Project Euler Problem 55

Problem 55

24 October 2003

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.

Answer: 249

 

 

C#

 

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;

namespace Euler {
    class Problem55 {
        static bool isPalindrome<T>(T value) {
            var str = value.ToString();
            var to = str.Length / 2;
            for (var i = 0; i <= to; i++) {
                if (str[i] != str[str.Length - 1 - i]) return false;
            }
            return true;
        }

        static bool isLychrel<T>(T value) {
            var str = value.ToString();
            for (var i = 1; i < 50; i++) {
                var r = str.ToArray();
                Array.Reverse(r);
                str = (BigInteger.Parse(str) + BigInteger.Parse(new string(r))).ToString();
                if (isPalindrome(str)) return false;
            }
            return true;
        }

        public static void run() {
            Console.WriteLine(Enumerable.Range(1, 9999).Where(isLychrel).Count());
        }
    }
}