Thank you. There it is listed out.

I'm unsettled that a strategy involving using information that must have 0 correlation to each person's own correct answer could yield a collectively correct answer. I have heard problems similar to this before where I have been able to say "oohhhhhh" and find out why the answer does not seem to violate other overarching truths, but I'm not there with this one yet.

This is a like a person spelling out, step by step, how to build a perpetual motion machine, with no clear missteps, and the machine works, and I'm trying to understand how it jives with the second law of thermodynamics.