We're all mad here! IV
Everyone in Wonderland is either sane or mad. A sane person believes a statement if and only if it is true, while a mad person believes a statement if and only if it is false.
The King of Hearts, Queen of Hearts, and Alice all know whether each of the three is sane or mad (although they might not believe it).
The King says, "I believe that Alice believes I'm sane."
Alice says, "I believe that the Queen believes the King is mad."
The Queen says, "I believe that Alice is mad!"
Each person told the truth. Which of the three are mad?