BrainDen.com - Brain Teasers
• 0

# The always liar

## Question

Mike joins a campfire with three friends. After five minutes, Mike is bored and decides to start up a conversation:

(speaker- dialogue)

Mike- Tell me something interesting.

Adam-one of us is always a liar.

Mike-Really?

Eric- Yes. They always lie, but one of us is also always a truth teller.

Mike- Oh, cool, well then …that would mean that Sam is the ‘always liar.’

Sam- Yes, yes I am.

Mike-…What? Wait a minute. I thought you were always a liar.

Sam- Yes I am.

Eric-He is.

Mike-He is?

Eric-yes

Sam-yes

Mike-yes?

Mike-no.

Sam-no.

Mike-wait….then does that make Eric the liar?

Eric- Yes

Sam- No

Mike- What??

**Who is the ‘always’ liar?

## Recommended Posts

• 0

Let us indicate always liar by 'L' and always truth teller by 'T'.

There are four sets of conversation:

Mike- Tell me something interesting.
Adam-one of us is always a liar.
Mike-Really?
Eric- Yes. They always lie, but one of us is also always a truth teller.
Mike- Oh, cool, well then …that would mean that Sam is the ‘always liar.’
Sam- Yes, yes I am.

Above tells us:

[1] Adam can't be 'L' if one of them is 'L'. He cold be 'T'.

[2] Eric can't be 'L', if one of them is 'T', but he could be 'T'.

[3] Mike's interpretation from the conversation is not correct, as the conversation which took so far between them could not ascertain that Sam is 'L'. So Mike could be 'L'.

[4] Sam can't be 'L', he is not 'T' also.

Second set of conversation:

Mike-…What? Wait a minute. I thought you were always a liar.

Sam- Yes I am.
Eric-He is.
Mike-He is?
Eric-yes
Sam-yes
Mike-yes?
Mike-no.
Sam-no.

Above tells us:

[5] Mike could be 'L'.

[6] Sam can't be 'L' or 'T'.

[7] Eric can't be 'T'. Though here he is lying but if one of them was 'T', then he can't be 'L' as he could be 'T' in First set of conversation.

[8] Adam is right here, so he could be 'T'. So he can't be 'L'.

Third set of conversation:

Mike-wait….then does that make Eric the liar?
Eric- Yes
Sam- No
Mike- What??

Above tells us:

[9] Mike could not be put into any catagoury.

[10] Eric could not be 'T'.

[11] Sam could be speaking truth.

[12] Adam could be telling truth here.

So if one of them is 'L', then it has to be Mike only. And then Adam will be 'T'.

Edited by bhramarraj
##### Share on other sites

• 0

Adam always lies, and the other two are just messing with him.

The question 'yes?' is rather vague. I have no idea what he's trying to ask.

Edited by ParaLogic
##### Share on other sites

• 0

the "yes?" is meant to convey his repeating of their answers with disbelief or confusion.

Adam always lies, and the other two are just messing with him.

The question 'yes?' is rather vague. I have no idea what he's trying to ask.

##### Share on other sites

• 0

Adam always lies, and the other two are just messing with him.

The question 'yes?' is rather vague. I have no idea what he's trying to ask.

##### Share on other sites

• 0

Oops. I accidentally (mentally) switched Eric/Adam's names when I read the first few lines.

Edited by ParaLogic
##### Share on other sites

• 0

Oops. I accidentally (mentally) switched Eric/Adam's names when I read the first few lines.

What would that mean with regards to Eric's last line?

##### Share on other sites

• 0

None of them are either always liars or always truthtellers. Adam just happened to be lying in the first line.

##### Share on other sites

• 0

None of them are either always liars or always truthtellers. Adam just happened to be lying in the first line.

I disagree.

##### Share on other sites

• 0

Though I disagree with your view that Adam is the truth teller.

Let us indicate always liar by 'L' and always truth teller by 'T'.

There are four sets of conversation:

Mike- Tell me something interesting.

Adam-one of us is always a liar.

Mike-Really?

Eric- Yes. They always lie, but one of us is also always a truth teller.

Mike- Oh, cool, well then that would mean that Sam is the always liar.

Sam- Yes, yes I am.

Above tells us:

[1] Adam can't be 'L' if one of them is 'L'. He cold be 'T'.

[2] Eric can't be 'L', if one of them is 'T', but he could be 'T'.

[3] Mike's interpretation from the conversation is not correct, as the conversation which took so far between them could not ascertain that Sam is 'L'. So Mike could be 'L'.

[4] Sam can't be 'L', he is not 'T' also.

Second set of conversation:

Mike-What? Wait a minute. I thought you were always a liar.

Sam- Yes I am.

Eric-He is.

Mike-He is?

Eric-yes

Sam-yes

Mike-yes?

Mike-no.

Sam-no.

Above tells us:

[5] Mike could be 'L'.

[6] Sam can't be 'L' or 'T'.

[7] Eric can't be 'T'. Though here he is lying but if one of them was 'T', then he can't be 'L' as he could be 'T' in First set of conversation.

[8] Adam is right here, so he could be 'T'. So he can't be 'L'.

Third set of conversation:

Mike-wait.then does that make Eric the liar?

Eric- Yes

Sam- No

Mike- What??

Above tells us:

[9] Mike could not be put into any catagoury.

[10] Eric could not be 'T'.

[11] Sam could be speaking truth.

[12] Adam could be telling truth here.

So if one of them is 'L', then it has to be Mike only. And then Adam will be 'T'.

##### Share on other sites

• 0

I am getting - Mike always lies, and rest 3 sometimes tell truth and sometimes lie.

Edited by dark_magician_92

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.