90 lines
2.8 KiB
Markdown
90 lines
2.8 KiB
Markdown
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---
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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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---
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## Description
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<section id='description'>
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A positive integer is a <a href="https://en.wikipedia.org/wiki/Kaprekar number">Kaprekar number</a> 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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</section>
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## Instructions
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<section id='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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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>isKaprekar</code> should be a function.
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testString: assert(typeof isKaprekar == 'function');
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- text: <code>isKaprekar(1, 10)</code> should return a boolean.
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testString: assert(typeof isKaprekar(1, 10) == 'boolean');
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- text: <code>isKaprekar(1, 10)</code> should return <code>true</code>.
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testString: assert.equal(isKaprekar(1, 10), true);
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- text: <code>isKaprekar(9, 10)</code> should return <code>true</code>.
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testString: assert.equal(isKaprekar(9, 10), true);
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- text: <code>isKaprekar(2223, 10)</code> should return <code>true</code>.
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testString: assert.equal(isKaprekar(2223, 10), true);
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- text: <code>isKaprekar(22823, 10)</code> should return <code>false</code>.
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testString: assert.equal(isKaprekar(22823, 10), false);
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- text: <code>isKaprekar(9, 17)</code> should return <code>false</code>.
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testString: assert.equal(isKaprekar(9, 17), false);
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- text: <code>isKaprekar(225, 17)</code> should return <code>true</code>.
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testString: assert.equal(isKaprekar(225, 17), true);
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- text: <code>isKaprekar(999, 17)</code> should return <code>false</code>.
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testString: assert.equal(isKaprekar(999, 17), false);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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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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</div>
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</section>
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## Solution
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<section id='solution'>
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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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</section>
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