PROJECT EULER #24

Link to Project Euler problem 24

A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:

012 021 102 120 201 210

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?

using System;

namespace project_euler
{
   class Program
   {
       static void Main()
       {
           //Problem 24
           //There are 10! permutations of 0123456789
           //There are 9! permutations of 123456789 = 362880
           //So for numbers beginning with 0 and 1 there are 725760 permutations
           //Thus we want the 1000000 - 725760 = 274240. permutation in the 2xxxxxxxxx group.
           //20xxxxxxxx has 8! permutations = 40320. 274240/40320 = 6.8....etc
           DateTime start = DateTime.Now;
           char[] result= new char[10];
           double permutation = 1000000;
           string s = "0123456789";
           for (int i = s.Length-1; i >= 0; i--)
           {
               double index = Math.Ceiling(permutation/FactorialSmallInt(s.Length-1))-1;
               result[i] = s[(int) index];
               s=s.Remove((int) index, 1);
               permutation -= FactorialSmallInt(i)*index;
           }
           Array.Reverse(result);
           Console.WriteLine(new string(result));
           TimeSpan time = DateTime.Now - start;
           Console.WriteLine("This took {0}", time);
           Console.ReadKey();
       }
       public static double FactorialSmallInt(int n)
       {
           int factorial=1;
           for (int i = 1; i <= n; i++)
           {
               factorial *= i;
           }
           return factorial;
       }
   }
}