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.
Naive solution, do as instructed.
import sys, os; sys.path.append(os.path.abspath('..'))
from timer import timethis
def get_palindrome(n):
m = 0
while n:
m = m * 10 + n % 10
n //= 10
return m
def is_palindrome(n):
return n == get_palindrome(n)
is_palindrome(101)
is_palindrome(198)
@timethis
def solve():
cnt = 0
for i in range(10000):
m = i
process_cnt = 0
while process_cnt < 50:
process_cnt += 1
m += get_palindrome(m)
if is_palindrome(m):
break
if process_cnt >= 50:
cnt += 1
return cnt
solve()