---
id: 5900f4481000cf542c50ff5a
challengeType: 5
title: 'Problem 219: Skew-cost coding'
---

## Description
<section id='description'>
Let A and B be bit strings (sequences of 0's and 1's).
If A is equal to the leftmost length(A) bits of B, then A is said to be a prefix of B.
For example, 00110 is a prefix of 001101001, but not of 00111 or 100110.

A prefix-free code of size n is a collection of n distinct bit strings such that no string is a prefix of any other.  For example, this is a prefix-free code of size 6:

0000, 0001, 001, 01, 10, 11

Now suppose that it costs one penny to transmit a '0' bit, but four pence to transmit a '1'.
Then the total cost of the prefix-free code shown above is 35 pence, which happens to be the cheapest possible for the skewed pricing scheme in question.
In short, we write Cost(6) = 35.

What is Cost(109) ?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler219()</code> should return 64564225042.
    testString: assert.strictEqual(euler219(), 64564225042, '<code>euler219()</code> should return 64564225042.');

```

</section>

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

<div id='js-seed'>

```js
function euler219() {
  // Good luck!
  return true;
}

euler219();
```

</div>



</section>

## Solution
<section id='solution'>

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