KöMaL 2008 K182

In a certain town, each inhabitant is either truthful or a liar, and each of them is either sane or insane. Truthful people say what they think and liars say the opposite of what they think. Sane people think what is true, and insane people think the opposite of the truth. Four inhabitants of the town said the following: Andy: I am insane. Mandy: I am truthful. Sandy: I am a liar. Dandy: I am sane. Andy: Sandy is truthful. Mandy: Dandy is insane. Sandy: Mandy is a liar. Dendi: Sandy is sane. Determine who is truthful and who is a liar, who is sane and who is insane.