Find elements in a list that, together add up to a target number

Question

Suppose I have a list:

List _arr = new List {1, 3, 4};

And a target of 4

I want to return

Answer 1

It's easy once we have a method to get all subsets of an enumerator/list
(found here: Answer: Most Elegant Way to Get All Subsets of an Array in C#)

using System;
using System.Collections.Generic;
using System.Linq;

public static class Program
{
    static void Main(string[] args)
    {
        var test = new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 };

        var target = 6;

        var matches = from subset in test.SubSetsOf()
                      where subset.Sum() == target
                      select subset;

        Console.WriteLine("Numbers: {0}", test.Select(i => i.ToString()).Aggregate((a, n) => a + ", " + n));
        Console.WriteLine("Target: {0}", target);

        foreach (var match in matches)
        {
            Console.WriteLine(match.Select(m => m.ToString()).Aggregate((a, n) => a + " + " + n) + " = " + target.ToString());
        }

        Console.ReadKey();
    }

    public static IEnumerable> SubSetsOf(this IEnumerable source)
    {
        // Deal with the case of an empty source (simply return an enumerable containing a single, empty enumerable)
        if (!source.Any())
            return Enumerable.Repeat(Enumerable.Empty(), 1);

        // Grab the first element off of the list
        var element = source.Take(1);

        // Recurse, to get all subsets of the source, ignoring the first item
        var haveNots = SubSetsOf(source.Skip(1));

        // Get all those subsets and add the element we removed to them
        var haves = haveNots.Select(set => element.Concat(set));

        // Finally combine the subsets that didn't include the first item, with those that did.
        return haves.Concat(haveNots);
    }
}

Output:

Numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9
Target: 6
1 + 2 + 3 = 6
1 + 5 = 6
2 + 4 = 6
6 = 6