Add Every Combination Of List Of Numbers

VS2010
VB

I would like to be able to add every combination of a list of numbers to determine which combinations equal a specific result.

Simple Example:

List: 2, 4, 6
Result: 10

How many and which combinations of numbers result in the number 10? The correct anwser is only one which is 4 + 6 = 10. The example is simple but the actual list may contain as many as 10 - 15 decimal numbers.

I have thought of the following as a possible way of checking each combination by using binary:

- There are 3 total number so the possible combinations would be:
123 - Three numbers
000 - Add no numbers
001 - Add the last number

[Code].....

However, I don't know how to actually match up the bitwise bits to the numbers in the array to actually add. Example:

101 - I should check if 2 + 6 != 10 per the example above so this wouldn't satisfy the result... does this make sense? The answer would be 4 + 6 = 10.

how to check and add all combinations from a list of numbers to determine if the result is a specific number?