79 lines
2.0 KiB
Markdown
79 lines
2.0 KiB
Markdown
---
|
||
id: 5900f3941000cf542c50fea7
|
||
challengeType: 5
|
||
title: 'Problem 40: Champernowne''s constant'
|
||
---
|
||
|
||
## Description
|
||
<section id='description'>
|
||
An irrational decimal fraction is created by concatenating the positive integers:
|
||
<span style='display: block; text-align: center;'>0.12345678910<b style='color: red;'>1</b>112131415161718192021...</span>
|
||
It can be seen that the 12<sup>th</sup> digit of the fractional part is 1.
|
||
If <i>d<sub>n</sub></i> represents the <i>n</i><sup>th</sup> digit of the fractional part, find the value of the following expression.
|
||
<span style='display: block; text-align: center;'>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></span>
|
||
</section>
|
||
|
||
## Instructions
|
||
<section id='instructions'>
|
||
|
||
</section>
|
||
|
||
## Tests
|
||
<section id='tests'>
|
||
|
||
```yml
|
||
tests:
|
||
- text: <code>champernownesConstant(100)</code> should return 5.
|
||
testString: assert.strictEqual(champernownesConstant(100), 5, '<code>champernownesConstant(100)</code> should return 5.');
|
||
- text: <code>champernownesConstant(1000)</code> should return 15.
|
||
testString: assert.strictEqual(champernownesConstant(1000), 15, '<code>champernownesConstant(1000)</code> should return 15.');
|
||
- text: <code>champernownesConstant(1000000)</code> should return 210.
|
||
testString: assert.strictEqual(champernownesConstant(1000000), 210, '<code>champernownesConstant(1000000)</code> should return 210.');
|
||
|
||
```
|
||
|
||
</section>
|
||
|
||
## Challenge Seed
|
||
<section id='challengeSeed'>
|
||
|
||
<div id='js-seed'>
|
||
|
||
```js
|
||
function champernownesConstant(n) {
|
||
// Good luck!
|
||
return true;
|
||
}
|
||
|
||
champernownesConstant(100);
|
||
```
|
||
|
||
</div>
|
||
|
||
|
||
|
||
</section>
|
||
|
||
## Solution
|
||
<section id='solution'>
|
||
|
||
|
||
```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;
|
||
}
|
||
```
|
||
|
||
</section>
|