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g1001_1100.s1025_divisor_game.readme.md Maven / Gradle / Ivy

1025\. Divisor Game

Easy

Alice and Bob take turns playing a game, with Alice 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 `x` with `0 < x < n` and `n % x == 0`.
*   Replacing the number `n` on the chalkboard with `n - x`.

Also, if a player cannot make a move, they lose the game.

Return `true` _if and only if Alice wins the game, assuming both players play optimally_.

**Example 1:**

**Input:** n = 2

**Output:** true

**Explanation:** Alice chooses 1, and Bob has no more moves.

**Example 2:**

**Input:** n = 3

**Output:** false

**Explanation:** Alice chooses 1, Bob chooses 1, and Alice has no more moves.

**Constraints:**

*   `1 <= n <= 1000`