Question 12
$A$ and $B$ are adjacent vertices of a $12$-gon. Vertex $A$ is marked $-$ and the other vertices are marked $+$. You are allowed to change the sign of any $n$ adjacent vertices. Show that by a succession of moves of this type with $n = 6$ you cannot get $B$ marked $-$ and the other vertices marked $+$. Show that the same is true if all moves have $n = 3$ or if all moves have $n = 4$.