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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
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:
[Brainteaser]
[Math]
[Dynamic Programming]
[Game Theory]
Hints
Hint 1
If the current number is even, we can always subtract a 1 to make it odd. If the current number is odd, we must subtract an odd number to make it even.