solve55.rb

# https://projecteuler.net/problem=55
# Run with: 'ruby solve55.rb'
# using Ruby 2.7.0
# by Zack Sargent

# Prompt:

# 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?

class Integer
  def reverse
    self.to_s.reverse.to_i
  end
end

def produces_palindrome?(i)
  50.times do
    i += i.reverse
    return true if i == i.reverse
  end
  false
end

p (0..10_000).reject{|i| produces_palindrome? i}.size