---
id: 5900f51a1000cf542c51002d
challengeType: 5
title: 'Problem 430: Range flips'
---

## Description
<section id='description'>
N disks are placed in a row, indexed 1 to N from left to right.
Each disk has a black side and white side. Initially all disks show their white side.

At each turn, two, not necessarily distinct, integers A and B between 1 and N (inclusive) are chosen uniformly at random.
All disks with an index from A to B (inclusive) are flipped.

The following example shows the case N = 8. At the first turn A = 5 and B = 2, and at the second turn A = 4 and B = 6.



Let E(N, M) be the expected number of disks that show their white side after M turns.
We can verify that E(3, 1) = 10/9, E(3, 2) = 5/3, E(10, 4) ≈ 5.157 and E(100, 10) ≈ 51.893.

Find E(1010, 4000).
Give your answer rounded to 2 decimal places behind the decimal point.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler430()</code> should return 5000624921.38.
    testString: assert.strictEqual(euler430(), 5000624921.38, '<code>euler430()</code> should return 5000624921.38.');

```

</section>

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

<div id='js-seed'>

```js
function euler430() {
  // Good luck!
  return true;
}

euler430();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>