I didn’t use degrees or radians.
Carleas,[tab]
You were better off before.
“A color cannot be deduced from a set of colors”?
What the hell is that?? Did you leave out some words or something?
And:
“…the set C of known correct answers…”
What?? Where is it a given that there is a set of known correct answers before they have even began deducing?
I agree but I contend that your example is also merely an educated guess based upon what is seen and the presumption that there is no way to resolve it except by using what is directly seen.
It is not logically deducible that each color is necessarily seen by its wearer.
What you cannot deduce is that you know the closed set. Assuming the set to be already closed is no different than assuming it to be closed by merely one more color. Either way it is an assumption.
The fact that the master said that the problem is solvable does not change which of those assumptions would be more probable and certainly not which would be a certainty.
The bottom line is that everything deduced must be directly or indirectly defined to be correct. All logic resolves to recognizing what has already been defined to be true.
…even worse than the blue-eyed problem. You and those who believe that such puzzles can be resolved in that way are deluding yourselves.
“If this problem was different than it is…”
… is not a valid premise to solve any puzzle.
“it wasn’t common knowledge that even one of them had a muddy forehead.”
…is incorrect.[/tab]