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---
id: 5900f50a1000cf542c51001c
title: 'Problem 413: One-child Numbers'
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challengeType: 5
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forumTopicId: 302082
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dashedName: problem-413-one-child-numbers
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---
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# --description--
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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.
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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.
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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.
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Find F(1019).
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# --hints--
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`euler413()` should return 3079418648040719.
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```js
assert.strictEqual(euler413(), 3079418648040719);
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```
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# --seed--
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## --seed-contents--
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```js
function euler413() {
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return true;
}
euler413();
```
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# --solutions--
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```js
// solution required
```