055_Lychrel_numbers.rb

# 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.

class SpecialNumbers

	def preform_lychrization(number)
		return number + number.to_s.reverse.to_i
	end

	def is_palendrome?(number)
		string = number.to_s
		if (
			string.length == 1 or
			(string.length == 2 and string[0] == string[1])
			)
			return true
		elsif string[0] != string[-1]
			return false
		else
			return is_palendrome?(string[1..-2])
		end
	end

	def is_lychrel?(number)
		counter = 0
		while counter < 51
			if is_palendrome?(number)
				return false
			else
				number = preform_lychrization(number)
				counter +=1
			end
		end
		return true
	end
end

lychrel_count = 0
number = 1

while number <= 10000
	lychrel_count += 1 if SpecialNumbers.new.is_lychrel?(number)
	number += 1
end

puts lychrel_count