olymmath

ISL 2018 C1

    Let n⩾3n \geqslant 3 be an integer. Prove that there exists a set SS of 2n2 n positive integers satisfying the following property: For every m=2,3,…,nm=2,3, \ldots, n the set SS can be partitioned into two subsets with equal sums of elements, with one of subsets of cardinality mm. (Iceland)

    Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.

    Official text: IMO 2018 Shortlist booklet, page 6.

    Solutions

    Official solution Solution 1 by the IMO Problem Selection Committee

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