82 lines
1.6 KiB
Markdown
82 lines
1.6 KiB
Markdown
---
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id: 5900f3a01000cf542c50feb3
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title: 'Problem 52: Permuted multiples'
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challengeType: 5
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forumTopicId: 302163
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dashedName: problem-52-permuted-multiples
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---
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# --description--
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It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits, but in a different order.
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Find the smallest positive integer, such that multiplied by integers $\\{2, 3, \ldots, n\\}$, contain the same digits.
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# --hints--
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`permutedMultiples(2)` should return a number.
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```js
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assert(typeof permutedMultiples(2) === 'number');
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```
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`permutedMultiples(2)` should return `125874`.
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```js
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assert.strictEqual(permutedMultiples(2), 125874);
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```
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`permutedMultiples(6)` should return `142857`.
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```js
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assert.strictEqual(permutedMultiples(6), 142857);
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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 permutedMultiples(n) {
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return true;
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}
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permutedMultiples(2);
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```
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# --solutions--
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```js
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function permutedMultiples(n) {
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const isPermutation = (a, b) =>
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a.length !== b.length
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? false
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: a.split('').sort().join() === b.split('').sort().join();
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let start = 1;
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let found = false;
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let result = 0;
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while (!found) {
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start *= 10;
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for (let i = start; i < start * 10 / n; i++) {
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found = true;
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for (let j = 2; j <= n; j++) {
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if (!isPermutation(i + '', j * i + '')) {
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found = false;
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break;
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}
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}
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if (found) {
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result = i;
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break;
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}
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}
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}
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return result;
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}
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```
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