Three logics, one simple question and three answers. The last one is a categorical “yes” — although no one has said anything directly to him.
The three logicians in the bar
Riddle statement
A waiter approaches a table where there are three logicians and asks them:
“Do you three want beer?”
The first one answers:
“I don't know.”
The second one answers:
“I don't know.”
The third party answers:
“Yes.”
Why can you say this with certainty?
Show solution
Solution
If the first one didn't want beer, he would know immediately that the answer to "Do all three of you want beer?" is no, and he would have said it.
As he answers “I don't know”, that means that he does want beer, but he doesn't know what the other two want.
The second one hears that answer. If he did not want beer, he could also immediately answer “no”, because he would already know that not all three of them want beer.
As he also answers “I don't know”, that means that he also wants beer.
The third party hears both answers and also knows that he himself wants beer.
So he can now conclude that the first one wants beer, the second wants beer and so does he.