# Solution to Project Euler Problem 55: Lychrel numbers - 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.

**Updated:**Aug. 10, 2022 —

**Training Time:**3 minutes

Overseen by: Archangel Macsika

**Topic:** Project Euler Problem 55: Lychrel numbers.

**Difficulty:** Easy.

**Objective: ** 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?

NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.

**Input:** None.

**Expected Output:** 249.

### Sikademy Solution in Java Programming Language

```
package sikademy;
/**
*
* @author Archangel Macsika
* Copyright (c) Sikademy. All rights reserved
*/
import java.math.BigInteger;
public class SikademyEulerSolution {
public String run() {
int count = 0;
for (int i = 0; i < 10000; i++) {
if (isLychrel(i))
count++;
}
return Integer.toString(count);
}
public static String reverse(String s) {
return new StringBuilder(s).reverse().toString();
}
public static boolean isPalindrome(String s) {
return s.equals(reverse(s));
}
private static boolean isLychrel(int n) {
BigInteger temp = BigInteger.valueOf(n);
for (int i = 0; i < 49; i++) {
temp = temp.add(new BigInteger(reverse(temp.toString())));
if (isPalindrome(temp.toString()))
return false;
}
return true;
}
public static void main(String[] args) {
SikademyEulerSolution solution = new SikademyEulerSolution();
System.out.println(solution.run());
}
}
```

### Sikademy Solution in Python Programming Language

```
#
# @author Archangel Macsika
# Copyright (c) Sikademy. All rights reserved.
#
def compute():
ans = sum(1 for i in range(10000) if is_lychrel(i))
return str(ans)
def is_lychrel(n):
for i in range(50):
n += int(str(n)[ : : -1])
if str(n) == str(n)[ : : -1]:
return False
return True
if __name__ == "__main__":
print(compute())
```