---
id: 5900f3b81000cf542c50fecb
title: 'Problem 76: Counting summations'
challengeType: 5
forumTopicId: 302189
dashedName: problem-76-counting-summations
---

# --description--

It is possible to write five as a sum in exactly six different ways:

<div style='margin-left: 4em;'>
  4 + 1<br>
  3 + 2<br>
  3 + 1 + 1<br>
  2 + 2 + 1<br>
  2 + 1 + 1 + 1<br>
  1 + 1 + 1 + 1 + 1<br>
</div>

How many different ways can one hundred be written as a sum of at least two positive integers?

# --hints--

`countingSummations()` should return a number.

```js
assert(typeof countingSummations() === 'number');
```

`countingSummations()` should return 190569291.

```js
assert.strictEqual(countingSummations(), 190569291);
```

# --seed--

## --seed-contents--

```js
function countingSummations() {

  return true;
}

countingSummations();
```

# --solutions--

```js
// solution required
```