The contents of the green box make the labels paradoxical; but it's OK because paradoxes exist.
Consider a paradox such as "This sentence is false". There's a problem with deciding if it's true or false. Countless articles and books have been written about it, and there exist different ways of dealing with this "difficulty". However, nothing prevents you from actually writing these letters on a piece of paper, and nothing prevented me from typing them a few seconds ago. The puzzle we're talking about makes the same point in a more amusing fashion.
hm, isnt that obvious? if it's just "we do whatever we want regardless of whatever", then we dont need to go that far: elaborating a nonsense puzzle to prove nonsense.
Consider a paradox such as "This sentence is false". There's a problem with deciding if it's true or false. Countless articles and books have been written about it, and there exist different ways of dealing with this "difficulty". However, nothing prevents you from actually writing these letters on a piece of paper, and nothing prevented me from typing them a few seconds ago. The puzzle we're talking about makes the same point in a more amusing fashion.