The Next Day (Some Unusual Knights and Knaves Part VII)

On the next day I was in a rather frivolous mood. I passed a native and asked him: "Do you ever answer no to questions?"

He answered me—that is, he said either yes or no—and then knew for sure whether he was a knight or a knave. Which was he?

(Source: To Mock a Mockingbird and Other Logic Puzzles: Including an Amazing Adventure in Combinatory Logic by Raymond Smullyan)

A "yes" answer can be made by either a knight or a knave. A knight can be taken at his word, and a knave can say "yes" but be full of crap. A "no" answer, however, decides the issue. A knight cannot answer "no" because, in so doing, he is in effect making his answer a lie. On the other hand, a knave who says "no" is making his answer a lie as well. But that's very much the point. The answer was "no" and he was a "knave".

Smullyan continues:

The above puzzle occurred to me as a result of a clever story told to me by the mathematician Stanisław Ulam. Ulam referred to it as a paradox. The story is a true one and refers to a certain past president of the United States.

On television Professor Ulam saw this president address the cabinet on his first day in office. He said to them, in a supercilious tone of voice: "You men are not all yes-men, are you?" They all solemnly replied: "Noooo!"

And so it seems that a person doesn't necessarily have to answer yes to be a yes-man! 1 am also reminded of a cartoon sent to me by one of my readers. It is a drawing of a tough-looking employer saying to his meek-looking employee: "I hate yes-men, Jenkins; don't you?"