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---
id: 5a23c84252665b21eecc7eca
title: Kaprekar numbers
challengeType: 5
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forumTopicId: 302296
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dashedName: kaprekar-numbers
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---
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# --description--
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 >
< 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--
`isKaprekar` should be a function.
```js
assert(typeof isKaprekar == 'function');
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```
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`isKaprekar(1, 10)` should return a boolean.
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```js
assert(typeof isKaprekar(1, 10) == 'boolean');
```
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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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`isKaprekar(9, 10)` should return `true` .
```js
assert.equal(isKaprekar(9, 10), true);
```
`isKaprekar(2223, 10)` should return `true` .
```js
assert.equal(isKaprekar(2223, 10), true);
```
`isKaprekar(22823, 10)` should return `false` .
```js
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
assert.equal(isKaprekar(9, 17), false);
```
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`isKaprekar(225, 17)` should return `true` .
```js
assert.equal(isKaprekar(225, 17), true);
```
`isKaprekar(999, 17)` should return `false` .
```js
assert.equal(isKaprekar(999, 17), false);
```
# --seed--
## --seed-contents--
```js
function isKaprekar(n, bs) {
}
```
# --solutions--
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```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) {
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b += (a % bs) * s;
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a = Math.floor(a / bs);
if (b & & a + b == n) return true;
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}
return false;
}
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```