80 lines
1.9 KiB
Markdown
80 lines
1.9 KiB
Markdown
---
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id: 5900f3941000cf542c50fea7
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challengeType: 5
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title: 'Problem 40: Champernowne''s constant'
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forumTopicId: 302066
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---
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## Description
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<section id='description'>
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An irrational decimal fraction is created by concatenating the positive integers:
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<span style='display: block; text-align: center;'>0.12345678910<b style='color: red;'>1</b>112131415161718192021...</span>
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It can be seen that the 12<sup>th</sup> digit of the fractional part is 1.
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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.
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<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>
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>champernownesConstant(100)</code> should return 5.
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testString: assert.strictEqual(champernownesConstant(100), 5);
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- text: <code>champernownesConstant(1000)</code> should return 15.
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testString: assert.strictEqual(champernownesConstant(1000), 15);
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- text: <code>champernownesConstant(1000000)</code> should return 210.
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testString: assert.strictEqual(champernownesConstant(1000000), 210);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function champernownesConstant(n) {
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// Good luck!
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return true;
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}
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champernownesConstant(100);
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function champernownesConstant(n) {
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let fractionalPart = '';
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for (let i = 0; fractionalPart.length <= n; i++) {
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fractionalPart += i.toString();
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}
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let product = 1;
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for (let i = 0; i < n.toString().length; i++) {
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const index = 10 ** i;
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product *= parseInt(fractionalPart[index], 10);
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}
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return product;
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}
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```
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</section>
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