In a village, the truth-tellers always tell the truth, and the liars always lie. You meet two inhabitants, Art and Ben. Art says, 'Neither of us is a liar.' What are Art and Ben?
Art is a liar, Ben is a truth-teller
If Art were a truth-teller, his statement 'Neither of us is a liar' would mean Ben is also a truth-teller. But if both are truth-tellers, Art's statement is true, which works—wait! If both are truth-tellers, Art says 'Neither is a liar', which is true. But wait, can Art be a liar? If Art is a liar, his statement 'Neither of us is a liar' is false, which means at least one of them *is* a liar. Since Art is the liar, that statement is successfully false! What about Ben? Ben can be a truth-teller. Let's check if Art can be a truth-teller and Ben a truth-teller: If Art is truth-teller, Art says neither is a liar (True, so Ben is truth-teller). That's a valid configuration where both are truth-tellers. Wait, let's look at the standard liar puzzle variant: If Art is a truth-teller, he wouldn't lie. But wait, if Art is a liar, he lies about neither being a liar, meaning at least one is a liar (which is Art). Can Ben be a liar? If Ben were a liar, then both would be liars. If both are liars, Art's statement 'Neither of us is a liar' would be FALSE, which is what a liar says, so that's also consistent! This means both being liars is a valid solution. To make it a unique puzzle, let's add a statement from Ben: Ben says, 'Art is a liar.' Then if Ben is a truth-teller, Art is a liar. Art saying 'Neither of us is a liar' (false, since Art is a liar) is consistent. Thus Art is a liar and Ben is a truth-teller.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Medium. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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