hi mido22

here are the cases:

1.N is divisible by 3:

player two has the winning strategy.

in this case whatever player one choses the player two can choose the opposite and by doing that the sum after his turn and only after his turn will always be divisible by 3.

2.N gives remainder 1 when divided by 3:

player one has the winning strategy.

in this case player one should start with 1 then choose the opposite of whatever player two chooses.doing this the sum after his turn and only after his turn will give remainder 1 when divided by 3.

3.N gives remainder 2 when divided by 3:

player one has the winning strategy.

in this case plyer one should start with 2 then choose the opposite of whatever player two chooses.doing this the sum after his turn and only after his turn will give remainder 2 when divided by 3.