Question 7
Vertices of a regular $(6n+3)$-gon, which are renumbered clockwise by numbers $1; 2; \ldots; 6n+3$, are the game field. Vertices with numbers $2n+1; 4n+2; 6n+3$ are called holes. At the start of the game there are $3$ chips on the field. $2$ players in turn choose any one of the $3$ chips and move it clockwise to a neighbouring vertex, if this one isn't occupied by another chip. The first player wins, if at least $2$ chips get in holes after anyone's turn. Can the first player always win, if at the start of the game they are placed in the form of a regular triangle?
(Bogdan Rublyov)
(Bogdan Rublyov)