Anna, Ben, and Carl each hold a card numbered 1, 2, or 3. No two cards are the same. Anna says, 'My number is higher than Ben's.' Ben says, 'My number is not 1.' Carl says, 'My number is 1.' If only one of them is lying, what number does Ben hold?
3
Let's test who is lying. If Carl is telling the truth, his card is 1. If Ben's card is not 1 (say 2 or 3), and Anna's card is higher than Ben's, Anna must be 3 and Ben must be 2. This means Carl(1), Ben(2), Anna(3). In this scenario, Anna(3 > 2) is true, Ben(!= 1) is true, Carl(1) is true. That's zero liars, but the prompt says 'only one of them is lying'. Let's re-evaluate. If Carl is lying, his card is NOT 1. Then Carl's card is 2 or 3. If Carl's card is 2, and Ben's card is not 1 (say 1? No, Ben says 'My number is not 1' - if Ben holds 1, Ben is lying). Let's trace: Suppose Ben holds 1, making Ben's statement false (1 liar). Then Carl's card is 1? Impossible, numbers are unique. Thus Ben cannot hold 1. Let's assume Ben holds 3, Anna holds 2, Carl holds 1. Anna says '2 > 3' (False). Ben says '3 is not 1' (True). Carl says '1' (True). Exactly one liar (Anna). Thus, Anna holds 2, Ben holds 3, Carl holds 1. Ben holds 3.
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: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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