James and Oliver take turns playing a game, with James starting first.
Initially, there is a number
N on the chalkboard. On each player's turn, that player makes a move consisting of:
- Choosing any
0 < x < Nand
N % x == 0where 1 <= N <= 1000.
- Replacing the number
Non the chalkboard with
N - x.
Also, if a player cannot make a move, they lose the game.
True if and only if James wins the game, assuming both players play optimally.
Oliver has no more moves.
James has no more moves.