freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-15-lattice-paths.md

---
id: 5900f37b1000cf542c50fe8e
title: 'Problem 15: Lattice paths'
challengeType: 5
forumTopicId: 301780
dashedName: problem-15-lattice-paths
---

# --description--

Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

<img class="img-responsive center-block" alt="a diagram of 6 2 by 2 grids showing all the routes to the bottom right corner" src="https://cdn-media-1.freecodecamp.org/project-euler/1Atixoj.gif" style="background-color: white; padding: 10px;">

How many such routes are there through a given `gridSize`?

# --hints--

`latticePaths(4)` should return a number.

```js
assert(typeof latticePaths(4) === 'number');
```

`latticePaths(4)` should return 70.

```js
assert.strictEqual(latticePaths(4), 70);
```

`latticePaths(9)` should return 48620.

```js
assert.strictEqual(latticePaths(9), 48620);
```

`latticePaths(20)` should return 137846528820.

```js
assert.strictEqual(latticePaths(20), 137846528820);
```

# --seed--

## --seed-contents--

```js
function latticePaths(gridSize) {

  return true;
}

latticePaths(4);
```

# --solutions--

```js
function latticePaths(gridSize) {
  let paths = 1;

  for (let i = 0; i < gridSize; i++) {
    paths *= (2 * gridSize) - i;
    paths /= i + 1;
  }
  return paths;
}
```
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 22:01:58 +00:00
+								---
 								id: 5900f37b1000cf542c50fe8e
 								title: 'Problem 15: Lattice paths'
-												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: 301780
-												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-15-lattice-paths
-												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
+								Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.
-												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
+								<img class="img-responsive center-block" alt="a diagram of 6 2 by 2 grids showing all the routes to the bottom right corner" src="https://cdn-media-1.freecodecamp.org/project-euler/1Atixoj.gif" style="background-color: white; padding: 10px;">
 								How many such routes are there through a given `gridSize`?
-												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
+								`latticePaths(4)` 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 latticePaths(4) === '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
+								`latticePaths(4)` should return 70.
-												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(latticePaths(4), 70);
 								```
 								`latticePaths(9)` should return 48620.
-												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(latticePaths(9), 48620);
-												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
+								`latticePaths(20)` should return 137846528820.
-												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(latticePaths(20), 137846528820);
 								```
 								# --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 latticePaths(gridSize) {
-												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;
 								}
 								latticePaths(4);
 								```
-												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
 								function latticePaths(gridSize) {
 								  let paths = 1;
 								  for (let i = 0; i < gridSize; i++) {
 								    paths *= (2 * gridSize) - i;
 								    paths /= i + 1;
 								  }
 								  return paths;
 								}
 								```