---
id: 5900f3d01000cf542c50fee3
challengeType: 5
title: 'Problem 100: Arranged probability'
forumTopicId: 301724
---

## Description
<section id='description'>
If a box contains twenty-one coloured discs, composed of fifteen blue discs and six red discs, and two discs were taken at random, it can be seen that the probability of taking two blue discs, P(BB) = (15/21)×(14/20) = 1/2.
The next such arrangement, for which there is exactly 50% chance of taking two blue discs at random, is a box containing eighty-five blue discs and thirty-five red discs.
By finding the first arrangement to contain over 1012 = 1,000,000,000,000 discs in total, determine the number of blue discs that the box would contain.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler100()</code> should return 756872327473.
    testString: assert.strictEqual(euler100(), 756872327473);

```

</section>

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

<div id='js-seed'>

```js
function euler100() {
  // Good luck!
  return true;
}

euler100();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>