7e921fb9d6
* fix: reworck challenge to use argument in function * fix: add solution * fix: use MathJax to improve math notation
98 lines
1.9 KiB
Markdown
98 lines
1.9 KiB
Markdown
---
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id: 5900f3aa1000cf542c50febd
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title: 'Problem 62: Cubic permutations'
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challengeType: 5
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forumTopicId: 302174
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dashedName: problem-62-cubic-permutations
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---
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# --description--
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The cube, 41063625 ($345^3$), can be permuted to produce two other cubes: 56623104 ($384^3$) and 66430125 ($405^3$). In fact, 41063625 is the smallest cube which has exactly three permutations of its digits which are also cube.
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Find the smallest cube for which exactly `n` permutations of its digits are cube.
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# --hints--
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`cubicPermutations(2)` should return a number.
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```js
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assert(typeof cubicPermutations(2) === 'number');
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```
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`cubicPermutations(2)` should return `125`.
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```js
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assert.strictEqual(cubicPermutations(2), 125);
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```
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`cubicPermutations(3)` should return `41063625`.
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```js
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assert.strictEqual(cubicPermutations(3), 41063625);
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```
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`cubicPermutations(4)` should return `1006012008`.
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```js
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assert.strictEqual(cubicPermutations(4), 1006012008);
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```
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`cubicPermutations(5)` should return `127035954683`.
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```js
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assert.strictEqual(cubicPermutations(5), 127035954683);
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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 cubicPermutations(n) {
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return true;
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}
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cubicPermutations(2);
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```
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# --solutions--
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```js
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function cubicPermutations(n) {
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function getDigits(num) {
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const digits = [];
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while (num > 0) {
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digits.push(num % 10);
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num = Math.floor(num / 10);
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}
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return digits;
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}
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function getCube(num) {
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return num ** 3;
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}
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const digitsToCubeCounts = {};
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let curNum = 1;
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let digits;
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while (!digitsToCubeCounts[digits] || digitsToCubeCounts[digits].count < n) {
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const cube = getCube(curNum);
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digits = getDigits(cube).sort().join();
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if (!digitsToCubeCounts[digits]) {
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digitsToCubeCounts[digits] = {
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count: 1,
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smallestCube: cube
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};
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} else {
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digitsToCubeCounts[digits].count += 1;
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}
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curNum++;
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}
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return digitsToCubeCounts[digits].smallestCube;
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}
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```
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