---
id: 5900f4a21000cf542c50ffb5
title: 'Problem 310: Nim Square'
challengeType: 5
forumTopicId: 301966
dashedName: problem-310-nim-square
---

# --description--

Alice and Bob play the game Nim Square.

Nim Square is just like ordinary three-heap normal play Nim, but the players may only remove a square number of stones from a heap.

The number of stones in the three heaps is represented by the ordered triple ($a$, $b$, $c$).

If $0 ≤ a ≤ b ≤ c ≤ 29$ then the number of losing positions for the next player is 1160.

Find the number of losing positions for the next player if $0 ≤ a ≤ b ≤ c ≤ 100\\,000$.

# --hints--

`nimSquare()` should return `2586528661783`.

```js
assert.strictEqual(nimSquare(), 2586528661783);
```

# --seed--

## --seed-contents--

```js
function nimSquare() {

  return true;
}

nimSquare();
```

# --solutions--

```js
// solution required
```
