Question 126
Ada and Charles play a game. At the beginning an integer $n \gt 1$ is written on the board. Taking turns, Ada and Charles erase the number $k$ they find on the board and replace it
1 - either with a positive divisor of $k$ different from 1 and from $k$ itself
2 - or with $k+1$.
Initially each player has one thousand points. When a player plays move 1, he gains one point; when he plays move 2, he loses one point. The game ends when one of the players reaches zero points, and this player has lost. Ada plays first. For which values of $n$ does Charles have a winning strategy?
1 - either with a positive divisor of $k$ different from 1 and from $k$ itself
2 - or with $k+1$.
Initially each player has one thousand points. When a player plays move 1, he gains one point; when he plays move 2, he loses one point. The game ends when one of the players reaches zero points, and this player has lost. Ada plays first. For which values of $n$ does Charles have a winning strategy?