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# The liar, the truth teller....and the random answerer

Best Answer Writersblock , 30 July 2007 - 01:31 AM

Martini,

Spoiler for ...
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94 replies to this topic

### #71 carlo1974

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Posted 20 September 2009 - 07:19 PM

This i think is the soultion ok.ask the first two if they are male if yes yes then you know who the liar is
then ask the liar if the first man is the truth teller if no he is if yes he isnt thats only half solved it
but i think to find out the liar is the key to solving it.
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### #72 carlo1974

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Posted 20 September 2009 - 11:25 PM

ask the 2 men if they are male if yes yes then the third man is the liar then ask the liar if the first man is the random teller if the liae responds yes then the random teller is the middle man and the first man is truth teller
then you know who is who if the liar responds no then the first man is the truth teller etc etc.second answer if you ask first two men are you male and the answer
is yes no then the secon is the liar ask the liar if the first man is the truth teller if yes the truth teller is the third man etc etc.

Edited by carlo1974, 20 September 2009 - 11:28 PM.

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### #73 JazC

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Posted 14 January 2010 - 12:08 AM

You could ask them to stand in a row. Let’s name them A, B and C. So ask A if there is a person standing in front of him/her , if he/she says YES he/she could either be the R.A or the T if he/she says NO then he/she is the L. Then ask B the same question, he/she again can say YES so he/she is the R.A or the T, if he/she says NO we are dealing with the L. Now what we have to determine, and after doing this we will, is who is the L so when we get him/her we must ask “Is the person next to you or in front of you (depends where the liar is spotted) the T? If he/she says NO then we know it IS (because he/she will lie) and if he/she says YES we know it isn’t so we know the other person is. That way we will know who the T is, the L is and finally the R.A.
Does it make sense?
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### #74 Zarcc

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Posted 30 January 2010 - 11:50 AM

Martini,
<div style="margin:20px; margin-top:5px">
<div class="smallfont" style="margin-bottom:2px">Spoiler for ...: <input type="button" value="Show" style="width:45px;font-size:10px;margin:0px;padding:0px;" onClick="if (this.parentNode.parentNode.getElementsByTagName('div')[1].getElementsByTagName('div')[0].style.display != '') { this.parentNode.parentNode.getElementsByTagName('div')[1].getElementsByTagName('div')[0].style.display = ''; this.innerText = ''; this.value = 'Hide'; } else { this.parentNode.parentNode.getElementsByTagName('div')[1].getElementsByTagName('div')[0].style.display = 'none'; this.innerText = ''; this.value = 'Show'; }">
</div><div class="alt2" style="margin: 0px; padding: 6px; border: 1px inset;"><div style="display: none;">Originally I thought this was impossible, but I think I have solved it. Nice one.

I saw that:

There are 6 possible states for the order of the men: TRL, TLR, LTR, LRT, RTL, RLT

There are 8 possible combinations of anwers for questions: TTT, TTL, TLT, TLL, LTT, LTL, LLT, LLL.

Theoretically it's possbile if you could figure out a way to get any of the 8 combinations of answers assigned to the states, but with the unreliability of Random's answers, I thought it was impossible. There is always a possiblity in any solution where Random will exactly mirror T or L for answers. He could always lie or always tell the truth and you can never tell when he is lying or telling the truth. This being given, I thought you can NEVER separate 6 distinct answers to apply to the 6 states, and therefore can never be sure who is who.

After a minute though, I saw through my own error in logic. I was always dealing with questions where T and L would give the same answer regardless of the order of the men. I saw that if you can get T and L to give a Yes/NO answer, then you can figure out where R's worthless answers are. The only way I saw to do this is to ask about the order of the men themselves.

So:
Ask #1 if L is standing on R's right arm (our left if they are facing us).
The answer gives you a split in the order they are standing:
If YES, then it has to be T telling the truth, L telling a lie, or one of R's worthless answers, so: TLR, LTR, or RTL, RLT.
If NO, then it has to be T telling the truth, L telling a lie, or R and his worthless answers, so: TRL, LRT, or RTL, RLT.

Now we know, based on the answer to #1 where to avoid R's worthless answers. We now ask T or L "Is T in the lineup?" If answer 1 was Yes, we ask person 2, if it was no we ask person 3.

The answer now will give us some more info. If it's Yes, it's T answering the truth, if it's no, it's L answering a lie. So based on who we asked, we now know:

Yes, Yes: Has to be LTR, or RTL
Yes, No: TLR, RLT
No, Yes: LRT, RLT
No, No: TRL, RTL

Now any question separating the two possiblities works - just make sure you are avoiding R's worthless answers.

For example:
Yes, Yes - ask #2 if #1 is L. (We know #2 is T and will tell the truth) - Yes = LTR, No = RTL
Yes, No, - ask #2 if #1 is T. ( We know #2 is L and will tell a lie) - Yes = RLT, No = TLR
No, Yes - ask # 3 if #1 is L. (We know #3 is T and will tell the truth) - Yes = LRT, No = RLT
No, No, - ask #3 if #1 is T. (We know #3 is L and will tell a lie) - Yes = RTL, No = TRL

So we have the order and know who is who.</div></div></div>

I like where you are going with this, however you can't answer it in 3. Your solution involves 4 which is still the random check. At best you can get lucky.

'Truth is T
'Lie is L
'Random is R

'Three men and lined up.
'No other given

'Possibilities TRL TLR LRT LTR RTL RLT

Ask 1 if it is R
Yes
'Possibilities LRT RLT RTL Senario 1
No
'Possibilities TLR TRL RLT RTL Senario 2

Senario 1
Ask 3 if person to your left is a liar
Yes
'Possibilities RLT RTL Senario 1a
No
Answer is RLT
Senario 1a
3 are you a man
Y = RLT
N = RTL

Senario 2
2 is the person to your left truth?
Yes then insolvable in 3 as random is not isolated.
No TRL RTL Senario 2a

Is the person to your left T?
Yes, answer is TRL
No answer is RLT

Ashamed I can't think of 3 which wins every time and to think it is impossible and sorry for my sloppy format. It is nearly 6am and I am in bed on a stubborn iPod. Let me know if anyone has better.
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### #75 Zarcc

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Posted 30 January 2010 - 12:06 PM

You could ask them to stand in a row. Let’s name them A, B and C. So ask A if there is a person standing in front of him/her , if he/she says YES he/she could either be the R.A or the T if he/she says NO then he/she is the L. Then ask B the same question, he/she again can say YES so he/she is the R.A or the T, if he/she says NO we are dealing with the L. Now what we have to determine, and after doing this we will, is who is the L so when we get him/her we must ask “Is the person next to you or in front of you (depends where the liar is spotted) the T? If he/she says NO then we know it IS (because he/she will lie) and if he/she says YES we know it isn’t so we know the other person is. That way we will know who the T is, the L is and finally the R.A.
Does it make sense?

That makes sense but should you run into N Y then you have
LRT
RTL
LTR

Thusly you haven't narrowed down R, where to go from there?
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### #76 Zarcc

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Posted 31 January 2010 - 08:21 AM

All day at work I thought this through completely convinced you couldn't isolate R which is key as you must do it on the first question. Then as I fell into a much needed nap it hit me. Use a condition question to isolate random. "1 assume that random's answer would be the same, what would the person to your right say if I was to ask him if he was a man."

Should the answer be yes then we know that is either TRL or RLT.
Should the answer be no then we know it is LRT or RLT .

Because random now has to be one of those two you not only eliminate a false answer but you also make it so 3 has to be either T or L. Now you can go from there.

I choose, "3, are you a man?". Yes mean T no means L. Then from there you can simply ask if the person to your you left is random. Knowing which one it is will let you decide how to interpret the answer. Now I can finally sleep.
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### #77 vaughngray

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Posted 25 April 2010 - 05:45 AM

i have a solution too and it seems simple:D

so:
we have 1 2 3
We ask 1:" do i have 5 figers at one hand?" ( and i do ) )
He answers: NO => 1 = L
then i ask 1 : " is 2 random?" => he answers yes =>2= T and 3 = R
no => 2 = R ; 3 = T

He answers YES: => 1 = T or R
then i ask 2" is 1 L?" => YES => 2 = L then i ask 2" is 1 T?" => YES => 1= R and 3= T
NO => 1= t and 3= R
=> NO => 2 = R or T and 3 = L ; so i ask 3 "if 1 is T?" = > YES => 1=R and 3=T
NO => 1= T and 3 = R

Is it OK ?

If he answers "no" he can be the random. bc of this, the rest of the logic doesn't follow
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### #78 Zak

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Posted 06 September 2010 - 04:06 PM

Spoiler for ok guys this is how i solve it and its a bit long explination hope to be clear

Edited by Zak, 06 September 2010 - 04:08 PM.

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### #79 peanut

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Posted 24 September 2010 - 01:41 AM

Spoiler for let me see if I have it clear

Edited by peanut, 24 September 2010 - 01:45 AM.

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### #80 Zak

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Posted 24 September 2010 - 11:03 AM

Spoiler for let me see if I have it clear

i tried alot of direct question like that but its never right all the way, its solve 80% of the possibilities but not 100%

like now in the third possibilities you put (if m1 is T or R, m2 is L or R then m3 canot be R and has to be T or L)

but m3 can be the R, if m1 T and m2 L then m3 will be R

so in this case m3 can be R,T,L and we have one more question to go which make it impossible
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