---
id: 5900f50a1000cf542c51001c
challengeType: 5
title: 'Problem 413: One-child Numbers'
---

## Description
<section id='description'>
We say that a d-digit positive number (no leading zeros) is a one-child number if exactly one of its sub-strings is divisible by d.

For example, 5671 is a 4-digit one-child number. Among all its sub-strings 5, 6, 7, 1, 56, 67, 71, 567, 671 and 5671, only 56 is divisible by 4.
Similarly, 104 is a 3-digit one-child number because only 0 is divisible by 3.
1132451 is a 7-digit one-child number because only 245 is divisible by 7.

Let F(N) be the number of the one-child numbers less than N.
We can verify that F(10) = 9, F(103) = 389 and F(107) = 277674.

Find F(1019).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler413()</code> should return 3079418648040719.
    testString: assert.strictEqual(euler413(), 3079418648040719, '<code>euler413()</code> should return 3079418648040719.');

```

</section>

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

<div id='js-seed'>

```js
function euler413() {
  // Good luck!
  return true;
}

euler413();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>