Bruce:

I concure with your conceptual analysis of the math involved and extend it further.

We cannot ignore single sum solutions = where the solution is itself a member of the original list.

Also, we would need to allow for more than one solution - a set of solutions that could include any combination of single and multiple-number solutions.

I decided I had used up more than enough discretionary time this morning and stopped writing. At the heart of the algorithm I was playing with was a decision to arrange the list in descending order and to work down the list testing combinations of numbers as to whether they are less than or equal to the given sum.


Godfrey