Question 188
On each vertex of a regular $n$-gon we place a sign $+$ or $-$. At each step, we are allowed to change the signs of three consecutive vertices of the $n$-gon.
For which $n$ is it true that, whatever the starting configuration, one can obtain $+$ on all the vertices in a finite number of steps?
For which $n$ is it true that, whatever the starting configuration, one can obtain $+$ on all the vertices in a finite number of steps?