olymmath

ISL 2010 A3

  • Answer

Let x1,…,x100x_{1}, \ldots, x_{100} be nonnegative real numbers such that xi+xi+1+xi+2≤1x_{i}+x_{i+1}+x_{i+2} \leq 1 for all i=1,…,100i=1, \ldots, 100 (we put x101=x1,x102=x2x_{101}=x_{1}, x_{102}=x_{2} ). Find the maximal possible value of the sum S=∑i=1100xixi+2S=\sum_{i=1}^{100} x_{i} x_{i+2} (Russia)

Dataset text NuminaMath olympiads. Quoted with source.

Official text: IMO 2010 Shortlist booklet, page 11.

Show the answer

\frac{25}{2}

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

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