89 lines
1.9 KiB
Markdown
89 lines
1.9 KiB
Markdown
---
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id: 5900f3721000cf542c50fe85
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challengeType: 5
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title: 'Problem 6: Sum square difference'
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forumTopicId: 302171
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---
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## Description
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<section id='description'>
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The sum of the squares of the first ten natural numbers is,
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<div style='text-align: center;'>1<sup>2</sup> + 2<sup>2</sup> + ... + 10<sup>2</sup> = 385</div>
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The square of the sum of the first ten natural numbers is,
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<div style='text-align: center;'>(1 + 2 + ... + 10)<sup>2</sup> = 55<sup>2</sup> = 3025</div>
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Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640.
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Find the difference between the sum of the squares of the first `n` natural numbers and the square of the sum.
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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>sumSquareDifference(10)</code> should return a number.
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testString: assert(typeof sumSquareDifference(10) === 'number');
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- text: <code>sumSquareDifference(10)</code> should return 2640.
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testString: assert.strictEqual(sumSquareDifference(10), 2640);
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- text: <code>sumSquareDifference(20)</code> should return 41230.
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testString: assert.strictEqual(sumSquareDifference(20), 41230);
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- text: <code>sumSquareDifference(100)</code> should return 25164150.
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testString: assert.strictEqual(sumSquareDifference(100), 25164150);
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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 sumSquareDifference(n) {
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return true;
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}
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sumSquareDifference(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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const sumSquareDifference = (number)=>{
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let squareOfSum = Math.pow(sumOfArithmeticSeries(1,1,number),2);
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let sumOfSquare = sumOfSquareOfNumbers(number);
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return squareOfSum - sumOfSquare;
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}
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function sumOfArithmeticSeries(a,d,n){
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return (n/2)*(2*a+(n-1)*d);
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}
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function sumOfSquareOfNumbers(n){
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return (n*(n+1)*(2*n+1))/6;
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}
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```
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</section>
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