## DEV Community

Abhishek Chaudhary

Posted on

# Nim Game

You are playing the following Nim Game with your friend:

• Initially, there is a heap of stones on the table.
• You and your friend will alternate taking turns, and you go first.
• On each turn, the person whose turn it is will remove 1 to 3 stones from the heap.
• The one who removes the last stone is the winner.

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`

SOLUTION:

``````class Solution:
def canWinNim(self, n: int) -> bool:
return n != (n >> 2) << 2
``````