Problem A. 475. (February 2009)
A. 475. To each vertex of a regular n-gon a real number is assigned in such a way that the sum of all n numbers is positive. If three consecutive vertices are assigned the numbers x, y, z respectively and y<0 then the following operation is allowed: the numbers 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 n numbers is negative. Determine whether this procedure necessarily terminates after a finite number of steps.
Deadline expired on 16 March 2009.