The Math Joke

Three logicians walk into a bar. The barman asks them, “Do you all want a drink?”
The first logician says, “I don't know.”
The second logician says, “I don't know either.”
The third logician exclaims, “Yes!”

Can you explain the joke?

Solution

The logicians each give an answer to the literal question, that is not whether they individually want a drink, but whether the three of them all want a drink. Yup, funny guys, those mathematicians.

So then we know that the first logician wants a drink. If he didn't, then not all of three them wanted a drink, and he would have answered “No”. But he does — yet without knowing what the other two want, he has to answer “I don't know”.

The reasoning for the second logician is similar. She wants a drink, but she doesn't know yet what the third logician wants, so she doesn't know either.

The third logician reasons all of the above, and since he himself also wants a drink, he can now confidently answer the question.