freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-229-four-representa...

---
id: 5900f4521000cf542c50ff64
title: 'Problem 229: Four Representations using Squares'
challengeType: 5
forumTopicId: 301872
dashedName: problem-229-four-representations-using-squares
---

# --description--

Consider the number 3600. It is very special, because

3600 = 482 + 362 3600 = 202 + 2×402 3600 = 302 + 3×302 3600 = 452 + 7×152

Similarly, we find that 88201 = 992 + 2802 = 2872 + 2×542 = 2832 + 3×522 = 1972 + 7×842.

In 1747, Euler proved which numbers are representable as a sum of two squares. We are interested in the numbers n which admit representations of all of the following four types:

n = a12 + b12n = a22 + 2 b22n = a32 + 3 b32n = a72 + 7 b72,

where the ak and bk are positive integers.

There are 75373 such numbers that do not exceed 107.

How many such numbers are there that do not exceed 2×109?

# --hints--

`euler229()` should return 11325263.

```js
assert.strictEqual(euler229(), 11325263);
```

# --seed--

## --seed-contents--

```js
function euler229() {

  return true;
}

euler229();
```

# --solutions--

```js
// solution required
```
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 22:01:58 +00:00
+								---
 								id: 5900f4521000cf542c50ff64
 								title: 'Problem 229: Four Representations using Squares'
-												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: 301872
-												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 02:31:00 +00:00
+								dashedName: problem-229-four-representations-using-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
+								# --description--
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 22:01:58 +00:00
+								Consider the number 3600. It is very special, because
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 18:02:05 +00:00
+= 482 + 362 3600 = 202 + 2×402 3600 = 302 + 3×302 3600 = 452 + 7×152
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 22:01:58 +00:00
 								Similarly, we find that 88201 = 992 + 2802 = 2872 + 2×542 = 2832 + 3×522 = 1972 + 7×842.
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 18:02:05 +00:00
+								In 1747, Euler proved which numbers are representable as a sum of two squares. We are interested in the numbers n which admit representations of all of the following four types:
-												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
+								n = a12 + b12n = a22 + 2 b22n = a32 + 3 b32n = a72 + 7 b72,
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 22:01:58 +00:00
 								where the ak and bk are positive integers.
 								There are 75373 such numbers that do not exceed 107.
 								How many such numbers are there that do not exceed 2×109?
-												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
+								`euler229()` should return 11325263.
-												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(euler229(), 11325263);
-												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 euler229() {
-												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;
 								}
 								euler229();
 								```
-												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
 								```