Problem 55

Ckknight.ProjectEuler/.gitignore

@@ -0,0 +1,2 @@
+bin/
+obj/

Ckknight.ProjectEuler/Ckknight.ProjectEuler.csproj

@@ -112,6 +112,7 @@
     <Compile Include="Problems\Problem052.cs" />
     <Compile Include="Problems\Problem053.cs" />
     <Compile Include="Problems\Problem054.cs" />
+    <Compile Include="Problems\Problem055.cs" />
     <Compile Include="Problems\ProblemAttribute.cs" />
     <Compile Include="Program.cs" />
     <Compile Include="Properties\AssemblyInfo.cs" />

Ckknight.ProjectEuler/Problems/Problem055.cs

@@ -0,0 +1,67 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using Ckknight.ProjectEuler.Collections;
+
+namespace Ckknight.ProjectEuler.Problems
+{
+    [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.")]
+    public class Problem055 : BaseProblem
+    {
+        public override object CalculateResult()
+        {
+            return new Range(1, 10000)
+                .Count(i => !new Range(50)
+                    .SelectWithAggregate(MathUtilities.ToDigits(i), (x, n) =>
+                    {
+                        var digits = x.Zip(x.Reverse(), (a, b) => a + b).ToList();
+                        int carry = 0;
+                        for (int j = 0; j < digits.Count; j++)
+                        {
+                            int current = digits[j] + carry;
+                            digits[j] = current % 10;
+                            carry = current / 10;
+                        }
+                        while (carry > 0)
+                        {
+                            digits.Add(carry % 10);
+                            carry /= 10;
+                        }
+                        return digits.ToArray();
+                    })
+                    .SkipWhile(x => !x.IsPalindrome())
+                    .Any());
+        }
+    }
+}

Ckknight.ProjectEuler/Program.cs

@@ -12,7 +12,7 @@ class Program
     {
         static void Main(string[] args)
         {
-            RunProblem(54);
+            RunProblem(55);
         }
 
         public static void RunProblem(int number)