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Partition of {502,..., 2009} - BxMO 2010

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May 2, 2010
combinatorics proposedcombinatoricscombinatorics solvedsymmetrySubsetsBounding

Problem Statement

A finite set of integers is called bad if its elements add up to 20102010. A finite set of integers is a Benelux-set if none of its subsets is bad. Determine the smallest positive integer nn such that the set {502,503,504,...,2009}\{502, 503, 504, . . . , 2009\} can be partitioned into nn Benelux-sets. (A partition of a set SS into nn subsets is a collection of nn pairwise disjoint subsets of SS, the union of which equals SS.)
(2nd Benelux Mathematical Olympiad 2010, Problem 1)
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