IMO Shortlist 1986 problem 12
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Avg: 0,0 To each vertex of a regular pentagon an integer is assigned, so that the sum of all five numbers is positive. If three consecutive vertices are assigned the numbers respectively, and , then the following operation is allowed: are replaced by respectively. Such an operation is performed repeatedly as long as at least one of the five numbers is negative. Determine whether this procedure necessarily comes to an end after a finite number of steps.
Izvor: Međunarodna matematička olimpijada, shortlist 1986