olymmath

ISL 2019 C2

    You are given a set of nn blocks, each weighing at least 1 ; their total weight is 2n2 n. Prove that for every real number rr with 0⩽r⩽2n−20 \leqslant r \leqslant 2 n-2 you can choose a subset of the blocks whose total weight is at least rr but at most r+2r+2. (Thailand)

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

    Official text: IMO 2019 Shortlist booklet, page 8.

    Solutions

    Official solution Solution 1 by the IMO Problem Selection Committee

    The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

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