freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-150-searching-a-triangular-array-for-a-sub-triangle-having-minimum-sum.md

---
id: 5900f4031000cf542c50ff15
title: >-
  Problem 150: Searching a triangular array for a sub-triangle having
  minimum-sum
challengeType: 5
forumTopicId: 301781
---

# --description--

In a triangular array of positive and negative integers, we wish to find a sub-triangle such that the sum of the numbers it contains is the smallest possible.

In the example below, it can be easily verified that the marked triangle satisfies this condition having a sum of −42.

We wish to make such a triangular array with one thousand rows, so we generate 500500 pseudo-random numbers sk in the range ±219, using a type of random number generator (known as a Linear Congruential Generator) as follows: t := 0

for k = 1 up to k = 500500:

t := (615949\*t + 797807) modulo 220 sk := t−219 Thus: s1 = 273519, s2 = −153582, s3 = 450905 etc Our triangular array is then formed using the pseudo-random numbers thus:

s1 s2 s3 s4 s5 s6

s7 s8 s9 s10 ...

Sub-triangles can start at any element of the array and extend down as far as we like (taking-in the two elements directly below it from the next row, the three elements directly below from the row after that, and so on).

The "sum of a sub-triangle" is defined as the sum of all the elements it contains.

Find the smallest possible sub-triangle sum.

# --hints--

`euler150()` should return -271248680.

```js
assert.strictEqual(euler150(), -271248680);
```

# --seed--

## --seed-contents--

```js
function euler150() {

  return true;
}

euler150();
```

# --solutions--

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

											
										
										
											2018-09-30 23:01:58 +01:00
+								---
 								id: 5900f4031000cf542c50ff15
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								title: >-
 								  Problem 150: Searching a triangular array for a sub-triangle having
 								  minimum-sum
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
+								challengeType: 5
-												fix(curriculum): Added forumTopicId to remaining 1200 challeng… (#36558)


											
										
										
											2019-08-05 09:17:33 -07:00
+								forumTopicId: 301781
-												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
+								In a triangular array of positive and negative integers, we wish to find a sub-triangle such that the sum of the numbers it contains is the smallest possible.
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								In the example below, it can be easily verified that the marked triangle satisfies this condition having a sum of −42.
-												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
+								We wish to make such a triangular array with one thousand rows, so we generate 500500 pseudo-random numbers sk in the range ±219, using a type of random number generator (known as a Linear Congruential Generator) as follows: t := 0
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
 								for k = 1 up to k = 500500:
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								t := (615949\*t + 797807) modulo 220 sk := t−219 Thus: s1 = 273519, s2 = −153582, s3 = 450905 etc Our triangular array is then formed using the pseudo-random numbers thus:
-												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
+								s1 s2 s3 s4 s5 s6
-												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
+								s7 s8 s9 s10 ...
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
 								Sub-triangles can start at any element of the array and extend down as far as we like (taking-in the two elements directly below it from the next row, the three elements directly below from the row after that, and so on).
 								The "sum of a sub-triangle" is defined as the sum of all the elements it contains.
 								Find the smallest possible sub-triangle sum.
-												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
+								`euler150()` should return -271248680.
-												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(euler150(), -271248680);
-												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 euler150() {
-												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;
 								}
 								euler150();
 								```
-												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
 								```