3.2 KiB
id | challengeType | title | forumTopicId |
---|---|---|---|
5900f3a31000cf542c50feb6 | 5 | Problem 55: Lychrel numbers | 302166 |
Description
If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
Not all numbers produce palindromes so quickly. For example,
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 num
?
Note: Wording was modified slightly on 24 April 2007 to emphasize the theoretical nature of Lychrel numbers.
Instructions
Tests
tests:
- text: <code>countLychrelNumbers(1000)</code> should return a number.
testString: assert(typeof countLychrelNumbers(1000) === 'number');
- text: <code>countLychrelNumbers(1000)</code> should return 13.
testString: assert.strictEqual(countLychrelNumbers(1000), 13);
- text: <code>countLychrelNumbers(3243)</code> should return 39.
testString: assert.strictEqual(countLychrelNumbers(3243), 39);
- text: <code>countLychrelNumbers(5000)</code> should return 76.
testString: assert.strictEqual(countLychrelNumbers(5000), 76);
- text: <code>countLychrelNumbers(7654)</code> should return 140.
testString: assert.strictEqual(countLychrelNumbers(7654), 140);
- text: <code>countLychrelNumbers(10000)</code> should return 249.
testString: assert.strictEqual(countLychrelNumbers(10000), 249);
Challenge Seed
function countLychrelNumbers(num) {
return true;
}
countLychrelNumbers(10000);
Solution
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;
}