---
id: 5900f50a1000cf542c51001c
title: 'Problem 413: One-child Numbers'
challengeType: 5
forumTopicId: 302082
dashedName: problem-413-one-child-numbers
---

# --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 $F(10) = 9$, $F({10}^3) = 389$ and $F({10}^7) = 277\\,674$.

Find $F({10}^{19})$.

# --hints--

`oneChildNumbers()` should return `3079418648040719`.

```js
assert.strictEqual(oneChildNumbers(), 3079418648040719);
```

# --seed--

## --seed-contents--

```js
function oneChildNumbers() {

  return true;
}

oneChildNumbers();
```

# --solutions--

```js
// solution required
```