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Very hard ,isn't it?

Source: Romanian team selection test 1997, 1st round, problem 2

September 6, 2005
combinatorics unsolvedcombinatoricsAdditive combinatorics

Problem Statement

Find the number of sets AA containing 99 positive integers with the following property: for any positive integer n≤500n\le 500, there exists a subset B⊂AB\subset A such that ∑b∈Bb=n\sum_{b\in B}{b}=n.
Bogdan Enescu & Dan Ismailescu
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