---
id: 5900f4041000cf542c50ff17
title: 'Problem 152: Writing one half as a sum of inverse squares'
challengeType: 5
forumTopicId: 301783
dashedName: problem-152-writing-one-half-as-a-sum-of-inverse-squares
---

# --description--

There are several ways to write the number 1/2 as a sum of inverse squares using distinct integers.

For instance, the numbers {2,3,4,5,7,12,15,20,28,35} can be used:

In fact, only using integers between 2 and 45 inclusive, there are exactly three ways to do it, the remaining two being: {2,3,4,6,7,9,10,20,28,35,36,45} and {2,3,4,6,7,9,12,15,28,30,35,36,45}. How many ways are there to write the number 1/2 as a sum of inverse squares using distinct integers between 2 and 80 inclusive?

# --hints--

`euler152()` should return 301.

```js
assert.strictEqual(euler152(), 301);
```

# --seed--

## --seed-contents--

```js
function euler152() {

  return true;
}

euler152();
```

# --solutions--

```js
// solution required
```