freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-78-coin-partitions.md

---
id: 5900f3ba1000cf542c50fecd
title: 'Problem 78: Coin partitions'
challengeType: 5
forumTopicId: 302191
dashedName: problem-78-coin-partitions
---

# --description--

Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can be separated into piles in exactly seven different ways, so p(5)=7.

<div style='text-align: center;'>

| Coin piles        |
| ----------------- |
| OOOOO             |
| OOOO   O          |
| OOO   OO          |
| OOO   O   O       |
| OO   OO   O       |
| OO   O   O   O    |
| O   O   O   O   O |

</div>

Find the least value of `n` for which p(`n`) is divisible by one million.

# --hints--

`coinPartitions()` should return a number.

```js
assert(typeof coinPartitions() === 'number');
```

`coinPartitions()` should return 55374.

```js
assert.strictEqual(coinPartitions(), 55374);
```

# --seed--

## --seed-contents--

```js
function coinPartitions() {

  return true;
}

coinPartitions();
```

# --solutions--

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

											
										
										
											2018-09-30 22:01:58 +00:00
+								---
 								id: 5900f3ba1000cf542c50fecd
 								title: 'Problem 78: Coin partitions'
-												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: 302191
-												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-78-coin-partitions
-												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--
-												fix: improve Project Euler descriptions, challenge seeds, and test cases (#38016)

* fix: improve Project Euler descriptions and test case

Improve formatting of Project Euler test descriptions. Also add poker hands array and new test case for problem 54

* feat: add typeof tests and gave functions proper names for first 100 challenges

* fix: continue fixing test descriptions and adding "before test" sections

* fix: address review comments

* fix: adjust grids in 18 and 67 and fix some text that reference files rather than the given arrays

* fix: implement bug fixes and improvements from review

* fix: remove console.log statements from seed and solution

											
										
										
											2020-02-28 12:39:47 +00:00
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 22:01:58 +00:00
+								Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can be separated into piles in exactly seven different ways, so p(5)=7.
-												feat: add styles for markdown tables and convert some HTML tables to markdown (#38126)


											
										
										
											2020-02-07 08:47:35 +00:00
+								<div style='text-align: center;'>
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 18:02:05 +00:00
+								| Coin piles        |
 								| ----------------- |
 								| OOOOO             |
 								| OOOO   O          |
 								| OOO   OO          |
 								| OOO   O   O       |
 								| OO   OO   O       |
 								| OO   O   O   O    |
 								| O   O   O   O   O |
-												feat: add styles for markdown tables and convert some HTML tables to markdown (#38126)


											
										
										
											2020-02-07 08:47:35 +00:00
 								</div>
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 18:02:05 +00:00
+								Find the least value of `n` for which p(`n`) is divisible by one million.
-												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
+								`coinPartitions()` should return a number.
-												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(typeof coinPartitions() === 'number');
 								```
-												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
+								`coinPartitions()` should return 55374.
-												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(coinPartitions(), 55374);
-												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
-												fix: improve Project Euler descriptions, challenge seeds, and test cases (#38016)

* fix: improve Project Euler descriptions and test case

Improve formatting of Project Euler test descriptions. Also add poker hands array and new test case for problem 54

* feat: add typeof tests and gave functions proper names for first 100 challenges

* fix: continue fixing test descriptions and adding "before test" sections

* fix: address review comments

* fix: adjust grids in 18 and 67 and fix some text that reference files rather than the given arrays

* fix: implement bug fixes and improvements from review

* fix: remove console.log statements from seed and solution

											
										
										
											2020-02-28 12:39:47 +00:00
+								function coinPartitions() {
-												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;
 								}
-												fix: improve Project Euler descriptions, challenge seeds, and test cases (#38016)

* fix: improve Project Euler descriptions and test case

Improve formatting of Project Euler test descriptions. Also add poker hands array and new test case for problem 54

* feat: add typeof tests and gave functions proper names for first 100 challenges

* fix: continue fixing test descriptions and adding "before test" sections

* fix: address review comments

* fix: adjust grids in 18 and 67 and fix some text that reference files rather than the given arrays

* fix: implement bug fixes and improvements from review

* fix: remove console.log statements from seed and solution

											
										
										
											2020-02-28 12:39:47 +00:00
+								coinPartitions();
-												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
+								# --solutions--
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 22:01:58 +00:00
 								```js
 								// solution required
 								```