freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-218-perfect-right-angled-triangles.md

---
id: 5900f4461000cf542c50ff59
title: 'Problem 218: Perfect right-angled triangles'
challengeType: 5
forumTopicId: 301860
dashedName: problem-218-perfect-right-angled-triangles
---

# --description--

Consider the right angled triangle with sides a=7, b=24 and c=25.

The area of this triangle is 84, which is divisible by the perfect numbers 6 and 28.

Moreover it is a primitive right angled triangle as gcd(a,b)=1 and gcd(b,c)=1.

Also c is a perfect square.

We will call a right angled triangle perfect if -it is a primitive right angled triangle -its hypotenuse is a perfect square

We will call a right angled triangle super-perfect if -it is a perfect right angled triangle and -its area is a multiple of the perfect numbers 6 and 28.

How many perfect right-angled triangles with c≤1016 exist that are not super-perfect?

# --hints--

`euler218()` should return 0.

```js
assert.strictEqual(euler218(), 0);
```

# --seed--

## --seed-contents--

```js
function euler218() {

  return true;
}

euler218();
```

# --solutions--

```js
// solution required
```
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`---`
			`id: 5900f4461000cf542c50ff59`
			`title: 'Problem 218: Perfect right-angled triangles'`
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`challengeType: 5`
fix(curriculum): Added forumTopicId to remaining 1200 challeng… (#36558) 2019-08-05 09:17:33 -07:00			`forumTopicId: 301860`
feat(curriculum): restore seed + solution to Chinese (#40683) * feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com> 2021-01-13 03:31:00 +01:00			`dashedName: problem-218-perfect-right-angled-triangles`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`---`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --description--`

feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`Consider the right angled triangle with sides a=7, b=24 and c=25.`
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`The area of this triangle is 84, which is divisible by the perfect numbers 6 and 28.`
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`Moreover it is a primitive right angled triangle as gcd(a,b)=1 and gcd(b,c)=1.`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`Also c is a perfect square.`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`We will call a right angled triangle perfect if -it is a primitive right angled triangle -its hypotenuse is a perfect square`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`We will call a right angled triangle super-perfect if -it is a perfect right angled triangle and -its area is a multiple of the perfect numbers 6 and 28.`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
			`How many perfect right-angled triangles with c≤1016 exist that are not super-perfect?`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --hints--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`euler218()` should return 0.
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			```js
			`assert.strictEqual(euler218(), 0);`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			```

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --seed--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`## --seed-contents--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
			```js
			`function euler218() {`
fix: remove Good luck! comment from challenge seed code (#39575) 2020-09-15 09:57:40 -07:00
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`return true;`
			`}`

			`euler218();`
			```

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --solutions--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
			```js
			`// solution required`
			```