diff --git a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-76-counting-summations.md b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-76-counting-summations.md index dded902e52..bbc9618245 100644 --- a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-76-counting-summations.md +++ b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-76-counting-summations.md @@ -16,23 +16,41 @@ It is possible to write five as a sum in exactly six different ways: 3 + 1 + 1
2 + 2 + 1
2 + 1 + 1 + 1
- 1 + 1 + 1 + 1 + 1
+ 1 + 1 + 1 + 1 + 1

-How many different ways can one hundred be written as a sum of at least two positive integers? +How many different ways can `n` be written as a sum of at least two positive integers? # --hints-- -`countingSummations()` should return a number. +`countingSummations(5)` should return a number. ```js -assert(typeof countingSummations() === 'number'); +assert(typeof countingSummations(5) === 'number'); ``` -`countingSummations()` should return 190569291. +`countingSummations(5)` should return `6`. ```js -assert.strictEqual(countingSummations(), 190569291); +assert.strictEqual(countingSummations(5), 6); +``` + +`countingSummations(20)` should return `626`. + +```js +assert.strictEqual(countingSummations(20), 626); +``` + +`countingSummations(50)` should return `204225`. + +```js +assert.strictEqual(countingSummations(50), 204225); +``` + +`countingSummations(100)` should return `190569291`. + +```js +assert.strictEqual(countingSummations(100), 190569291); ``` # --seed-- @@ -40,16 +58,26 @@ assert.strictEqual(countingSummations(), 190569291); ## --seed-contents-- ```js -function countingSummations() { +function countingSummations(n) { return true; } -countingSummations(); +countingSummations(5); ``` # --solutions-- ```js -// solution required +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]; +} ```