44 lines
1.0 KiB
Markdown
44 lines
1.0 KiB
Markdown
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## Nim Game
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You are playing the following Nim Game with your friend:
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- Initially, there is a heap of stones on the table.
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- You and your friend will alternate taking turns, and **you go first**.
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- On each turn, the person whose turn it is will remove 1 to 3 stones from the heap.
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- The one who removes the last stone is the winner.
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- 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`.
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### Examples
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**Example 1**
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```text
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Input: n = 4
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Output: false
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Explanation: These are the possible outcomes:
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1. You remove 1 stone. Your friend removes 3 stones, including the last stone. Your friend wins.
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2. You remove 2 stones. Your friend removes 2 stones, including the last stone. Your friend wins.
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3. You remove 3 stones. Your friend removes the last stone. Your friend wins.
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In all outcomes, your friend wins.
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```
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**Example 2**
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```text
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Input: n = 1
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Output: true
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```
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**Example 3**
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```text
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Input: n = 2
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Output: true
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```
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---
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### Constraints
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- `1 <= n <= 231 - 1`
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