Question 157
Alina and Bogdan play a game on a $2 \times n$ rectangular grid ($n \ge 2$) whose sides of length $2$ are glued together to form a cylinder. Alternating moves, each player cuts out a unit square of the grid. A player loses if his/her move causes the grid to lose circular connection (two unit squares that only touch at a corner are considered to be disconnected). Suppose Alina makes the first move. Which player has a winning strategy?
Estonian Olympiad, 2009
Estonian Olympiad, 2009