IMO Shortlist 2010 problem A3


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 7,0
Dodao/la: arhiva
23. lipnja 2013.
LaTeX PDF
Let x_1, \ldots , x_{100} be nonnegative real numbers such that x_i + x_{i+1} + x_{i+2} \leq 1 for all i = 1, \ldots , 100 (we put x_{101 } = x_1, x_{102} = x_2). Find the maximal possible value of the sum S = \sum^{100}_{i=1} x_i x_{i+2}.


Proposed by Sergei Berlov, Ilya Bogdanov, Russia
Izvor: Međunarodna matematička olimpijada, shortlist 2010