Want a beer?

Logic Level 1

Three expert logicians - Expert A, Expert B and Expert C - walk into a bar. The bartender asks if all three would like a beer. All three of them answer one after another. The following statements do not necessarily follow the order in which they answered the bartender:

Expert A said "I don't know".

Expert B said "Yes".

Expert C said "I don't know".

Assume that: The logicians do not change their minds after answering. Each logician does not know if the other logicians would like a beer when the bartender asks them. The logicians answer the bartender without communicating amongst themselves who wants a beer.

Which of the following statements is always true?

Expert A or Expert C answered last Expert B answered second Expert B or Expert C answered last Expert C answered first

4 solutions

Dhruv Tyagi
Jun 21, 2015

We have to find out that did all of them want beer.

There are two cases: either B answered last or C answered last. Now consider B answered last.

Statement 1 by A : I don't know. Now there are two probabilities. A wants beer or does not wants beer. If he did not wanted the beer he would have said no. He said I don't know. This means he wanted beer and all of them knew this.

Statement 2 by C : I don't know. This again shows that C wanted beer but he isn't sure B wanted or not so he said I don't know.

Statement 3 by B : Yes. He wanted beer and he knew all of the others also wanted beer. Now, I don't know how C could have answered at last.

C cannot answer last

Sreenath sukumaran - 5 years, 11 months ago

Exactly. The wording of the answer is flawed, because C cannot answer last. The last person to answer will be able to say either yes or no. I just chose that answer choice because 1 of the 2 events in the answer will always be true, and since they're connected with an "or," the truth value will always be 1.

Ryan Tamburrino - 5 years, 11 months ago

Although I hated this problem as I knew the answer but it doesn't strongly fit in choices or at least as I wanted it to be, which made me choose the wrong answer ... but I have to say nothing is flawed in its phrasing, 'cause despite the fact that C can never answer last and B is the only one will always answer last .. but that choice is the only one that remains true as one of them will answer last which what the phrase is really telling, only in this case we are certain of the identity of that person

Ahmed Obaiedallah - 5 years, 8 months ago

The wording isn't flawed, I'm pretty sure it's intended to throw you off by prompting you to think about a part that doesn't actually matter. But $or$ is not $xor$ , it's all good.

Johannes Berger - 5 years, 8 months ago

B has to be the one that answers last. But that means that the statement B or C answers last is also a true statement.

Gary Venter - 3 years, 12 months ago

But it's not logic though. Because I'm another world B could of said yes and the other two could of said I dont know.

I'm a recovering alcoholic so I have people who speak up for me and I dont want to tell them my whole life story so i just say I dont know. Most people get the hunt cuz if I say a hard no they'll start pressing for answers.

So I ask again as i have before what is logic and is this app really teaching it?

Ariel Don't Worry - 2 years, 7 months ago

Nathan South
Nov 7, 2016

Lol the way I thought of it was "he asked ALL THREE if they would like a beer". Meaning, when he asked A and C, they answered I don't know, not knowing whether the three of them wanted a beer. B answered saying "yes, we would like a beer"

Greg Simay
Nov 12, 2017

The problem states, "Each logician does not know if the other logicians would like a beer when the bartender asks them." If the logicians take "I don't know" to really mean "yes" or "no," then it seems this condition would always be violated regardless of the sequence of answers. If "I don't know" really means "I don't know," then it seems B answering last is the only case that's guaranteed to be true. And if the "or" in "Expert B or Expert C answered last" is inclusive, then the Expert B case is true even if the Expert C case is false. (If the Expert C case can also true, my earlier remarks notwithstanding, then I've missed something.)

Marijn van Geest
Nov 10, 2018

The bartender asks whether all three want a beer. Since the first person who answers this question does not know if the other two want a beer, he answer "i don't know" , because if he had not wanted a beer, he would have said "no".

The second person now knows that the first person does not want a beer. However, he does not know whether the third person wants a beer, so he also answers "i don't know" , because, again, if he had not wanted a beer, he would have said "no".

The last person now knows that the other two persons want a beer. If he wants a beer too, he will answer "yes" , because now he knows that everyone of the three logicians want a beer.

The answer from person B is therefore the last answer.

Want a beer?

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