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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.
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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 $F(10) = 9$, $F({10}^3) = 389$ and $F({10}^7) = 277\\,674$.
Find $F({10}^{19})$.
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# --hints--
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`oneChildNumbers()` should return `3079418648040719` .
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```js
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assert.strictEqual(oneChildNumbers(), 3079418648040719);
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```
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# --seed--
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## --seed-contents--
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```js
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function oneChildNumbers() {
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return true;
}
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oneChildNumbers();
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```
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# --solutions--
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```js
// solution required
```