---
id: 5900f3fd1000cf542c50ff10
title: 'Problem 145: How many reversible numbers are there below one-billion?'
challengeType: 5
forumTopicId: 301774
dashedName: problem-145-how-many-reversible-numbers-are-there-below-one-billion
---

# --description--

Some positive integers $n$ have the property that the sum [ $n + reverse(n)$ ] consists entirely of odd (decimal) digits. For instance, $36 + 63 = 99$ and $409 + 904 = 1313$. We will call such numbers reversible; so 36, 63, 409, and 904 are reversible. Leading zeroes are not allowed in either $n$ or $reverse(n)$.

There are 120 reversible numbers below one-thousand.

How many reversible numbers are there below one-billion (${10}^9$)?

# --hints--

`reversibleNumbers()` should return `608720`.

```js
assert.strictEqual(reversibleNumbers(), 608720);
```

# --seed--

## --seed-contents--

```js
function reversibleNumbers() {

  return true;
}

reversibleNumbers();
```

# --solutions--

```js
// solution required
```