IMO Shortlist 2002 problem C6


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 8,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
Let n be an even positive integer. Show that there is a permutation \left(x_{1},x_{2},\ldots,x_{n}\right) of \left(1,\,2,\,\ldots,n\right) such that for every i\in\left\{1,\ 2,\ ...,\ n\right\}, the number x_{i+1} is one of the numbers 2x_{i}, 2x_{i}-1, 2x_{i}-n, 2x_{i}-n-1. Hereby, we use the cyclic subscript convention, so that x_{n+1} means x_{1}.
Izvor: Međunarodna matematička olimpijada, shortlist 2002