---
id: 5900f4151000cf542c50ff28
challengeType: 5
title: 'Problem 169: Exploring the number of different ways a number can be expressed as a sum of powers of 2'
---

## Description
<section id='description'>
Define f(0)=1 and f(n) to be the number of different ways n can be expressed as a sum of integer powers of 2 using each power no more than twice.
For example, f(10)=5 since there are five different ways to express 10:
1 + 1 + 8
1 + 1 + 4 + 41 + 1 + 2 + 2 + 4
2 + 4 + 4
2 + 8
What is f(1025)?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler169()</code> should return 178653872807.
    testString: assert.strictEqual(euler169(), 178653872807, '<code>euler169()</code> should return 178653872807.');

```

</section>

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

<div id='js-seed'>

```js
function euler169() {
  // Good luck!
  return true;
}

euler169();
```

</div>



</section>

## Solution
<section id='solution'>

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