The bartender asked if all of them wanted a drink.
Logician number one does not know whether logicians number two and three want a drink or not, so he can’t say yes. If he did not want a drink though, he could say no because then it would not be true that they all wanted a drink. But he wants a drink. Therefore he says he don’t know, because it will depend on whether the other two want drinks or not.
Same applies to logician number two. She is still missing info about the third logician and therefore says she doesn’t know.
The third logician now knows that both of the other two want drinks, and so can answer that all of them want drinks.
Logician number one does not know whether logicians number two and three want a drink or not, so he can’t say yes. If he did not want a drink though, he could say no because then it would not be true that they all wanted a drink. But he wants a drink. Therefore he says he don’t know, because it will depend on whether the other two want drinks or not.
Same applies to logician number two. She is still missing info about the third logician and therefore says she doesn’t know.
The third logician now knows that both of the other two want drinks, and so can answer that all of them want drinks.