{"status": "success", "data": {"description_md": "A set of positive numbers has the $\\text{triangle property}$ if it has three distinct elements that are the lengths of the sides of a triangle whose area is positive. Consider sets $\\{4, 5, 6, \\ldots, n\\}$ of consecutive positive integers, all of whose ten-element subsets have the triangle property. What is the largest possible value of $n$?\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 set of positive numbers has the <span class=\"katex--inline\">\\text{triangle property}</span> if it has three distinct elements that are the lengths of the sides of a triangle whose area is positive. Consider sets <span class=\"katex--inline\">\\{4, 5, 6, \\ldots, n\\}</span> of consecutive positive integers, all of whose ten-element subsets have the triangle property. What is the largest possible value of <span class=\"katex--inline\">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": 3, "problem_name": "2001 AIME II Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/01_aime_II_p06", "prev": "/problem/01_aime_II_p04"}}