q be positive relatively prime integers such that \\frac{p}{q} is the maximum possible value of x_1x_2x_3+x_2x_3x_4 + x_3x_4x_5 + x_4x_5x_6 + x_5x_6x_1 + x_6x_1x_2. Find p+q.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2011 AIME II Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/11_aime_II_p10", "prev": "/problem/11_aime_II_p08"}}