freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-139-pythagorean-til...

---
id: 5900f3f71000cf542c50ff0a
title: 'Problem 139: Pythagorean tiles'
challengeType: 5
forumTopicId: 301767
---

# --description--

Let (a, b, c) represent the three sides of a right angle triangle with integral length sides. It is possible to place four such triangles together to form a square with length c.

For example, (3, 4, 5) triangles can be placed together to form a 5 by 5 square with a 1 by 1 hole in the middle and it can be seen that the 5 by 5 square can be tiled with twenty-five 1 by 1 squares.

However, if (5, 12, 13) triangles were used then the hole would measure 7 by 7 and these could not be used to tile the 13 by 13 square. Given that the perimeter of the right triangle is less than one-hundred million, how many Pythagorean triangles would allow such a tiling to take place?

# --hints--

`euler139()` should return 10057761.

```js
assert.strictEqual(euler139(), 10057761);
```

# --seed--

## --seed-contents--

```js
function euler139() {

  return true;
}

euler139();
```

# --solutions--

```js
// solution required
```
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			`---`
			`id: 5900f3f71000cf542c50ff0a`
			`title: 'Problem 139: Pythagorean tiles'`
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`challengeType: 5`
fix(curriculum): Added forumTopicId to remaining 1200 challeng… (#36558) 2019-08-05 16:17:33 +00:00			`forumTopicId: 301767`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			`---`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --description--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`Let (a, b, c) represent the three sides of a right angle triangle with integral length sides. It is possible to place four such triangles together to form a square with length c.`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`For example, (3, 4, 5) triangles can be placed together to form a 5 by 5 square with a 1 by 1 hole in the middle and it can be seen that the 5 by 5 square can be tiled with twenty-five 1 by 1 squares.`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`However, if (5, 12, 13) triangles were used then the hole would measure 7 by 7 and these could not be used to tile the 13 by 13 square. Given that the perimeter of the right triangle is less than one-hundred million, how many Pythagorean triangles would allow such a tiling to take place?`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --hints--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`euler139()` should return 10057761.
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			```js
			`assert.strictEqual(euler139(), 10057761);`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			```

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --seed--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`## --seed-contents--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
			```js
			`function euler139() {`
fix: remove Good luck! comment from challenge seed code (#39575) 2020-09-15 16:57:40 +00:00
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			`return true;`
			`}`

			`euler139();`
			```

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --solutions--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
			```js
			`// solution required`
			```