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Found problems: 1

2009 AIME Problems, 12
Tags: AMC , 2009 AIME II , AIME
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\plus{}b_i$ are distinct and less than or equal to $ 2009$. Find the maximum possible value of $ k$.