78 lines
1.6 KiB
Markdown
78 lines
1.6 KiB
Markdown
---
|
||
id: 5900f3941000cf542c50fea7
|
||
title: 'Problem 40: Champernowne''s constant'
|
||
challengeType: 5
|
||
forumTopicId: 302066
|
||
dashedName: problem-40-champernownes-constant
|
||
---
|
||
|
||
# --description--
|
||
|
||
An irrational decimal fraction is created by concatenating the positive integers:
|
||
|
||
0.12345678910**1**112131415161718192021...
|
||
|
||
It can be seen that the 12<sup>th</sup> digit of the fractional part is 1.
|
||
|
||
If *d<sub>n</sub>* represents the *n*<sup>th</sup> digit of the fractional part, find the value of the following expression.
|
||
|
||
d<sub>1</sub> × d<sub>10</sub> × d<sub>100</sub> × d<sub>1000</sub> × d<sub>10000</sub> × d<sub>100000</sub> × d<sub>1000000</sub>
|
||
|
||
# --hints--
|
||
|
||
`champernownesConstant(100)` should return a number.
|
||
|
||
```js
|
||
assert(typeof champernownesConstant(100) === 'number');
|
||
```
|
||
|
||
`champernownesConstant(100)` should return 5.
|
||
|
||
```js
|
||
assert.strictEqual(champernownesConstant(100), 5);
|
||
```
|
||
|
||
`champernownesConstant(1000)` should return 15.
|
||
|
||
```js
|
||
assert.strictEqual(champernownesConstant(1000), 15);
|
||
```
|
||
|
||
`champernownesConstant(1000000)` should return 210.
|
||
|
||
```js
|
||
assert.strictEqual(champernownesConstant(1000000), 210);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function champernownesConstant(n) {
|
||
|
||
return true;
|
||
}
|
||
|
||
champernownesConstant(100);
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
function champernownesConstant(n) {
|
||
let fractionalPart = '';
|
||
for (let i = 0; fractionalPart.length <= n; i++) {
|
||
fractionalPart += i.toString();
|
||
}
|
||
|
||
let product = 1;
|
||
for (let i = 0; i < n.toString().length; i++) {
|
||
const index = 10 ** i;
|
||
product *= parseInt(fractionalPart[index], 10);
|
||
}
|
||
|
||
return product;
|
||
}
|
||
```
|