{"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 $ {1,2,3,\\ldots,2009}$, choose $ k$ pairs $ {a_i,b_i}$ with $ a_i&lt;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$.</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": 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"}}