Python Implementation of Problem 55
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Problem Solution
Project Euler Problem 55
Problem:
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.
1"""
2Project Euler Problem 55
3
4Problem:
5
6If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
7
8Not all numbers produce palindromes so quickly. For example,
9
10349 + 943 = 1292,
111292 + 2921 = 4213
124213 + 3124 = 7337
13
14That is, 349 took three iterations to arrive at a palindrome.
15
16Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that
17never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature
18of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise.
19In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than
20fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a
21palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a
22palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).
23
24Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
25
26How many Lychrel numbers are there below ten-thousand?
27
28NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.
29"""
30from .lib.utils import steps_to_palindrome
31
32
33def main() -> int:
34 answer = 0
35 for x in range(1, 10_000):
36 if not steps_to_palindrome(x):
37 answer += 1
38 return answer