989347387f
* fix: rework challenge to use argument in function * fix: update solution to challenge changes * fix: use MathJax to improve look of math notation
101 lines
2.3 KiB
Markdown
101 lines
2.3 KiB
Markdown
---
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id: 5900f3931000cf542c50fea5
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title: 'Problem 38: Pandigital multiples'
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challengeType: 5
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forumTopicId: 302042
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dashedName: problem-38-pandigital-multiples
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---
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# --description--
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Take the number 192 and multiply it by each of 1, 2, and 3:
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$$\begin{align}
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192 × 1 = 192\\\\
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192 × 2 = 384\\\\
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192 × 3 = 576\\\\
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\end{align}$$
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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).
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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).
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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?
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# --hints--
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`pandigitalMultiples(8)` should return a number.
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```js
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assert(typeof pandigitalMultiples(8) === 'number');
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```
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`pandigitalMultiples(8)` should return `78156234`.
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```js
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assert.strictEqual(pandigitalMultiples(8), 78156234);
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```
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`pandigitalMultiples(9)` should return `932718654`.
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```js
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assert.strictEqual(pandigitalMultiples(9), 932718654);
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```
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# --seed--
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## --seed-contents--
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```js
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function pandigitalMultiples(k) {
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return true;
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}
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pandigitalMultiples(8);
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```
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# --solutions--
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```js
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function pandigitalMultiples(k) {
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function getKDigitConcatenatedProduct(num, k) {
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// returns false if concatenated product is not k digits
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let concatenatedProduct = num.toString();
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for (let i = 2; concatenatedProduct.length < k; i++) {
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concatenatedProduct += num * i;
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}
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return concatenatedProduct.length === k ? concatenatedProduct : false;
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}
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function is1toKPandigital(num, k) {
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const numStr = num.toString();
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// check if length is not k
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if (numStr.length !== k) {
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return false;
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}
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// check if pandigital
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for (let i = k; i > 0; i--) {
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if (numStr.indexOf(i.toString()) === -1) {
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return false;
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}
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}
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return true;
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}
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let largestNum = 0;
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for (let i = 10 ** Math.floor(k / 2) + 1; i >= 1; i--) {
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const concatenatedProduct = getKDigitConcatenatedProduct(i, k);
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if (is1toKPandigital(concatenatedProduct, k)) {
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const number = parseInt(concatenatedProduct, 10);
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if (number > largestNum) {
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largestNum = number;
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}
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}
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}
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return largestNum;
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}
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```
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