diff --git a/src/Python/Problem055.py b/src/Python/Problem055.py new file mode 100644 index 0000000..53fcafc --- /dev/null +++ b/src/Python/Problem055.py @@ -0,0 +1,66 @@ +#!/usr/bin/env python3 +""" +Created on 02 Oct 2021 + +@author: David Doblas Jiménez +@email: daviddoji@pm.me + +Solution for problem 55 of Project Euler +https://projecteuler.net/problem=55 +""" + +from utils import timeit, is_palidrome + + +@timeit("Problem 55") +def compute(): + """ + 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? + """ + + ans = 0 + for n in range(11, 10_000): + num = n + is_lychrel = True + for it in range(50): + num += int(str(num)[::-1]) + if is_palidrome(num): + is_lychrel = False + break + if is_lychrel: + ans += 1 + + return ans + + +if __name__ == "__main__": + + print(f"Result for Problem 55: {compute()}") \ No newline at end of file