Project Euler Problem 55 Solution
If we take 47, reverse and add, , which is palindromic.
Not all numbers produce palindromes so quickly. For example,
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.
palindrome :: String -> Bool palindrome s = s == reverse s lychrel :: Int -> Bool lychrel n = not $ any palindrome $ take 50 $ tail (iterate (\x -> show $ (read x) + (read $ reverse x)) (show n)) main :: IO () main = print $ length $ filter lychrel [1..10000]
$ ghc -O2 -o lychrel lychrel.hs $ time ./lychrel real 0m0.295s user 0m0.288s sys 0m0.000s
#!/usr/bin/env python def is_palindrome(s): return s == ''.join(reversed(s)) def is_lychrel(n): s = str(n) i = 0 done = False while not done: if i > 50: return True s = str(int(s) + int(''.join(reversed(s)))) i += 1 if is_palindrome(s): done = True return False def main(): count = 0 for n in range(10000): if is_lychrel(n): count += 1 print(count) if __name__ == "__main__": main()
$ time python3 lychrel.py real 0m0.153s user 0m0.148s sys 0m0.004s
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