Quiz

Well, well... This solution doesn't seem to match the "examples" given in the question. It says that if 2 and 3 have the same color, then 1 must name exactly that color. But according to the "algorithm," if the colors are white, then 1 must name... blue.

Those weren't examples, but solutions for the cases of saving half and 2/3 of the sages; and a solution for the case of guaranteed rescue of 99 sages does not necessarily have to correspond to them.

Based on which Criminal Code article theorem, axiom, etc., is this conclusion made? ;)

I don't know. Probably also based on the fact that 2+2=4 and 4-2=2. In my opinion, it's clear even without any proofs.

Added after 4 minutes
If it really isn't clear, I will try to explain using an example with 10 sages. Set the colors of their hats then, and we'll count together.