Question 12
(GDR 3) IMO3. To each vertex $P_i$ ($i=1,\ldots,5$) of a pentagon an integer $x_i$ is assigned, the sum $s=\sum x_i$ being positive. The following operation is allowed, provided at least one of the $x_i$'s is negative: Choose a negative $x_i$, replace it by $-x_i$, and add the former value of $x_i$ to the integers assigned to the two neighboring vertices of $P_i$ (the remaining two integers are left unchanged).
This operation is to be performed repeatedly until all negative integers disappear. Decide whether this procedure must eventually terminate.
This operation is to be performed repeatedly until all negative integers disappear. Decide whether this procedure must eventually terminate.