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.
1, and Oliver has no more moves.
1, and Oliver chooses
1, and James has no more moves.