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 w

Answer 1

You can do something like this:

Func Euler = total=> 
    new List() {3,5}
        .Select(m => ((int) (total-1) / m) * m * (((int) (total-1) / m) + 1) / 2)
        .Aggregate( (T, m) => T+=m);

You still have the double counting problem. I'll think about this a little more.

Edit:

Here is a working (if slightly inelegant) solution in LINQ:

        var li = new List() { 3, 5 };
        Func Summation = (total, m) => 
           ((int) (total-1) / m) * m * (((int) (total-1) / m) + 1) / 2;

        Func Euler = total=> 
            li
                .Select(m => Summation(total, m))
                .Aggregate((T, m) => T+=m)
            - Summation(total, li.Aggregate((T, m) => T*=m));

Can any of you guys improve on this?

Explanation:

Remember the summation formula for a linear progression is n(n+1)/2. In the first case where you have multiples of 3,5 < 10, you want Sum(3+6+9,5). Setting total=10, you make a sequence of the integers 1 .. (int) (total-1)/3, and then sum the sequence and multiply by 3. You can easily see that we're just setting n=(int) (total-1)/3, then using the summation formula and multiplying by 3. A little algebra gives us the formula for the Summation functor.