It was 3:30 in the morning just a short while ago, and I woke up with a bunch of non-sensical ideas about the properties of this problem, and then while I was trying to get back to sleep I realized that one of the ideas made sense. Evidence that understanding this problem for myself required a right-brain reboot.

I'm not surprised about the reboot: I've been thinking about this problem a lot, which signals to my brain that it's important, and it literally hurt my brain to think about why the green roomers were losing for the group when they thought they were winning, strongly suggesting I was hitting my apologist limit.