Question 7
A regular polygon has 20 vertices $A_1,A_2,\ldots,A_{20}$ in cyclic order. Initially $A_1,A_2$ carry minus signs and all other vertices carry plus signs. In one move, reverse the signs at five consecutive vertices, changing minus to plus and plus to minus; consecutive vertices are counted cyclically. Can a sequence of moves leave minus signs exactly at $A_3,A_4$ and plus signs at all the other vertices? Why?
