easyBrainteaserGame TheoryMath 0 views

Nim Game

You are playing the following Nim Game with your friend: Given n, the number of stones in the heap, return true if you can win the game assuming both you and your friend play...

You are playing the following Nim Game with your friend:

Given n, the number of stones in the heap, return true if you can win the game assuming both you and your friend play optimally, otherwise return false.

Example 1

Input: n = 4

Output: false

Explanation: These are the possible outcomes: 1. You remove 1 stone. Your friend removes 3 stones, including the last stone. Your friend wins. 2. You remove 2 stones. Your friend removes 2 stones, including the last stone. Your friend wins. 3. You remove 3 stones. Your friend removes the last stone. Your friend wins. In all outcomes, your friend wins.

Example 2

Input: n = 1

Output: true

Example 3

Input: n = 2

Output: true

Constraints

  • 1 <= n <= 231 - 1

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