I never liked this type of puzzle. It is not formal logic but more about the idiosyncrasies and conventions of the English language. I put this puzzle on par with Agatha Christie’s murder mysteries. It requires a suspension of disbelief and logic to be believable.
Someone who always lies means in the purest sense means you cannot trust anything they say. Even the word “hat” could mean they are talking about their pet cat that they like to carry on their head.
What the author would probably say is “All my hats are green” means the liar is either lying about All or Green. Either all their hats are some other color or only one hat is green. This means you have to assume the liar has a hat. How do we know that?
We only know that because of similar puzzles that came before. In other words this is not logic but more pattern recognition.
Someone who always lies means in the purest sense means you cannot trust anything they say. Even the word “hat” could mean they are talking about their pet cat that they like to carry on their head.
What the author would probably say is “All my hats are green” means the liar is either lying about All or Green. Either all their hats are some other color or only one hat is green. This means you have to assume the liar has a hat. How do we know that?
We only know that because of similar puzzles that came before. In other words this is not logic but more pattern recognition.