---
id: 5900f4481000cf542c50ff5a
title: 'Problem 219: Skew-cost coding'
challengeType: 5
forumTopicId: 301861
dashedName: problem-219-skew-cost-coding
---

# --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) ?

# --hints--

`euler219()` should return 64564225042.

```js
assert.strictEqual(euler219(), 64564225042);
```

# --seed--

## --seed-contents--

```js
function euler219() {

  return true;
}

euler219();
```

# --solutions--

```js
// solution required
```