102 lines
3.3 KiB
Markdown
102 lines
3.3 KiB
Markdown
---
|
|
id: 5900f3a31000cf542c50feb6
|
|
challengeType: 5
|
|
title: 'Problem 55: Lychrel numbers'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
|
|
Not all numbers produce palindromes so quickly. For example,
|
|
349 + 943 = 1292,
|
|
1292 + 2921 = 4213
|
|
4213 + 3124 = 7337
|
|
That is, 349 took three iterations to arrive at a palindrome.
|
|
Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).
|
|
Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
|
|
How many Lychrel numbers are there below <code>num</code>?
|
|
NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>countLychrelNumbers(1000)</code> should return 13.
|
|
testString: 'assert.strictEqual(countLychrelNumbers(1000), 13, "<code>countLychrelNumbers(1000)</code> should return 13.");'
|
|
- text: <code>countLychrelNumbers(5000)</code> should return 76.
|
|
testString: 'assert.strictEqual(countLychrelNumbers(5000), 76, "<code>countLychrelNumbers(5000)</code> should return 76.");'
|
|
- text: <code>countLychrelNumbers(10000)</code> should return 249.
|
|
testString: 'assert.strictEqual(countLychrelNumbers(10000), 249, "<code>countLychrelNumbers(10000)</code> should return 249.");'
|
|
- text: Your function should count all Lychrel numbers.
|
|
testString: 'assert.strictEqual(countLychrelNumbers(3243), 39, "Your function should count all Lychrel numbers.");'
|
|
- text: Your function should pass all test cases.
|
|
testString: 'assert.strictEqual(countLychrelNumbers(7654), 140, "Your function should pass all test cases.");'
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function countLychrelNumbers(num) {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
countLychrelNumbers(10000);
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
|
|
```js
|
|
const countLychrelNumbers = (size) => {
|
|
const numReverse = (num) => {
|
|
return Number(num.toString().split('').reverse().join(''));
|
|
};
|
|
const isPalin = (num) => {
|
|
if (numReverse(num) === num) {
|
|
return true;
|
|
}
|
|
return false;
|
|
};
|
|
let total = 0;
|
|
for (let i = 1; i < size; i++) {
|
|
let loopCount = 1;
|
|
let sum = i;
|
|
while (loopCount < 50) {
|
|
sum = sum + numReverse(sum);
|
|
if (isPalin(sum)) {
|
|
break;
|
|
} else {
|
|
loopCount++;
|
|
}
|
|
}
|
|
if (loopCount === 50) {
|
|
total++;
|
|
}
|
|
}
|
|
return total;
|
|
}
|
|
```
|
|
|
|
</section>
|