47 lines
1.1 KiB
Markdown
47 lines
1.1 KiB
Markdown
---
|
|
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
|
|
```
|