2.3 KiB
2.3 KiB
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f3931000cf542c50fea5 | Problem 38: Pandigital multiples | 5 | 302042 | 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;
}
```