olymmath

ISL 2013 A2

    Prove that in any set of 2000 distinct real numbers there exist two pairs a>ba>b and c>dc>d with a≠ca \neq c or b≠db \neq d, such that ∣a−bc−d−1∣<1100000\left|\frac{a-b}{c-d}-1\right|<\frac{1}{100000} (Lithuania)

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

    Official text: IMO 2013 Shortlist booklet, page 3.

    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/2013/a2 · Tag 7MAGWMX1EN · Edit this page on GitHub · Keys: j next, k previous