**[INITIAL SOLUTION] Lychrel Numbers**

This problem can be approached in many different ways but most solutions fall into two groups:

1. Iterative solution (implemented by some form of a loop within a loop)

2. Recursive solution (a loop calling a recursive function)

The following code implements a recursive solution in Python. This problem actually lends itself nicely to a recursive solution.

The solution below was my first attempt and contains a fairly severe bug that returns a wrong (but reasonably sounding) result:

#!/usr/bin/env python MAX_ITERATIONS = 50 NRS_TO_CHECK = 10000 def reverse_number(number): return str(number)[::-1] def is_palindrome(number): nr_as_string = str(number) reverse_as_string = reverse_number(number) return str(number) == reverse_as_string def is_lychrel(number, invocation): if invocation > MAX_ITERATIONS: return True if is_palindrome(number): return False return is_lychrel(number + int(reverse_number(number)), invocation + 1) lychrel_numbers = 0 for cur_number in range(1, NRS_TO_CHECK): if is_lychrel(cur_number, 0): lychrel_numbers += 1 print 'Lychrel numbers below {0}: {1}'.format(NRS_TO_CHECK, lychrel_numbers)

which returns a result of

Lychrel numbers below 10000: 246

Unfortunately, the correct result it 249. We are off by 3... can you spot the bug?

The problem is that the above code immediately returns with "not a lychrel number" if the initial number (before reversing and adding) is already a palindrome. This solution doesn't consider 4994, 8778 and 9999 to be Lychrel numbers due to the above bug.

Go on to the next page to see the final (correct) solution.