Divisor game

Math Dynamic Programming Brainteaser Game Theory

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Feb 25, 2026

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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 integer 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.

Solution

Rust

Time O(1)

Space O(1)

LeetCode

solution.rs

impl Solution {
  pub fn divisor_game(n: i32) -> bool { n % 2 == 0 }
}