# The Truth-Teller And The Liar Puzzle

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?

### Posted by Edmark M. Law

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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1. I was wondering about this. Asking them anything where we can see the truth. Like the frog example above, or just so we absolutely know the truth something about ourselves.

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1. Graham says:

Sounds good to me…if you know someone is lying by sight you can’t beat a bit of entrapment. A guide for everyday life! 🙂

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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. I think that the form of the liar’s paradox that was used in Labyrinth was the original one. It’s frequently featured in classical literature and several variations have been developed over the years.

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3. 🤔…now I am intrigued. But Veritas is a liar right? Estanlished fact. So Truth gotta be telling the truth and so Veritas is the liar? Garfield logic may not work here haha!

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1. Lol :)

So far, we had only established that Alex spoke to Veritas. However, we still don’t know who among the sisters is the liar :)

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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?

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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.

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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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4. I am not good at this but if I could ask a question it would bluntly be…are you lying? Truth we know will never lie…I think…but I may be wrong too ha ha!

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5. I think there’s a trick here that I’m not fully comprehending….but I like it….

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1. Haha, I was hoping for someone to give this answer, as this is the most straightforward answer to my last question (who is the liar/truth-teller) that I’m aware of.

Thanks for sharing the video.

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