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Choosing numbers with condition

Source: Serbian JBTST 2, Day 2

May 31, 2009
combinatorics proposedcombinatorics

Problem Statement

From the set {1,2,3,,2009} \{1,2,3,\ldots,2009\} we choose 1005 1005 numbers, such that sum of any 2 2 numbers isn't neither 2009 2009 nor 2010 2010. Find all ways on we can choose these 1005 1005 numbers.