78 lines
1.8 KiB
Markdown
78 lines
1.8 KiB
Markdown
---
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id: 5900f3761000cf542c50fe88
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challengeType: 5
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title: 'Problem 9: Special Pythagorean triplet'
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forumTopicId: 302205
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---
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## Description
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<section id='description'>
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A Pythagorean triplet is a set of three natural numbers, <var>a</var> < <var>b</var> < <var>c</var>, for which,
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<div style='text-align: center;'><var>a</var><sup>2</sup> + <var>b</var><sup>2</sup> = <var>c</var><sup>2</sup></div>
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For example, 3<sup>2</sup> + 4<sup>2</sup> = 9 + 16 = 25 = 5<sup>2</sup>.
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There exists exactly one Pythagorean triplet for which <var>a</var> + <var>b</var> + <var>c</var> = 1000. Find the product <var>abc</var> such that <var>a</var> + <var>b</var> + <var>c</var> = <code>n</code>.
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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>specialPythagoreanTriplet(1000)</code> should return 31875000.
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testString: assert.strictEqual(specialPythagoreanTriplet(1000), 31875000);
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- text: <code>specialPythagoreanTriplet(24)</code> should return 480.
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testString: assert.strictEqual(specialPythagoreanTriplet(24), 480);
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- text: <code>specialPythagoreanTriplet(120)</code> should return 49920, 55080 or 60000
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testString: assert([49920, 55080, 60000].includes(specialPythagoreanTriplet(120)));
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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 specialPythagoreanTriplet(n) {
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let sumOfabc = n;
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// Good luck!
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return true;
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}
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specialPythagoreanTriplet(1000);
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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 specialPythagoreanTriplet = (n)=>{
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let sumOfabc = n;
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let a,b,c;
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for(a = 1; a<=sumOfabc/3; a++){
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for(b = a+1; b<=sumOfabc/2; b++){
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c = Math.sqrt(a*a+b*b);
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if((a+b+c) == sumOfabc){
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return a*b*c;
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}
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}
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}
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}
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```
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</section>
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