project_euler.problem_055.sol1¶
Lychrel numbers Problem 55: https://projecteuler.net/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?
Functions¶
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Returns True if a number is palindrome. |
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Returns the count of all lychrel numbers below limit. |
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Returns the sum of n and reverse of n. |
Module Contents¶
- project_euler.problem_055.sol1.is_palindrome(n: int) bool¶
Returns True if a number is palindrome. >>> is_palindrome(12567321) False >>> is_palindrome(1221) True >>> is_palindrome(9876789) True
- project_euler.problem_055.sol1.solution(limit: int = 10000) int¶
Returns the count of all lychrel numbers below limit. >>> solution(10000) 249 >>> solution(5000) 76 >>> solution(1000) 13
- project_euler.problem_055.sol1.sum_reverse(n: int) int¶
Returns the sum of n and reverse of n. >>> sum_reverse(123) 444 >>> sum_reverse(3478) 12221 >>> sum_reverse(12) 33