diff --git a/src/Julia/Problem055.jl b/src/Julia/Problem055.jl new file mode 100644 index 0000000..2278623 --- /dev/null +++ b/src/Julia/Problem055.jl @@ -0,0 +1,73 @@ +#= +Created on 03 Oct 2021 + +@author: David Doblas Jiménez +@email: daviddoji@pm.me + +Solution for Problem 55 of Project Euler +https://projecteuler.net/problem=55 +=# + +using BenchmarkTools + +function is_palindrome(num) + return num == reverse(num) +end + +function Problem55() + #= + 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 11:10_000 + num = n + is_lychrel = true + for it in 0:50 + num += parse(BigInt, reverse(string(num))) + if is_palindrome(digits(num, base=10)) + is_lychrel = false + break + end + end + if is_lychrel + ans += 1 + end + end + + return ans +end + + +println("Time to evaluate Problem 55:") +@btime Problem55() +println("") +println("Result for Problem 55: ", Problem55())