Question

ML - QUESTION OF THE DAY - 21/04/2013

LEVEL - * (difficulty level - 1 star )
[TO CATCH A LIAR]

In talking to three children you ask A if they always tell lies. Although A fully
understands you she answers in a language that only B understands.
B says that A just denied being a liar.
C says that although she doesn't know what A said, she is a liar and cannot be
trusted.
Given that each of the children will always lie or always tell the truth, how many liars
are there?



[You're supposed to put up the answer only and message me the solution . The one having the best solution will be allowed the put to his/her solution there and if no one gets the answer correctly , I will put the solution at the end of the day or on the next day]

BEST OF LUCK!

Answer 1

I have seen this problem somewhere... can't recall :-|

Answer 2

1 liar, I guess.

Answer 3

1 liar

Answer 4

Please message me your solutions , @u0860867 and @ParthKohli .

And , the question is still open. I welcome more and more opinions , answers.

Answer 5

1 liar

Answer 6

Yep, also got one liar.

Answer 7

I agree with the answer that all the users said(1 liar).....

Answer 8

If A is a liar then C told the truth, but if A is not a liar then C lied.
it is impossible to know whether or not A is a liar or said the truth
the only sure thing is that only one of A or C is a liar and the other must always tell the truth. So there is one liar.

Hope that helped.

Answer 9

"[You're supposed to put up the answer only and message me the solution . The one having the best solution will be allowed the put to his/her solution there and if no one gets the answer correctly , I will put the solution at the end of the day or on the next day] "

Answer 10

Putting up the actual solution (even if partial) is no fun.

Answer 11

Oh and by the way I'm posting this because she/ he told me to

so she did dude

Answer 12

Oh, all right, my bad, mate!

Answer 13

@Luis_Rivera i think your explanation is like as
It should be clear that a compulsive liar cannot admit to being a liar, so A would deny being a liar whether or not they always lied or always told the truth. In which case B told the truth about what A said and we establish that B is always truthful.

If A is a liar then C told the truth, but if A is not a liar then C lied.

Although it is impossible to establish whether or not A is a liar or a truth teller, we can be certain that only one of A or C is a liar and the other must always tell the truth.

Hence there is exactly one liar amongst the three children.

http://mathschallenge.net/full/to_catch_a_liar

Answer 14

Yep, I had more of a propositional logic proof for this case, but, here's it:

Note that child A will always deny being a liar, assume \(\neg B\) and, separately, \(A\) and \(\neg A\), then \(\neg B \wedge A \implies B\), but \(\neg B \wedge \neg A\implies B\), which is a contradiction, since, \(\neg B \implies B\). Therefore \(B\). Also note that \(C \iff \neg A\), then, exactly one of \(A, C\) must be a liar, hence, we are done.

\(A\) is "child A" is a truth-teller, the others follow the same pattern.