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Distinct Pairs with Distinct Sums

Source: AIME 2009II Problem 12

April 2, 2009
AMC2009 AIME IIAIME

Problem Statement

From the set of integers {1,2,3,…,2009} \{1,2,3,\ldots,2009\}, choose k k pairs {ai,bi} \{a_i,b_i\} with ai<bi 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 2009. Find the maximum possible value of k k.
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