RU-ALLRUSSIAN 1971 Problem 11

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 $\mathrm{n} = 6$ you cannot get B marked - and the other vertices marked +. Show that the same is true if all moves have $\mathrm{n} = 3$ or if all moves have $\mathrm{n} = 4$ .