Another Puzzle

charlieroot

Here's an interesting problem I came across recently. Its a variation of the "Knights and Knaves" type puzzle. Firstly, I'll admit I don't have a solution but I know a deterministic solution exists. Anyway here's the problem.

There are 3 people, one always tells the truth, one always lies and one answers randomly. You are allowed to asked 3 questions. The questions must have a yes/no answer. The only other information you are given is that the three people know who the others are, ie the liar knows the truthsayer and the random joe etc. You must determine which is the liar, which is the truthsayer and which is the random joe.


Enjoy


Noel.

Syth

A clarification: You say "you have 3 questions", does that mean you can ask a question and all 3 answer and counts as one question or does it mean that you can ask one question and one person answers and that counts as one question?

dave_eire

i dont know the answer, but surely the question has to be the same for all 3 and has to be something like:

"if i were to ask you "are you the liar", and you answered that question with the same amount of truth as this one, what would your answer be?"

reasoning --> maybe a bit hazy!!!

the truth guy will tell the truth about the truth and the liar will lie about the lie.

i.e. --> the truth guy would have answered "NO" to the hypothitical "are you the liar" question and then told the truth about that. so answer would be "NO"

while the liar would have lied about to the hypothitical "are you the liar" question and answered "NO" BUT then lied about that, turning the answer to "YES"

the random guy could say anything --> so heres where it goes a bit mad.

you now have to ask something about "if i were to ask the others XXsomethingXX, what would there answer be?"

if the real answer to the question is yes, the liar and the truthful one will both answer no as the truth will be telling the truth about the lie and the liar will be lying about the truth. but what about the random guy?

actually ignore all i said above (land penny on a parachute), it so much simpler.

answer:

3 people A,B,C

you need to ask a question that they dont know the answer to: i.e. "am i thinking about *something*"
--> only the randon person can answer as the liar cant lie about what he doesnt know and the truth teller cant tell the truth about it either.

so now you know, the random answer, ask the 2 remaining does 10*10=100, and the truth says yes and the liar say no!

i am assuming that the above is wrong, but it works, doesnt it?

i recon i might have been on the right track wth the compound questions, but i got confused! too early in the morning!

take care and have a good day!

daveH

charlieroot

Sorry for the delay in getting back to this. I've been a quite preoccupied. To clarify : you can ask a total of 3 questions. Each question answered by only one person.

Noel.

*Angel*

This is probably way off but I thought I'd give it a shot.

Firstly I'm assuming the random guy answers yes and no to questions alternatively.

If you ask one of the guys if his is the randomer twice, you will discover one of them. (the randomer would answer the questions with a yes and a no, the truth teller will reply with 'no' twice, and the liar will say 'yes' twice). If the truth teller is identified you could ask him if one of the guys is the randomer and therefore work it out. If the randomer is identified you could ask one of the others if the randomer that you just identified is the randomer, the honest guy would say yes but the liar would be forced to say no.

*Angel*

This is probably way off but I thought I'd give it a shot.

Firstly I'm assuming the random guy answers yes and no to questions alternatively.

If you ask one of the guys if his is the randomer twice, you will discover one of them. (the randomer would answer the questions with a yes and a no, the truth teller will reply with 'no' twice, and the liar will say 'yes' twice). If the truth teller is identified you could ask him if one of the guys is the randomer and therefore work it out. If the randomer is identified you could ask one of the others if the randomer that you just identified is the randomer, the honest guy would say yes but the liar would be forced to say no. If the liar was identified you could ask him if one of the guys is the randomer he would obviously lie so you'd figure it out.

smiles

Call them A, B and C.


Q1: Ask A: "Which of the other two is least likely to tell the truth?"
Say he points to someone and we call him B.
If A= Liar points to Truth Teller
If A = Truth Teller points to Liar
If A = Randommer points to either.

Thus B cannot be the randommer.

Q2: Ask B: If I asked the person who doesn't answer randomly whether you told the truth or a lie what would they say?
If B = Liar says he would say he's a truth teller
If B = Truth sayer then he say he's a Liar.

So you know what B is.

Q3. Ask B: Does A always tell the truth?
If B = Liar and says No, then A is the truth teller.
If B = Truth teller and says No then A is the randommer.

Thus you know what A is and by elimination you know what C is.

I think.

<< Fio >>

charlieroot

My hat's off to you! That puzzle was really beginning to bug me The questions aren't exactly yes/no answerable as you've stated them - but its easy to see how they can be changed to fit the bill. Kudos!


Noel.