The Truth-Teller And The Liar Puzzle

truth lie.jpg

Veritas and Truth are sisters. One of them (we don’t have any idea who) always tells the truth while the other always lies. Alex questioned one of them:

“Is Truth the one that lies?”

“Yes,” she replied.

Did Alex speak to Veritas or Truth?

Solution

Before I present the solution, think about this: Would someone who either always tells the truth or always lies call himself a liar?

The answer is obviously no. If someone always tells the truth, he would say that he is not a liar. Similarly, a person who constantly lies would also deny that he is a liar.

This is the basis for our solution. We can now conclude that Alex spoke to Veritas. Why? As stated above, neither the constant truth-teller nor constant liar would say that she is a liar. We know that one of the sisters is always telling the truth and the other is always telling lies. This means that when Alex asked whether Truth was the one who always lies, only Veritas could answer affirmatively.

Anyway, we still don’t know who among the siblings is the liar. Just for fun, can you think of one question (you can only ask one of them) that would enable you to determine which of them is the liar?

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My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is edmarklaw@learnfunfacts.com

30 thoughts on “The Truth-Teller And The Liar Puzzle

  1. The Tree Frog scene is the essence of Zen simplicity. The wise man constructs laborious traps of logic; the fool cuts through with a question as sharp as a sword.
    “Ahhhhh! Not fair!” cries the wise man….

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  2. Ask them if they’re a frog… I like it! (unless they ARE a frog in human form, they can only say no and it’d be the truth, since they’re not a frog and that’s ridiculous).

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      1. You may want to have a look at the video shared by gc-photo-art in the comments section. That was essentially the answer that I was looking for. Watch it until the end 🙂

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      2. Thanks! I prefer the “tree frog” – but it was not deduction and logic. Hmm then I am an illogical person LOL! Double negative – the other village…still don’t quite get it but it is the way of paraphrasing a double negative to get the right answer from a liar I guess. – if you can from the other village…..then it lost me!! Sigh! Care to help me understand better Edmark?

        Liked by 1 person

      3. It may not be a deductive logic but it’s an inductive logic.

        Yes, something like that. You can also ask, “If I ask you if you are from the liars’ village, would you say no?”

        The truth teller will certainly answer “yes” since he’s from the truth tellers’ village.

        On the other hand, the liar won’t admit that he’s from the liars’ village if you question him. But by also adding if “he would say no”, you have forced him to answer “no”. This in effect made him admit that he’s from the liars’ village.

        Anyway, in real life, you need both deductive and inductive reasoning to determine whether someone is lying. That’s why asking weird and seemingly illogical questions is a standard interrogation technique.

        Liked by 1 person

      4. I cannot thank you enough for teaching me this. I am learning valuable mathematical reasoning from you. Garfield hugs🤗and thank you for your passion in sharing😊

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