olymmath

ISL 2012 C2

  • Answer

Let n≥1n \geq 1 be an integer. What is the maximum number of disjoint pairs of elements of the set {1,2,…,n}\{1,2, \ldots, n\} such that the sums of the different pairs are different integers not exceeding nn ?

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

Official text: IMO 2012 Shortlist booklet, page 5.

Show the answer

\left\lfloor\frac{2 n-1}{5}\right\rfloor

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

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