Combinatorics · Pigeonhole principle · Subset sums · Counting subsets · Set difference
Problem 2, 1999
← Prev · 1 / 11 · Next →Let \(A\) be a set of \(10\) numbers chosen from \(\{1, 2, \ldots, 100\}\). Prove that \(A\) has two nonempty subsets \(S\) and \(T\) with no element in common such that the sum of the elements of \(S\) equals the sum of the elements of \(T\).
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Serbian Republic Competition (Republicko takmicenje) 1999, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source