97 lines
2.3 KiB
Markdown
97 lines
2.3 KiB
Markdown
---
|
||
id: 5900f3931000cf542c50fea5
|
||
title: 'Problem 38: Pandigital multiples'
|
||
challengeType: 5
|
||
forumTopicId: 302042
|
||
dashedName: problem-38-pandigital-multiples
|
||
---
|
||
|
||
# --description--
|
||
|
||
Take the number 192 and multiply it by each of 1, 2, and 3:
|
||
|
||
$$\begin{align} 192 × 1 = 192\\\\ 192 × 2 = 384\\\\ 192 × 3 = 576\\\\ \end{align}$$
|
||
|
||
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 `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(8)` should return a number.
|
||
|
||
```js
|
||
assert(typeof pandigitalMultiples(8) === 'number');
|
||
```
|
||
|
||
`pandigitalMultiples(8)` should return `78156234`.
|
||
|
||
```js
|
||
assert.strictEqual(pandigitalMultiples(8), 78156234);
|
||
```
|
||
|
||
`pandigitalMultiples(9)` should return `932718654`.
|
||
|
||
```js
|
||
assert.strictEqual(pandigitalMultiples(9), 932718654);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function pandigitalMultiples(k) {
|
||
|
||
return true;
|
||
}
|
||
|
||
pandigitalMultiples(8);
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
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 < k; i++) {
|
||
concatenatedProduct += num * i;
|
||
}
|
||
return concatenatedProduct.length === k ? concatenatedProduct : false;
|
||
}
|
||
|
||
function is1toKPandigital(num, k) {
|
||
const numStr = num.toString();
|
||
|
||
// check if length is not k
|
||
if (numStr.length !== k) {
|
||
return false;
|
||
}
|
||
|
||
// check if pandigital
|
||
for (let i = k; i > 0; i--) {
|
||
if (numStr.indexOf(i.toString()) === -1) {
|
||
return false;
|
||
}
|
||
}
|
||
return true;
|
||
}
|
||
|
||
let largestNum = 0;
|
||
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;
|
||
}
|
||
```
|