---
id: 5900f5061000cf542c510017
challengeType: 5
title: 'Problem 409: Nim Extreme'
---

## Description
<section id='description'>
Let n be a positive integer. Consider nim positions where:There are n non-empty piles.
Each pile has size less than 2n.
No two piles have the same size.
Let W(n) be the number of winning nim positions satisfying the above
conditions (a position is winning if the first player has a winning strategy). For example, W(1) = 1, W(2) = 6, W(3) = 168, W(5) = 19764360 and W(100) mod 1 000 000 007 = 384777056.

Find W(10 000 000) mod 1 000 000 007.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler409()</code> should return 253223948.
    testString: assert.strictEqual(euler409(), 253223948, '<code>euler409()</code> should return 253223948.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler409() {
  // Good luck!
  return true;
}

euler409();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>