{"status": "success", "data": {"description_md": "A point $ P$ is chosen at random in the interior of a unit square $ S$. Let $ d(P)$ denote the distance from $ P$ to the closest side of $ S$. The probability that $ \\frac15\\le d(P)\\le\\frac13$ is equal to $ \\frac{m}{n}$, 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>A point $ P$ is chosen at random in the interior of a unit square $ S$. Let $ d&#167;$ denote the distance from $ P$ to the closest side of $ S$. The probability that $ \\frac15\\le d&#167;\\le\\frac13$ is equal to $ \\frac{m}{n}$, where $ m$ and $ n$ are relatively prime positive integers. Find $ m+n$.</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": 3, "problem_name": "2010 AIME II Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/10_aime_II_p03", "prev": "/problem/10_aime_II_p01"}}