"Our objective has been modified (in form, not in nature) to accommodate this change (and I've updated the original post's definitions as well): Given a Number Pool of "x through y," create the maximum possible Fixed List Length variations of our Fixed List that contain some variation of our Guaranteed Combination, without any duplication (i.e. 1, 2, 3 is equal to 2, 3, 1 and would only count as one match), and return the results."