{"status": "success", "data": {"description_md": "From the set of integers $\\{1,2,3,\\ldots,2009\\}$, choose $k$ pairs $\\{a_i,b_i\\}$ with $a_i<b_i$ so that no two pairs have a common element. Suppose that all the sums $a_i+b_i$ are distinct and less than or equal to $2009$. Find the maximum possible value of $k$.\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>From the set of integers <span class=\"katex--inline\">\\{1,2,3,\\ldots,2009\\}</span>, choose <span class=\"katex--inline\">k</span> pairs <span class=\"katex--inline\">\\{a_i,b_i\\}</span> with <span class=\"katex--inline\">a_i&lt;b_i</span> so that no two pairs have a common element. Suppose that all the sums <span class=\"katex--inline\">a_i+b_i</span> are distinct and less than or equal to <span class=\"katex--inline\">2009</span>. Find the maximum possible value of <span class=\"katex--inline\">k</span>.</p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2009 AIME II Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/09_aime_II_p13", "prev": "/problem/09_aime_II_p11"}}