yes/no logic problem

Question

*There is a Truth Teller (always tells the truth), a Liar (always lies), and an Occasional Liar (sometimes lies, and sometimes says the truth). Each of them knows who is who.

You may ask three 'yes or no' questions to determine who is who. Each time you ask a question, it must only be directed to one of them (of your choice). You may ask the same question more than once, but of course it will count towards your total. What are your questions and to whom will you ask them? ?*

In all honesty, I don't know where to start with this type of question. I'm really not looking for an answer, but guidance on how to approach a problem like this.

The condition that

"Each person knows who is who"

Seems to me to be the important part of this, and means I should start with trying to discover the occasional liar, but what I can't work out is the starting question I should ask.

So I then tried to ask each person if they're a liar, which caused me confusion because if I ask 'A' if he is the liar, and he says 'yes', then he is not the liar, as the liar would say 'no'; therefore, he is telling the truth.

But if he says 'no', then he could be telling the truth or a lie and doing this for the other outputs the same result, which confused me even more.

Is there a possibility someone could break this down a little, it would be much appreciated.

Also I am new here and not sure what tags I should tag, so sorry for the wrong input.

Does this answer your question? A Possible Solution to George Boolos' "The Hardest Logic Puzzle Ever" — ben svenssohn, Sep 07 '23 at 11:27
@bensvenssohn Not a duplicate. This puzzle is solvable with 3 questions and the respondents are speaking a language where you know the difference between "yes" and "no". The other puzzle is not solvable with 3 questions (see the answer) because you don't know which word means "yes" and which one means "no". — Rand al'Thor, Sep 08 '23 at 04:58

Excited Raichu · Accepted Answer · 2018-10-29T14:29:22.297

5

Here's a bit of guidance:

The person who answers randomly is a big problem, because you don't get any useful information from them. You may want to consider using your first question to single out one who does not speak randomly. After that, ask them about the identities of the other two, but make sure that you figure out if they tell the truth or not!

My solution (as OP requested in comments):

Question 1:

Pick one person at random and ask "If I were to ask the person who answered randomly if 2+2=4, what would they say?" The truth teller and the liar have no way to answer this, so will say something along the lines of "I don't know" or just not answer. The person who speaks randomly will give a random yes or no answer. If you don't get an answer, you are talking to someone who is NOT random, if you do get an answer, you are talking to someone who IS random.

Question 2:

Ask someone who is NOT random "Is 2+2 equal to 4?" On a yes, you are talking to a truth teller. If the answer is no, you are talking to the liar. If you already know the identity of the random person from question 1, you're done. Otherwise, go to Question 3...

Question 3:

Ask the person you've identified as a liar or truth teller, "Is the person to the left (or right) of you (the other one of truth teller or liar)? Then, based on the response, you'll know all 3 of their identities!

edited Oct 29 '18 at 14:29

answered Oct 27 '18 at 14:40

Excited Raichu

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Thank you, I think I am nearly there hopefully. – james2018 Oct 27 '18 at 15:55
Could you ask the random guy if he random as the only answer to give would be 'No' as he cant ans 'Yes' – james2018 Oct 28 '18 at 16:22
@james2018 the only problem with that is you don’t know who is random to start. In addition, (s)he could answer “yes” because (s)he answers randomly- (s)he is as likely to answer no as (s)he is to answer yes – Excited Raichu Oct 28 '18 at 18:52
Yes I suddenly realised, which is now causing an issue. So I feel like I am back to square one, I know what I need is somthing a question for T, L to give the same ans, but this is what troubling me, I cant see how. – james2018 Oct 28 '18 at 19:36
@james2018 not knowing the answer can also contain information... – Excited Raichu Oct 28 '18 at 22:00
are you reffering to what combination of yes/no there can be for each line up? i.e TLR: Yes, Yes, N/A, N/A as I would not need to know the ans from R as I have two yes from T and L. Other wise I am lost to what you mean. – james2018 Oct 28 '18 at 22:50
I cannot honeslty see a way through this problem as if u ask A 'Dose B always tell the truth' the lair and the truth teller would give same response but it still dose not help identify the random guy as if he as A he would respond yes/no, so to me you just going round in a circle-@Excited Raichu

james2018

Oct 29 '18 at 13:50

@james2018 if you want I can edit in my solution. – Excited Raichu Oct 29 '18 at 13:52

That would be much appreciated as iv been at this now for sometime and think I am just going in cirlces. – james2018 Oct 29 '18 at 14:21

score 3 · Answer 2 · answered Oct 27 '18 at 13:45

Assume you have them standing in front of you, with 1 to 2’s left and 2 to 3’s left. You can

First ask 1 if Sometimes stands to the right of the Liar. If YES, then 1 truth teller => order is TLS. 1 liar => order is LTS. 1 sometimes => order is either SLT or STL. Note that if YES, then person 2 is never the sometimes. If NO, then 1 truthteller => order is TSL. 1 list => order is LST. 1 sometimes => order is either SLT or STL. Note that person 3 is never the sometimes.

Then for the second question,

Ask 2 if answer 1 was YES, or ask 3 if answer 1 was NO. Ask: is there a truthteller in the lineup? Then obviously a YES means truthteller and a NO means liar. So: YES YES => order is LTS or STL. YES NO => order is TLS or SLT. NO YES => SLT or LST. NO NO => order is STL or TSL.

We then can lock down each combination.

YES YES => ask #2 (truthteller) if 1 is a liar. YES = LTS, NO = STL. YES NO => ask 2 (liar) if 1 is a truthteller. YES = SLT, NO = TLS. NO YES => ask 3 (truthteller) if 1 is a liar. YES = LST, NO = SLT. NO NO => ask 3 (liar) if 1 is a truthteller. YES = STL, NO = TSL.

"And really not looking for an answers but guidance on how to approach a problem like this." I like the answer (it's a lot simpler than the one I was thinking of) but I don't think it's what the OP is asking for... — Excited Raichu, Oct 27 '18 at 13:50

yes/no logic problem

2 Answers2