How many liars?

Logic Level 1

You decide to take a trip to an island where each inhabitant either always the truth or always lies.

You encounter two inhabitants and ask, "Which of you are liars?" One of them replies, "We are both liars!"

How many of the two inhabitants are liars?

0 1 2 Impossible to determine from information given

3 solutions

Denton Young
Jun 3, 2015

A's statement cannot be true, because then they both would be liars. So clearly A is a liar.

So A's statement is false: they are not both liars. B is a truth-teller.

i don't get it

Adrian Doctolero - 6 years ago

native A's statement was "Both of us" (A and B) "are liars."

If that statement were true, A and B would both be liars, and we would have a liar (A) making a true statement, which violates the conditions of the problem.

Therefore the statement is false. So A and B are not both liars.

Since A made a false statement, he must be a liar. Since they are not both liars, B must be a truth-teller.

Denton Young - 6 years ago

if A said both are liars, means B is honest and A is a liar, then A made a honest statement that he is a liar, which again contradicts!!!

Srinivasan Chandrasekar - 5 years, 8 months ago

@Srinivasan Chandrasekar – But A's statement was "both of us are liar" not "I am liar" so A is lying that they both are liar only himself is liar but B is not.

Nehem Tudu - 5 years, 8 months ago

thank you i get it now. I'm sorry

Adrian Doctolero - 6 years ago

@Adrian Doctolero – Don't be sorry; this stuff isn't always easy.

Whitney Clark - 4 years, 11 months ago

B can also be a trulth teller.. How do you know he is not?

Abhinav Sharma - 5 years, 8 months ago

I get it now.

Zachariah Dodson - 5 years, 7 months ago

That was a little bit tricky, BUT, you explained it VERY well, thx, and good luck with your next question!

mash religion - 3 years, 6 months ago

I still don't get it--wouldn't this be an infinite loop?

Alan Gibbons - 1 year, 10 months ago

Nevermind--I just got it.

Alan Gibbons - 1 year, 10 months ago

Noel Lo
Jun 4, 2015

There are only 3 possibilities as to how many of them lie - 0, 1 and 2. If one of them lies, we need not determine who is the liar for the purpose of this question. Assume none of them lie. This means that Native A's statement that both are liars has to be true, resulting in a contradiction. Assume both are liars. Then Native A's statement that both are liars is false which also results in a contradiction. This leaves only one possibility - that exactly $\boxed{one}$ of them is lying.

If it's true that "we are both liars" then that statement itself is a lie hence it is not the case that both are liars. if it's false that "we are both liars" then it's not the case they are both liars. so the conclusion is: either only one is a liar or both are not liars, and it's impossible to tell whether 1 or zero is the answer to how many liars there are.

Kopanang Mabote - 4 years, 11 months ago

Actually, it is quite possible to tell. The opposite of "we are both liars" is "at least one of us is not a liar". The one is a liar but they aren't both liars, so the other is a truth-teller.

Whitney Clark - 3 years, 6 months ago

Saya Suka
Feb 16, 2021

Liars won't tell the truth of the actual numbers of liars, while truth tellers can't even admit to being one of the liars. Between the two inhabitants, the statement of "We are both liars" include all of them, so it can't be a truth teller saying that, but a liar cannot have been truthful with that all-inclusive statement, so the silent one must be a truth teller.

How many liars?

3 solutions

0 pending reports