[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.