diff --git a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-38-pandigital-multiples.md b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-38-pandigital-multiples.md index e0ccd868bb..e385d29d0f 100644 --- a/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-38-pandigital-multiples.md +++ b/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-38-pandigital-multiples.md @@ -10,30 +10,36 @@ dashedName: problem-38-pandigital-multiples Take the number 192 and multiply it by each of 1, 2, and 3: -
- 192 × 1 = 192
- 192 × 2 = 384
- 192 × 3 = 576
-
+$$\begin{align} + 192 × 1 = 192\\\\ + 192 × 2 = 384\\\\ + 192 × 3 = 576\\\\ +\end{align}$$ By concatenating each product we get the 1 to 9 pandigital, 192384576. We will call 192384576 the concatenated product of 192 and (1, 2, 3). The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4, and 5, giving the pandigital, 918273645, which is the concatenated product of 9 and (1, 2, 3, 4, 5). -What is the largest 1 to 9 pandigital 9-digit number that can be formed as the concatenated product of an integer with (1, 2, ... , `n`) where `n` > 1? +What is the largest 1 to `k` pandigital `k`-digit number that can be formed as the concatenated product of an integer with (1, 2, ..., `n`) where `n` > 1? # --hints-- -`pandigitalMultiples()` should return a number. +`pandigitalMultiples(8)` should return a number. ```js -assert(typeof pandigitalMultiples() === 'number'); +assert(typeof pandigitalMultiples(8) === 'number'); ``` -`pandigitalMultiples()` should return 932718654. +`pandigitalMultiples(8)` should return `78156234`. ```js -assert.strictEqual(pandigitalMultiples(), 932718654); +assert.strictEqual(pandigitalMultiples(8), 78156234); +``` + +`pandigitalMultiples(9)` should return `932718654`. + +```js +assert.strictEqual(pandigitalMultiples(9), 932718654); ``` # --seed-- @@ -41,38 +47,37 @@ assert.strictEqual(pandigitalMultiples(), 932718654); ## --seed-contents-- ```js -function pandigitalMultiples() { +function pandigitalMultiples(k) { return true; } -pandigitalMultiples(); +pandigitalMultiples(8); ``` # --solutions-- ```js -function pandigitalMultiples() { - - function get9DigitConcatenatedProduct(num) { - // returns false if concatenated product is not 9 digits +function pandigitalMultiples(k) { + function getKDigitConcatenatedProduct(num, k) { + // returns false if concatenated product is not k digits let concatenatedProduct = num.toString(); - for (let i = 2; concatenatedProduct.length < 9; i++) { + for (let i = 2; concatenatedProduct.length < k; i++) { concatenatedProduct += num * i; } - return concatenatedProduct.length === 9 ? concatenatedProduct : false; + return concatenatedProduct.length === k ? concatenatedProduct : false; } - function is1to9Pandigital(num) { + function is1toKPandigital(num, k) { const numStr = num.toString(); - // check if length is not 9 - if (numStr.length !== 9) { + // check if length is not k + if (numStr.length !== k) { return false; } // check if pandigital - for (let i = 9; i > 0; i--) { + for (let i = k; i > 0; i--) { if (numStr.indexOf(i.toString()) === -1) { return false; } @@ -81,11 +86,13 @@ function pandigitalMultiples() { } let largestNum = 0; - for (let i = 9999; i >= 9000; i--) { - const concatenatedProduct = get9DigitConcatenatedProduct(i); - if (is1to9Pandigital(concatenatedProduct) && concatenatedProduct > largestNum) { - largestNum = parseInt(concatenatedProduct); - break; + for (let i = 10 ** Math.floor(k / 2) + 1; i >= 1; i--) { + const concatenatedProduct = getKDigitConcatenatedProduct(i, k); + if (is1toKPandigital(concatenatedProduct, k)) { + const number = parseInt(concatenatedProduct, 10); + if (number > largestNum) { + largestNum = number; + } } } return largestNum;