---
id: 5900f3dd1000cf542c50feef
title: 'Problem 112: Bouncy numbers'
challengeType: 5
forumTopicId: 301738
dashedName: problem-112-bouncy-numbers
---

# --description--

Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.

Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420.

We shall call a positive integer that is neither increasing nor decreasing a "bouncy" number; for example, 155349.

Clearly there cannot be any bouncy numbers below one-hundred, but just over half of the numbers below one-thousand (525) are bouncy. In fact, the least number for which the proportion of bouncy numbers first reaches 50% is 538.

Surprisingly, bouncy numbers become more and more common and by the time we reach 21780 the proportion of bouncy numbers is equal to 90%.

Find the least number for which the proportion of bouncy numbers is exactly 99%.

# --hints--

`bouncyNumbers()` should return `1587000`.

```js
assert.strictEqual(bouncyNumbers(), 1587000);
```

# --seed--

## --seed-contents--

```js
function bouncyNumbers() {

  return true;
}

bouncyNumbers();
```

# --solutions--

```js
// solution required
```
