Problem 55

Problem 55
Filename: prob55.hs

-- 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?
-- 
-- NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.


reverseNumber n = (read(reverse(show n))::Integer)
isPalindromic n = n==(reverseNumber n)

reverseAdd 0 = []
reverseAdd n = [n] ++ reverseAdd(n + (reverseNumber n))

isLychrel n = not (foldr (||) False (map (isPalindromic) (take 50 (tail(reverseAdd n)))))

answer = length(filter isLychrel [1..10000])

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