Wow, thanks tilly. I really appreciate your taking time to look at my meditation and read my code. I'd like to respond to a few of the things you said, and mostly in the form of questions (if you don't mind)

You said:

"If you got through the Fibonacci and directory walk examples then you obviously understand the principle of recursion. Why would you balk on this example? My most likely guess is that you try to visualize what is happening. In the case of Fibonacci it is easy enough to verify, number by number, what is happening. In the case of a directory walk, it is easy enough to visualize what it is doing, and see how it works."

YES, exactly. I can confidently say that I know what recursion is, and more importantly I'd like to believe that I "understand" recursion; the directory walk is a piece of cake (I've written very similar code in the past), and the Fibonacci exercise was also very easy to grasp. I could easily see where/why the code recursed and when/what it returned.

The two things I don't understand:

1.) Why the ambiguous output?

My confusion lies in the final 3 lines of the output of my (more verbose) version of the MJD recursive solution, as shown in the original post. I don't understand why something that appears to be a partial answer gets passed back up the stack and marked as a "solution", per the "$solution" variable name taken from the MJD code. When the code claims to have found a solution the first time, the solution it finds is not the real solution to the problem. Only higher on up the stack is the real solution identified. The first claim to have found a solution doesn't ring true. Sub-question: What made this solution work then?

2.) When is recursion the right thing to do?

What criteria make recursion the method of choice for approaching problems as opposed to iteration? For a predefined tree structure, the answer is obvious, however I don't see why it is the only way to accomplish the solution of the Partition Problem which has no pre-defined tree that I can see. I don't doubt your assertion that recursion is the correct methodology for finding a solution to the Partition Problem, but could you tell me why? How would I recognize that I needed recursion there?

I had to jot this down quickly before taking the kids to school and going to $work, so please forgive me if there's any muddled grammar or disjointed sentences...