Duncan's blog

October 19, 2014

Project Euler: problem 55 (PHP) – Lychrel numbers

Filed under: PHP,Project Euler — duncan @ 8:00 am

747I previously blogged about this Project Euler puzzle over 5 years ago, using Coldfusion and Python.  This is my approach using PHP as a simple practical exercise for myself, and I’d appreciate any feedback on my PHP code.

Problem 55:

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 ten-thousand?

Phew, quite a lengthy question. Here’s my code:

$countLychrels = 0;
$limit = 9999;
$maxIterations = 50;

function isPalindrome($number) {
	return $number == strrev($number);

function isLychrel($iterations) {
	global $maxIterations;
	return $iterations >= $maxIterations;

foreach (range(1, $limit) as $currentNumber) {
	$number = $currentNumber;

	foreach (range(1, $maxIterations) as $iteration) {
		$sum = $number + strrev($number);

		if (isPalindrome($sum)) {
		$number = $sum;
	if (isLychrel($iteration)) {
echo $countLychrels;

Looping from 1 to ten thousand.  For each iteration  of that loop, looping again up to fifty times, adding the number to its reverse.  If we find a palindrome at any point, it’s not a Lychrel number.  Otherwise, if we’ve looped as much as 50 times, then it must be a Lychrel.


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