Turn on thread page Beta

# A logic puzzle. watch

1. (Original post by louiscbrooks)
"A states that at least person A or B is a liar(never tells the truth). Is A a liar? And what about B ?"
Within the parameters you've specified? Wholly inconclusive.

Envisage the following: you are confronted by two individuals, one of whom states that at least one of the two is a compulsive liar (i.e. never tells the truth). There is absolutely no way to deduce which person is a liar on the basis of the information given.
2. If A is telling the truth then B is lying, since one of A and B is lying it has to be B. If A is lying then one of A or B is Lying B is also Lying since if B was telling the truth A could not be lying. And A cannon be Lying and telling the truth.
3. (Original post by Profesh)
Within the parameters you've specified? Wholly inconclusive.
I'm afraid it is conclusive and please try and prove me wrong.

If A and B are both telling the truth then A lied at the beginning. Contradiction.

If A is the liar, then he told the truth at the beginning. A never tells the truth, hence contradiction

If A and B are both liars, then A told the truth at the beginning (at least one liar). A never tells the truth though, hence contradiction.

If B is the liar, then A told the truth and is the truth teller. B cannot be the truth teller as outlined previously.

A = truther B = liar

What do you say to that? All possible situations have been accounted for.

Also, I'm just amazed at how logicians can formulate such logic puzzles. Genius in my opinion.
4. Ok that was a bit rushed

A is telling the truth, so one of A or B is lying that must be true. Since we know it's not A that is lying it must be B

If A is lying then one of A or B cannot be lying, so they both either tell the truth or both are both lying. The former cannot be true since we know A is lying so B must also be Lying

So B is always lying
5. If A is telling the truth, ie. his statement is true, then B is a liar.

A must be telling the truth, as if A is a liar, his statement that at least one of them is a liar would be untrue, which essentially means that neither of them are liars; however, A would have lied in order to make that statement.

Therefore, I would say A is telling the truth and B is a liar
6. (Original post by aster100)
I'm afraid it is conclusive and please try and prove me wrong.

If A and B are both telling the truth then A lied at the beginning. Contradiction.

If A is the liar, then he told the truth at the beginning. A never tells the truth, hence contradiction

If A and B are both liars, then A told the truth at the beginning (at least one liar). A never tells the truth though, hence contradiction.

If B is the liar, then A told the truth and is the truth teller. B cannot be the truth teller as outlined previously.

A = truther B = liar

What do you say to that?
I say touché, and that I should probably have actually worked through the various premises beforehand rather than relying on intuition; but it's 9.54 a.m., and a lack of caffeine impairs my judgment.
7. well the last part follows that if B is not a liar then neither is A
8. (Original post by Profesh)
I say touché, and that I should probably have actually worked through the various premises beforehand rather than relying on intuition; but it's 9.54 a.m., and a lack of caffeine impairs my judgment.
You seem good at argument from previous posts and you never concede.

Do I not get rep for your concession?
9. I read it wrong -"atleast one is lying" i thought it was only one

so

A telling the truth - Means that B is lying
A is lying then they both must be telling the truth which leads to a contradiction
A is lying B is telling the truth then A is not lying

so the First one is the only possibility
10. (Original post by aster100)
You seem good at argument from previous posts and you never concede.

Do I not get rep for your concession?
Pfft. As though the only concession I've made in three-and-a-half years shouldn't be quite sufficient.
11. (Original post by Profesh)
Pfft. As though the only concession I've made in three-and-a-half years shouldn't be quite sufficient.
Scrooge
12. No, A can be lying.

A said that one of them always lies.

If A is lying, then neither of them always lies.

If neither of them always lies, it can mean that they either one, or both sometimes lie.
13. actually it says "atleast person A or B" is lying so either one is lying or they are both lying
14. (Original post by psanghaLFC)
actually it says "atleast person A or B" is lying so either one is lying or they are both lying
Yeah, and if A is lying then you can have any other combination you want.
15. (Original post by SillyFencer)
No, A can be lying.

A said that one of them always lies.

If A is lying, then neither of them always lies.

If neither of them always lies, it can mean that they either one, or both sometimes lie.
sometimes lying does not come in to it, the liar never tells the truth.
Edit: wait, ignore this I think your right
16. Hmm

A is telling the truth: This means B is a lier, since A cannot lie about who is lieing
A is lieing: You cannot really say if B is a lier or not, since A's statement was a lie
17. It is beautiful how the simplest of logic can evade people. Of course, the "correct" answer has been posted many times (A tells the truth, B lies), but as the problem stands, SillyFencer is right, it's inconclusive.

Let us imagine A is lying. Just because the statement "one of us always lies" is a lie, that doesn't mean A always lies. The converse of the statement "one of us always lies" is "neither of us always lies". That's not the same thing as "neither of us ever lies", so A could be lying when he says "one of us always lies" without lying every time he says anything else. So that's another perfectly valid conclusion to draw.
18. (Original post by generalebriety)
It is beautiful how the simplest of logic can evade people. Of course, the "correct" answer has been posted many times (A tells the truth, B lies), but as the problem stands, SillyFencer is right, it's inconclusive.

Let us imagine A is lying. Just because the statement "one of us always lies" is a lie, that doesn't mean A always lies. The converse of the statement "one of us always lies" is "neither of us always lies". That's not the same thing as "neither of us ever lies", so A could be lying when he says "one of us always lies" without lying every time he says anything else. So that's another perfectly valid conclusion to draw.
****, you're right.

I guess most people didn't consider the "intermediate" option
19. OK I'll rectify my previous error:

If A is a perfect liar, then he told the truth at the beginning: contradiction

If A is a perfect truth teller, then B must be a liar for consistency

Normal = randomly tells truth or lies

If A is normal, he could have told the truth, hence B could be a liar

If A is normal he could have lied, hence B could tell the truth

If A is normal he could have lied, hence B could be normal

So there are 4 possibilities and is consequently inconclusive.
20. The correct puzzle is a village of truth tellers (never lie) or liars (always lie). You come to a fork in the road, one fork leads where you want to go, the other doesn't. A man is at the fork. Given that you have no way of telling whether he is a truth teller or a liar, ask him one question to determine which road to take.

Turn on thread page Beta
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: September 17, 2009
Today on TSR

### Which business legend are you?

We have the answer...

### University open days

• University of Bradford
Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
• Heriot-Watt University