Trello challenge performance comparison

TrelloTest

namespace TrelloTest
{
    using System;
    using System.Collections.Generic;
    using System.Diagnostics;
    using System.Globalization;

    public class Program
    {
        private const long ChallengeHash = 956446786872726;

        private const string ChallengeWord = "trellises";

        private const string Letters = "acdegilmnoprstuw";

        public static void Main(string[] args)
        {
            const int Iterations = 1000000;
            var repeats = 1;
            if (args.Length > 0)
            {
                if (!int.TryParse(args[0], out repeats))
                {
                    repeats = 1;
                }
            }

            for (var repeat = 0; repeat < repeats; repeat++)
            {
                Time("Analytical", () => Analytical(ChallengeHash), Iterations);
                Time("Heuristic", () => Heuristic(ChallengeHash), Iterations);
            }
        }

        private static void Time(string name, Func<string> func, int iterations)
        {
            var stopwatch = Stopwatch.StartNew();
            for (var i = 0; i < iterations; i++)
            {
                if (func() != ChallengeWord)
                {
                    throw new Exception("Didn't calculate expected word");
                }
            }

            stopwatch.Stop();
            Console.WriteLine(
                "{0}: {1} iterations took {2}ms. {3} ticks per iteration",
                name,
                iterations,
                stopwatch.ElapsedMilliseconds,
                stopwatch.ElapsedTicks / iterations);
        }

        private static string Analytical(long encoded)
        {
            var result = new List<char>();

            var remaining = encoded;
            while (remaining > 7)
            {
                var current = (int)(remaining % 37);
                result.Insert(0, Letters[current]);
                remaining = (remaining - current) / 37;
            }

            return new string(result.ToArray());
        }

        private static string Heuristic(long desiredOutput)
        {
            var input = "aaaaaaaaa";
            var pos = 0;

            for (var i = 0; i < 9; i++)
            {
                var bestMatch = long.MaxValue;
                var bestChar = 'a';
                foreach (var letter in Letters)
                {
                    input = input.Remove(pos, 1).Insert(pos, letter.ToString(CultureInfo.InvariantCulture));
                    var difference = desiredOutput - Hash(input);
                    if (Math.Abs(difference) < bestMatch)
                    {
                        bestMatch = difference;
                        bestChar = letter;
                    }
                }

                input = input.Remove(pos, 1).Insert(pos, bestChar.ToString(CultureInfo.InvariantCulture));
                pos++;
            }

            return input;
        }

        private static long Hash(string s)
        {
            long result = 7;
            foreach (char c in s)
            {
                result = (result * 37 + Letters.IndexOf(c));
            }

            return result;
        }
    }
}