Partition Problem

[Donovan Hide]

Hi,
    I'm very new to combinatorics (in fact my interest has only arisen from
a problem in a magazine) and have been scouring the net for help with said
problem.
    The difficuly is phrasing the question in mathematical language.
Basically how can I find all the sets of six numbers which sum to 17 and
also to 20. I have found all sorts of research and information about Bell
Numbers and Stirling numbers but I think that they only refer to the total
number of sets?
    I have come across algorithms written twenty years ago, but they are
written in Pascal and Fortran. I am learning to program with Python, so it
is difficult to translate them. I would be very grateful if someone could
supply some c, python or even pseudocode to generate the solution to this
problem.
    Also is generation the correct phrase or is enumeration better?
    Thanks in advance for your time,
    Donovan Hide.