OK, the hint helped me a LOT. I've got something that I think makes sense. However, now that so many supersmart people submitted, but no answer yet, it makes me wonder if I should even submit tonight. I went through a few steps but I keep thinking I'm missing one extra step.
EDIT: OK, I submitted something. I'm not super-confident, but what I did was take the 'simpler' answer I got (and I think everyone else who put an answer in had) and I think I went a step further. Only time will tell if I'm making things too simple or too complex.