# 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.

(5 pont)

**Deadline expired on March 16, 2009.**

### Statistics:

4 students sent a solution. 5 points: Backhausz Tibor, Nagy 235 János, Nagy 648 Donát, Tomon István.

Problems in Mathematics of KöMaL, February 2009