MEMO 2009 ekipno problem 3

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Dodao/la: arhiva
28. travnja 2012.
The numbers 0, 1, \dots, n (n \ge 2) are written on a blackboard. In each step we erase an integer which is the arithmetic mean of two different numbers which are still left on the blackboard. We make such steps until no further integer can be erased. Let g(n) be the smallest possible number of integers left on the blackboard at the end. Find g(n) for every n.
Izvor: Srednjoeuropska matematička olimpijada 2009, ekipno natjecanje, problem 3