---
id: 5900f4991000cf542c50ffab
title: 'Problem 301: Nim'
challengeType: 5
forumTopicId: 301955
dashedName: problem-301-nim
---

# --description--

Nim is a game played with heaps of stones, where two players take it in turn to remove any number of stones from any heap until no stones remain.

We'll consider the three-heap normal-play version of Nim, which works as follows:

-   At the start of the game there are three heaps of stones.
-   On his turn the player removes any positive number of stones from any single heap.
-   The first player unable to move (because no stones remain) loses.

If (n1,n2,n3) indicates a Nim position consisting of heaps of size n1, n2 and n3 then there is a simple function X(n1,n2,n3) — that you may look up or attempt to deduce for yourself — that returns: zero if, with perfect strategy, the player about to move will eventually lose; or non-zero if, with perfect strategy, the player about to move will eventually win. For example X(1,2,3) = 0 because, no matter what the current player does, his opponent can respond with a move that leaves two heaps of equal size, at which point every move by the current player can be mirrored by his opponent until no stones remain; so the current player loses. To illustrate:

-   current player moves to (1,2,1)
-   opponent moves to (1,0,1)
-   current player moves to (0,0,1)
-   opponent moves to (0,0,0), and so wins.

For how many positive integers n ≤ 230 does X(n,2n,3n) = 0 ?

# --hints--

`euler301()` should return 2178309.

```js
assert.strictEqual(euler301(), 2178309);
```

# --seed--

## --seed-contents--

```js
function euler301() {

  return true;
}

euler301();
```

# --solutions--

```js
// solution required
```