freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-149-searching-for-a-maximum-sum-subsequence.md

---
id: 5900f4021000cf542c50ff13
title: 'Problem 149: Searching for a maximum-sum subsequence'
challengeType: 5
forumTopicId: 301778
---

# --description--

Looking at the table below, it is easy to verify that the maximum possible sum of adjacent numbers in any direction (horizontal, vertical, diagonal or anti-diagonal) is 16 (= 8 + 7 + 1).

−25329−6513273−18−4 8

Now, let us repeat the search, but on a much larger scale:

First, generate four million pseudo-random numbers using a specific form of what is known as a "Lagged Fibonacci Generator":

For 1 ≤ k ≤ 55, sk = \[100003 − 200003k + 300007k3] (modulo 1000000) − 500000. For 56 ≤ k ≤ 4000000, sk = \[sk−24 + sk−55 + 1000000] (modulo 1000000) − 500000.

Thus, s10 = −393027 and s100 = 86613.

The terms of s are then arranged in a 2000×2000 table, using the first 2000 numbers to fill the first row (sequentially), the next 2000 numbers to fill the second row, and so on.

Finally, find the greatest sum of (any number of) adjacent entries in any direction (horizontal, vertical, diagonal or anti-diagonal).

# --hints--

`euler149()` should return 52852124.

```js
assert.strictEqual(euler149(), 52852124);
```

# --seed--

## --seed-contents--

```js
function euler149() {

  return true;
}

euler149();
```

# --solutions--

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

											
										
										
											2018-09-30 23:01:58 +01:00
+								---
 								id: 5900f4021000cf542c50ff13
 								title: 'Problem 149: Searching for a maximum-sum subsequence'
-												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: 301778
-												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
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								Looking at the table below, it is easy to verify that the maximum possible sum of adjacent numbers in any direction (horizontal, vertical, diagonal or anti-diagonal) is 16 (= 8 + 7 + 1).
-												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
+								−25329−6513273−18−4 8
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
 								Now, let us repeat the search, but on a much larger scale:
 								First, generate four million pseudo-random numbers using a specific form of what is known as a "Lagged Fibonacci Generator":
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								For 1 ≤ k ≤ 55, sk = \[100003 − 200003k + 300007k3] (modulo 1000000) − 500000. For 56 ≤ k ≤ 4000000, sk = \[sk−24 + sk−55 + 1000000] (modulo 1000000) − 500000.
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
 								Thus, s10 = −393027 and s100 = 86613.
 								The terms of s are then arranged in a 2000×2000 table, using the first 2000 numbers to fill the first row (sequentially), the next 2000 numbers to fill the second row, and so on.
 								Finally, find the greatest sum of (any number of) adjacent entries in any direction (horizontal, vertical, diagonal or anti-diagonal).
-												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
+								`euler149()` should return 52852124.
-												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(euler149(), 52852124);
-												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 euler149() {
-												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;
 								}
 								euler149();
 								```
-												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
 								```