Question 139
A positive integer $N_0$ is written on the board. Two persons, $A$ and $B$, play the following game: $A$ erases $N_0$ and writes a number $N_1 \in \{N_0 - 1; [N_0/3]\}$. Then $B$ erases $N_1$ and writes a number $N_2 \in \{N_1 - 1; [N_1/3]\}$. At his turn, $A$ erases $N_2$ and so on. They continue to play until on the board appears the number $0$; the player who writes first the number $0$ is considered as the winner and the other player is considered lost.
Determine whether the player $A$ or the player $B$ has a strategy to guarantee his win when:
$$
1/\ N_0 = 120 ?
$$
$$
2/\ N_0 = (3^{2002} - 1)/2 ?
$$
$$
3/\ N_0 = (3^{2002} + 1)/2 ?
$$
Determine whether the player $A$ or the player $B$ has a strategy to guarantee his win when:
$$
1/\ N_0 = 120 ?
$$
$$
2/\ N_0 = (3^{2002} - 1)/2 ?
$$
$$
3/\ N_0 = (3^{2002} + 1)/2 ?
$$