> For the complete documentation index, see [llms.txt](https://jaywin.gitbook.io/leetcode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jaywin.gitbook.io/leetcode/solutions/1908-game-of-nim.md).

# 1908. Game of Nim

<https://leetcode.com/problems/game-of-nim>

## Description

Alice and Bob take turns playing a game with **Alice starting first**.

In this game, there are `n` piles of stones. On each player's turn, the player should remove any **positive** number of stones from a non-empty pile **of his or her choice**. The first player who cannot make a move loses, and the other player wins.

Given an integer array `piles`, where `piles[i]` is the number of stones in the `ith` pile, return `true` *if Alice wins, or* `false` *if Bob wins*.

Both Alice and Bob play **optimally**.

**Example 1:**

```
**Input:** piles = [1]
**Output:** true
**Explanation:** There is only one possible scenario:
- On the first turn, Alice removes one stone from the first pile. piles = [0].
- On the second turn, there are no stones left for Bob to remove. Alice wins.
```

**Example 2:**

```
**Input:** piles = [1,1]
**Output:** false
**Explanation:** It can be proven that Bob will always win. One possible scenario is:
- On the first turn, Alice removes one stone from the first pile. piles = [0,1].
- On the second turn, Bob removes one stone from the second pile. piles = [0,0].
- On the third turn, there are no stones left for Alice to remove. Bob wins.
```

**Example 3:**

```
**Input:** piles = [1,2,3]
**Output:** false
**Explanation:** It can be proven that Bob will always win. One possible scenario is:
- On the first turn, Alice removes three stones from the third pile. piles = [1,2,0].
- On the second turn, Bob removes one stone from the second pile. piles = [1,1,0].
- On the third turn, Alice removes one stone from the first pile. piles = [0,1,0].
- On the fourth turn, Bob removes one stone from the second pile. piles = [0,0,0].
- On the fifth turn, there are no stones left for Alice to remove. Bob wins.
```

**Constraints:**

* `n == piles.length`
* `1 <= n <= 7`
* `1 <= piles[i] <= 7`

**Follow-up:** Could you find a linear time solution? Although the linear time solution may be beyond the scope of an interview, it could be interesting to know.

## ac

```java
```