Okay, I think I can just do the thing I do usually, and comment at least in a general way on whatever is posted here. I have said already before that earlier on, lots of very good remarks have been made earlier on this thread by some people. You might also try to find gaps in your own reasoning in there.
Ardent, your post, for instance, is a good summary, certainly making good effort to create a system in it, I should point out only that somewhere in your post, there is one assumption you make which, if you read the riddle properly from start to the end, does not really exactly reflect the whole truth. (That was very diplomatically phrased, but that's exactly what it is
Find for yourself. Or just ignore it and try different approaches, whichever you prefer.)
That's not to say that everything besides that one assumption is correct, but the thing I'm pointing out it something you might realise if you check with the riddle - i.e. should be able to figure out with the information you have. But again, don't spend a day trying to look for it, it isn't crucial that you get that thing right (it concerns only one of the many ways you can get to the correct answer). But if you do, it might bring some interesting revelations. Hm, I could also mention that on top of that, the topic has been touched on here earlier on.
I hope I managed to confuse you enough with this post. Apologies
