freeCodeCamp/curriculum/challenges/portuguese/10-coding-interview-prep/project-euler/problem-76-counting-summations.md

id	title	challengeType	forumTopicId	dashedName
5900f3b81000cf542c50fecb	Problem 76: Counting summations	5	302189	problem-76-counting-summations

--description--

It is possible to write five as a sum in exactly six different ways:

4 + 1
3 + 2
3 + 1 + 1
2 + 2 + 1
2 + 1 + 1 + 1
1 + 1 + 1 + 1 + 1

How many different ways can n be written as a sum of at least two positive integers?

--hints--

countingSummations(5) should return a number.

assert(typeof countingSummations(5) === 'number');

countingSummations(5) should return 6.

assert.strictEqual(countingSummations(5), 6);

countingSummations(20) should return 626.

assert.strictEqual(countingSummations(20), 626);

countingSummations(50) should return 204225.

assert.strictEqual(countingSummations(50), 204225);

countingSummations(100) should return 190569291.

assert.strictEqual(countingSummations(100), 190569291);

--seed--

--seed-contents--

function countingSummations(n) {

  return true;
}

countingSummations(5);

--solutions--

function countingSummations(n) {
  const combinations = new Array(n + 1).fill(0);
  combinations[0] = 1;

  for (let i = 1; i < n; i++) {
    for (let j = i; j < n + 1; j++) {
      combinations[j] += combinations[j - i];
    }
  }
  return combinations[n];
}