Inspector Craig and the Vampire Sisters
In Smullyan's Transylvania, every inhabitant is a human (always truthful) or a vampire (always lying) — and separately, either sane (correct about what's true) or insane (convinced every true thing is false). Two sisters, one human and one vampire, sanity unknown. The first says, 'We are both insane.' The second says, 'That's not true!' Which sister is the vampire?
Reveal the answer
The first sister is the vampire. Working through both possible truth-values of her claim shows the two are only ever mutually consistent when she is the vampire — the second sister's contradiction is forced into being true in every consistent scenario, which only a human or an insane vampire could state truly, and elimination fixes the first sister as the liar. From Raymond Smullyan's What Is the Name of This Book?
— Raymond Smullyan, What Is the Name of This Book? The Riddle of Dracula and Other Logical Puzzles — 1978, 'Dracula in Transylvania' chapters
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