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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

Solution

class Solution:
    def divisorGame(self, n: int) -> bool:
        # If n is even Alice can subtract 1 and give Bob an odd number.
        # Odd numbers have odd factors so Bob will give an even number back to Alice.
        # The base case is 2 which can be won by choosing 1.
        return n % 2 == 0