Euler 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?


In [1]:
def reverse(n):
    return int(str(n)[::-1])

def lyrchel(n):
    rev = reverse(n)
    for i in range(50):
        n = n + rev
        rev = reverse(n)
        if rev == n:
            return False
    return True

print(sum(lyrchel(n) for n in range(1, 10000)))


249

In [ ]: