A finite set of integers is called bad if its elements add up to 2010. A finite set of integers is a Benelux-set if none of its subsets is bad. Determine the smallest positive integer n such that the set {502,503,504,...,2009} can be partitioned into n Benelux-sets.
(A partition of a set S into n subsets is a collection of n pairwise disjoint subsets of S, the union of which equals S.)(2nd Benelux Mathematical Olympiad 2010, Problem 1) combinatorics proposedcombinatoricscombinatorics solvedsymmetrySubsetsBounding