Truth and Lie

Logic Level 1

There was once three fortune tellers, namely Truth (who always tell the truth), Lie (who always lies), and Wise (who sometimes tells the truth or lies). An investigator was sent to know if who is the Truth, Lie, and Wise.

The investigator asks the one who is sitting on the left: "Who is sitting next to you?" She replied: "Truth".

The investigator asks the one who is sitting on the middle: "Who are you?" She replied: "Wise".

The investigator asks the one who is sitting on the right: "Who is sitting next to you?" She replied: "Lie."

Who is sitting on the left, middle, and right respectively?

Image credit: Wikipedia Joseolgon
Wise, Truth, and Lie Truth, Wise, and Lie Lie, Truth, and Wise Wise, Lie, and Truth

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11 solutions

Ameya Salankar
Apr 26, 2014

Let's analyze each sentence.

The first lady (on the left) can't be Truth because she never lies. She would certainly not have said her own name.

The second lady (at the middle) also can't be Truth . If she were, she would have said her own name.

The above two statements imply that the last lady (at the right) is Truth . Her statement would imply that the middle lady is Lie & that implies that the first lady would be Wise .

Mayank Holmes
Apr 26, 2014

it's very simple......... if the first lady is telling the truth and the second one is indeed TRUTH why would he lie and tell that he is WISE! it implies that the first lady is not TRUTH at least! then, coming to the second lady, she's also not truth hence the third lady is bound to be truth! There is only one option which says that the third lady is TRUTH ! hence that option is bound to be the answer

3 possibilities for left:

  1. She is truth

  2. She is wise

  3. She is lie

Scenario 1: If left is truth, then, according to what truth said, the middle one must be truth. This scenario is obviously wrong.

Scenario 3: If left is lie, then, since she said that middle was truth, middle has to be wise. That means, right has to be truth. But when we asked right who middle was, she said 'lie'. Thus this scenario is also wrong.

Scenario 2:

This one has two sub-cases. Since left is wise, she could have told either the truth or a lie. So, sub-cases:

  1. If wise is telling the truth, then middle has to be truth. But when we asked middle about herself, she said she was lie. So, this sub-case is invalid.

  2. If wise was telling a lie, then middle was to be lie. This makes sense because when we asked middle who she was, she lied saying that she was wise. Now, when we asked right (who, according to this must be truth) who middle was, she said lie - which is the truth in this situation.

Therefore, scenario 2, sub-case 2 must be correct.

Why does it have to be a she

Seamus McGuinness - 4 years, 10 months ago
Mohit Sharma
May 5, 2014

The first lady says middle one is Truth , but middle one says she is Wise also if first was Truth she wouldn't lie, similarly middle one is also not Truth which means last lady is Truth, last one says lady next to her is Liar which makes middle one Liar and first one Wise

according to left lady .... the middle person is truth. if this statement was true , the middle one would have said that she was truth(since 'truth' always tells truth).Since she did not.... left one is NOT telling truth. Also both of them must not be 'truth' (since middle one is telling that she is 'wise'). hence the third one is truth. And hence she says middle one is Lie, the other one should be wise....

Saya Suka
Feb 16, 2021

All 3, including the person herself, were telling 3 different versions of who the middle person is. Having the right one 'accusingly' naming the middle one as Lie, then one of them must have told the truth while the other lies. The middle one could NOT have been Truth who would identify herself, and it's also impossible for Truth to introduce another Truth when they have different name for each, so the left one couldn't be Truth, either. Then, in conclusion we have Truth on the right, Lie in the middle, and Wise on the left.

• ·
May 4, 2020

If wise (middle) was telling the truth then (right) would have said middle was lies (left) certainly is telling false about middle

Mario Egie
Apr 22, 2018

Let's analyze their response from person to last (left to right).

  1. She is Truth
  2. I'm Wise
  3. She is Lie

Lie - always tells lies, Wise-may tell lie or truth, Truth - always tells truth.

We have to start reasoning with the only certain reply we may have which is the response from "Truth".

If person 1 says person 2 is Truth, then person 1 cannot be Truth, since she will always tell the truth!

Person 2 say I'm Wise. If person 2 were Truth, then she will tell us the true by saying she is "Truth", thus person 2 cannot be Truth. Which leaves only one option. Person 3 = "Truth"

If person 3 is Truth then since she will always say the truth means person 2 = "Lie" according to Truth. Leaving person 1= "Wise".

Thus: wise, lie, truth

The first lady says that the person next to her is Truth.

The second lady says that she's Wise.

The third lady says that the person next to her is Lie.

Therefore, The second lady is either Lie or Wise. If she was Truth she would have said her own name, so we can rule that out.

The other two ladies are either saying the truth or lying. They can both say the truth, but they can't both lie.

Considering that none of the other two ladies state that they're next to Wise, that must mean that the Second lady is Lie.

The third lady was right so she's Truth, while the first is Wise telling a lie.

Jessica Bilger
Dec 17, 2015

I started with the first choice and pretended as if it was correct, then looked up at the text to see if what they said would have made sense. It did, but in case I made an error, I did the same with the other 3. The first choice was the only one that made sense, so I picked it. Too simple?

Ahmed Obaiedallah
Jun 11, 2015

first: If Truth got asked about others

1- She will say the truth

2-She can't answer with the word "truth" her name

second:

there are 2 of them have been asked about others, one said "truth" and the other said "lie" and the 3rd said "wise"... from first we know that the left can't be truth also the middle; so it has to be the right lady which said that the middle one is "lie" so the left will be "wise"

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