Question 6
The numbers $0$, $1$, and $2$ are written in the vertices of a triangle. One step involves increasing two of the three numbers by $m$ or decreasing one of the three numbers by $n$. Is it possible that after some steps there are numbers $1$, $2$, and $3$ (in an arbitrary order) written in the vertices if
a) $m = 3$, $n = 6$;
b) $m = 4\frac{1}{2}$, $n = 6$?
a) $m = 3$, $n = 6$;
b) $m = 4\frac{1}{2}$, $n = 6$?