Question 42
Let $N$ be a positive integer. $N$ squares are lined up contiguously from left to right. Students A and B play a game according to the following rules:
(1) To start off, A will write 1 non-negative integer into each of the $N$ squares.
(2) The game ends when the following condition is achieved: For every $i$ satisfying $1 \le i \le N - 1$, the number in the $i$-th square from the left is less than or equal to the number in the $(i+1)$-th square from the left. The game continues as long as this condition is not achieved by repeating the following procedure:
(a) A designates 1 non-negative integer.
(b) B chooses one of the $N$ squares and replaces the number in that square by the number designated by A in (a).
Is it possible for B to end the game no matter how A plays?
(1) To start off, A will write 1 non-negative integer into each of the $N$ squares.
(2) The game ends when the following condition is achieved: For every $i$ satisfying $1 \le i \le N - 1$, the number in the $i$-th square from the left is less than or equal to the number in the $(i+1)$-th square from the left. The game continues as long as this condition is not achieved by repeating the following procedure:
(a) A designates 1 non-negative integer.
(b) B chooses one of the $N$ squares and replaces the number in that square by the number designated by A in (a).
Is it possible for B to end the game no matter how A plays?