A detective interrogates three suspects: Tom, Dick, and Harry. Exactly one of them committed the crime. Tom says: 'Dick did it.' Dick says: 'Harry did it.' Harry says: 'Tom is lying.' If only one suspect is telling the truth, who is the guilty party?
Dick
Let's check each case. If Tom is telling the truth (Dick is guilty), then Dick lied (Harry did it is false) and Harry told the truth ('Tom is lying' - wait, if Tom told the truth, Harry saying 'Tom is lying' means Harry lied. That works: Tom true, Dick false, Harry false. That's one truth-teller). If Dick is guilty: Tom lied (Dick did it), Dick lied (Harry did it), Harry told the truth (Tom is lying). That's one truth-teller. Wait, let's verify who is guilty. If Dick is guilty, Tom's statement 'Dick did it' is TRUE. Dick's statement 'Harry did it' is FALSE. Harry's statement 'Tom is lying' is FALSE (because Tom told the truth). So truth-tellers = Tom and Harry (two truth-tellers, but prompt says *only one* is telling the truth). Let's re-test Tom being guilty: Tom is guilty -> Tom lies (Dick did it is false). Dick tells the truth ('Harry did it' is false? No, Dick says Harry did it, which is false). Harry tells the truth ('Tom is lying' is true). Truth-tellers = Harry (1 truth-teller). So Tom is guilty? Wait, if Tom is guilty, Dick didn't do it, so Tom's statement is false. Dick's statement 'Harry did it' is false. Harry's statement 'Tom is lying' is true (since Tom lied). So Harry is the only one telling the truth. Thus, Tom is guilty? Wait, if Tom is guilty, Tom lied. Let's test Dick being guilty: Dick is guilty -> Tom says 'Dick did it' (TRUE). Dick says 'Harry did it' (FALSE). Harry says 'Tom is lying' (FALSE, because Tom told the truth). Here, only Tom is telling the truth! Therefore, Dick is the guilty party.
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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