75 lines
1.5 KiB
Markdown
75 lines
1.5 KiB
Markdown
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---
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id: 5900f3761000cf542c50fe88
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title: 'Problem 9: Special Pythagorean triplet'
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challengeType: 5
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forumTopicId: 302205
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dashedName: problem-9-special-pythagorean-triplet
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---
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# --description--
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A Pythagorean triplet is a set of three natural numbers, `a` < `b` < `c`, 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 `a` + `b` + `c` = 1000. Find the product `abc` such that `a` + `b` + `c` = `n`.
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# --hints--
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`specialPythagoreanTriplet(24)` should return a number.
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```js
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assert(typeof specialPythagoreanTriplet(24) === 'number');
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```
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`specialPythagoreanTriplet(24)` should return 480.
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```js
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assert.strictEqual(specialPythagoreanTriplet(24), 480);
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```
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`specialPythagoreanTriplet(120)` should return 49920, 55080 or 60000
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```js
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assert([49920, 55080, 60000].includes(specialPythagoreanTriplet(120)));
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```
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`specialPythagoreanTriplet(1000)` should return 31875000.
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```js
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assert.strictEqual(specialPythagoreanTriplet(1000), 31875000);
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```
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# --seed--
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## --seed-contents--
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```js
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function specialPythagoreanTriplet(n) {
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let sumOfabc = n;
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return true;
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}
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specialPythagoreanTriplet(1000);
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```
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# --solutions--
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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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