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n weights weigh < 2n

Source: Turkey TST 1989 - P5

September 11, 2013
inequalities proposedinequalities

Problem Statement

There are n≥2n\geq2 weights such that each weighs a positive integer less than nn and their total weights is less than 2n2n. Prove that there is a subset of these weights such that their total weights is equal to nn.
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