---
id: 5900f49a1000cf542c50ffac
title: 'Problem 300: Protein folding'
challengeType: 5
forumTopicId: 301954
dashedName: problem-300-protein-folding
---

# --description--

In a very simplified form, we can consider proteins as strings consisting of hydrophobic (H) and polar (P) elements, e.g. HHPPHHHPHHPH.

For this problem, the orientation of a protein is important; e.g. HPP is considered distinct from PPH. Thus, there are $2^n$ distinct proteins consisting of $n$ elements.

When one encounters these strings in nature, they are always folded in such a way that the number of H-H contact points is as large as possible, since this is energetically advantageous.

As a result, the H-elements tend to accumulate in the inner part, with the P-elements on the outside.

Natural proteins are folded in three dimensions of course, but we will only consider protein folding in <u>two dimensions</u>.

The figure below shows two possible ways that our example protein could be folded (H-H contact points are shown with red dots).

<img class="img-responsive center-block" alt="two possible ways to fold example protein" src="https://cdn.freecodecamp.org/curriculum/project-euler/protein-folding.gif" style="background-color: white; padding: 10px;">

The folding on the left has only six H-H contact points, thus it would never occur naturally. On the other hand, the folding on the right has nine H-H contact points, which is optimal for this string.

Assuming that H and P elements are equally likely to occur in any position along the string, the average number of H-H contact points in an optimal folding of a random protein string of length 8 turns out to be $\frac{850}{2^8} = 3.3203125$.

What is the average number of H-H contact points in an optimal folding of a random protein string of length 15? Give your answer using as many decimal places as necessary for an exact result.

# --hints--

`proteinFolding()` should return `8.0540771484375`.

```js
assert.strictEqual(proteinFolding(), 8.0540771484375);
```

# --seed--

## --seed-contents--

```js
function proteinFolding() {

  return true;
}

proteinFolding();
```

# --solutions--

```js
// solution required
```
