---
id: 5900f48a1000cf542c50ff9d
challengeType: 5
title: 'Problem 286: Scoring probabilities'
---

## Description
<section id='description'>
Barbara is a mathematician and a basketball player. She has found that the probability of scoring a point when shooting from a distance x is exactly (1 - x/q), where q is a real constant greater than 50.

During each practice run, she takes shots from distances x = 1, x = 2, ..., x = 50 and, according to her records, she has precisely a 2 % chance to score a total of exactly 20 points.

Find q and give your answer rounded to 10 decimal places.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler286()</code> should return 52.6494571953.
    testString: assert.strictEqual(euler286(), 52.6494571953);

```

</section>

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

<div id='js-seed'>

```js
function euler286() {
  // Good luck!
  return true;
}

euler286();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>