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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/kaprekar-numbers.md

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+---
+id: 5a23c84252665b21eecc7eca
+title: Kaprekar numbers
+challengeType: 5
+forumTopicId: 302296
+---
+
+## Description
+
+<section id='description'>
+A positive integer is a <a href="https://en.wikipedia.org/wiki/Kaprekar number">Kaprekar number</a> if:
+<ul>
+  <li>It is 1, or,</li>
+  <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>
+</ul>
+Note that a split resulting in a part consisting purely of 0s is not valid, as 0 is not considered positive.Example
+Kaprekar numbers:
+<ul>
+  <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>
+  <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>
+</ul>
+</section>
+
+## Instructions
+
+<section id='instructions'>
+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.
+</section>
+
+## Tests
+
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>isKaprekar</code> should be a function.
+    testString: assert(typeof isKaprekar == 'function');
+  - text: <code>isKaprekar(1, 10)</code> should return a boolean.
+    testString: assert(typeof isKaprekar(1, 10) == 'boolean');
+  - text: <code>isKaprekar(1, 10)</code> should return <code>true</code>.
+    testString: assert.equal(isKaprekar(1, 10), true);
+  - text: <code>isKaprekar(9, 10)</code> should return <code>true</code>.
+    testString: assert.equal(isKaprekar(9, 10), true);
+  - text: <code>isKaprekar(2223, 10)</code> should return <code>true</code>.
+    testString: assert.equal(isKaprekar(2223, 10), true);
+  - text: <code>isKaprekar(22823, 10)</code> should return <code>false</code>.
+    testString: assert.equal(isKaprekar(22823, 10), false);
+  - text: <code>isKaprekar(9, 17)</code> should return <code>false</code>.
+    testString: assert.equal(isKaprekar(9, 17), false);
+  - text: <code>isKaprekar(225, 17)</code> should return <code>true</code>.
+    testString: assert.equal(isKaprekar(225, 17), true);
+  - text: <code>isKaprekar(999, 17)</code> should return <code>false</code>.
+    testString: assert.equal(isKaprekar(999, 17), false);
+```
+
+</section>
+
+## Challenge Seed
+
+<section id='challengeSeed'>
+  <div id='js-seed'>
+
+```js
+function isKaprekar(n, bs) {
+
+}
+```
+
+  </div>
+</section>
+
+## Solution
+
+<section id='solution'>
+
+```js
+function isKaprekar(n, bs) {
+  if (n < 1) return false;
+  if (n == 1) return true;
+  for (var a = n * n, b = 0, s = 1; a; s *= bs) {
+    b += (a % bs) * s;
+    a = Math.floor(a / bs);
+    if (b && a + b == n) return true;
+  }
+  return false;
+}
+```
+
+</section>