olymmath

ISL 2011 C2

    Suppose that 1000 students are standing in a circle. Prove that there exists an integer kk with 100≤k≤300100 \leq k \leq 300 such that in this circle there exists a contiguous group of 2k2 k students, for which the first half contains the same number of girls as the second half.

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

    Official text: IMO 2011 Shortlist booklet, page 7.

    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).

    Locator isl/2011/c2 · Tag 61J7SN4QW7 · Edit this page on GitHub · Keys: j next, k previous