{"status": "success", "data": {"description_md": "Two unit squares are selected at random without replacement from an $n\\times n$ grid of unit squares. Find the least positive integer $n$ such that the probability that the two selected squares are horizontally or vertically adjacent is less than $\\frac{1}{2015}$.\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>Two unit squares are selected at random without replacement from an <span class=\"katex--inline\">n\\times n</span> grid of unit squares. Find the least positive integer <span class=\"katex--inline\">n</span> such that the probability that the two selected squares are horizontally or vertically adjacent is less than <span class=\"katex--inline\">\\frac{1}{2015}</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": 3, "problem_name": "2015 AIME II Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/15_aime_II_p06", "prev": "/problem/15_aime_II_p04"}}