One sister is human, one's a vampire. A single sentence gives her away
On Smullyan's island of Transylvania, every inhabitant is human or vampire, and separately sane or insane. Sane humans and insane vampires always tell the truth; insane humans and sane vampires always lie. Of two sisters, Lucy says, 'We are both insane.' Minna replies, 'That's not true.' Exactly one sister is a vampire — which one?
Reveal the answer
Lucy is the vampire. If Lucy's statement were true, both sisters would be insane, which only works if Lucy is an insane vampire (a truth-teller) — and that forces Minna, as the human, to be an insane liar, matching her false denial. If Lucy's statement is false, she must be a sane vampire (a liar), which again makes Minna the human. Either way, Lucy can't come out human.
— Raymond Smullyan, The Lady or the Tiger? and Other Logic Puzzles — 1982
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