>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.

Yes, these are good points - I was going to ask about the "more than one solution" issue, as it is somewhat important. I'll make a post to Marvin...I have some code and a technique for testing. No SQL, I found too many problems with it.