IMO Shortlist 1986 problem 12


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2. travnja 2012.
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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 x,y,z respectively, and y<0, then the following operation is allowed: x,y,z are replaced by x+y,-y,z+y 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