c# - Project Euler: Problem 1 (Possible refactorings and run time optimizations)

Question

I have been hearing a lot about Project Euler so I thought I solve one of the problems in C#. The problem as stated on the website is as follows:

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

I wrote my code as follows:

  class EulerProblem1
    {
        public static void Main()
        {
            var totalNum = 1000;
            var counter = 1;
            var sum = 0;

            while (counter < totalNum)
            {
                if (DivisibleByThreeOrFive(counter))
                    sum += counter;

                counter++;
            }

            Console.WriteLine("Total Sum: {0}", sum);
            Console.ReadKey();
        }

        private static bool DivisibleByThreeOrFive(int counter)
        {
            return ((counter % 3 == 0) || (counter % 5 == 0));

        }
    } 

It will be great to get some ideas on alternate implementations with less verbosity/cleaner syntax and better optimizations. The ideas may vary from quick and dirty to bringing out the cannon to annihilate the mosquito. The purpose is to explore the depths of computer science while trying to improve this particularly trivial code snippet.

Thanks

Answer 1

Updated to not double count numbers that are multiples of both 3 and 5:

int EulerProblem(int totalNum)
{
   int a = (totalNum-1)/3;
   int b = (totalNum-1)/5;
   int c = (totalNum-1)/15;
   int d = a*(a+1)/2;
   int e = b*(b+1)/2;
   int f = c*(c+1)/2;
   return 3*d + 5*e - 15*f;
}