MathDB

Alice and Brian are playing a game on a

1\times (N + 2)

board. To start the game, Alice places a checker on any of the

N

interior squares. In each move, Brian chooses a positive integer

n

. Alice must move the checker to the

n

-th square on the left or the right of its current position. If the checker moves off the board, Alice wins. If it lands on either of the end squares, Brian wins. If it lands on another interior square, the game proceeds to the next move. For which values of

N

does Brian have a strategy which allows him to win the game in a finite number of moves?

Problem Statement