111 lines
2.3 KiB
Markdown
111 lines
2.3 KiB
Markdown
---
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id: 5a23c84252665b21eecc7eca
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title: Kaprekar numbers
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challengeType: 5
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forumTopicId: 302296
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dashedName: kaprekar-numbers
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---
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# --description--
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A positive integer is a [Kaprekar number](https://en.wikipedia.org/wiki/Kaprekar number) if:
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<ul>
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<li>It is 1, or,</li>
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<li>The decimal representation of its square may be split once into two parts consisting of positive integers which sum to the original number. </li>
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</ul>
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Note that a split resulting in a part consisting purely of 0s is not valid, as 0 is not considered positive.Example
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Kaprekar numbers:
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<ul>
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<li><code>2223</code> is a Kaprekar number, as <code>2223 * 2223 = 4941729</code>, <code>4941729</code> may be split to <code>494</code> and <code>1729</code>, and <code>494 + 1729 = 2223</code></li>
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<li>The series of Kaprekar numbers is known as <a href='https://oeis.org/A006886' target='_blank'>A006886</a>, and begins as <code>1, 9, 45, 55, ...</code></li>
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</ul>
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# --instructions--
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Write a function that takes a number $n$, a base $bs$, and returns true if the number is a Kaprekar number for the given base. Otherwise, the function returns false.
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# --hints--
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`isKaprekar` should be a function.
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```js
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assert(typeof isKaprekar == 'function');
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```
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`isKaprekar(1, 10)` should return a boolean.
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```js
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assert(typeof isKaprekar(1, 10) == 'boolean');
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```
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`isKaprekar(1, 10)` should return `true`.
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```js
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assert.equal(isKaprekar(1, 10), true);
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```
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`isKaprekar(9, 10)` should return `true`.
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```js
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assert.equal(isKaprekar(9, 10), true);
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```
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`isKaprekar(2223, 10)` should return `true`.
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```js
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assert.equal(isKaprekar(2223, 10), true);
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```
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`isKaprekar(22823, 10)` should return `false`.
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```js
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assert.equal(isKaprekar(22823, 10), false);
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```
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`isKaprekar(9, 17)` should return `false`.
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```js
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assert.equal(isKaprekar(9, 17), false);
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```
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`isKaprekar(225, 17)` should return `true`.
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```js
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assert.equal(isKaprekar(225, 17), true);
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```
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`isKaprekar(999, 17)` should return `false`.
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```js
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assert.equal(isKaprekar(999, 17), false);
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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 isKaprekar(n, bs) {
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}
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```
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# --solutions--
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```js
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function isKaprekar(n, bs) {
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if (n < 1) return false;
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if (n == 1) return true;
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for (var a = n * n, b = 0, s = 1; a; s *= bs) {
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b += (a % bs) * s;
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a = Math.floor(a / bs);
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if (b && a + b == n) return true;
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}
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return false;
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}
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```
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