Crikey, Cuddly Sheep! - if you're wondering why you haven't been inundated with responses, it's possibly on two counts:
(1) your statement about being fairly new to knitting, in the context of your problem, and
(2) the intricacies of said problem.
I reckon a couple of the stars in this forum are off poring over hastily sketched charts, doing a lot of pencilling in and rubbing out ...
One of 'em will come up with something, no worries.
Meanwhile, is your degree in mathematics or logic?