Knights and Knaves

Knights and Knaves is a type of logic puzzle where some characters can only answer questions truthfully, and others only falsely.

[1] The puzzles are set on a fictional island where all inhabitants are either knights, who always tell the truth, or knaves, who always lie.

The puzzles involve a visitor to the island who meets small groups of inhabitants.

The puzzle may also be to determine a yes–no question which the visitor can ask in order to discover a particular piece of information.

Maurice Kraitchik presents the same puzzle in the 1953 book Mathematical Recreations, where two groups on a remote island – the Arbus and the Bosnins – either lie or tell the truth, and respond to the same question as above.

[2] A further complication is that the inhabitants may answer yes–no questions in their own language, and the visitor knows that "bal" and "da" mean "yes" and "no" but does not know which is which.

Familiarity with Boolean algebra and its simplification process will help with understanding the following examples.

This is perhaps the most famous rendition of this type of puzzle: John and Bill are standing at a fork in the road.

It had also appeared some ten years previously, in a very similar form, in the Doctor Who story Pyramids of Mars.

The philosopher Nelson Goodman anonymously published another version in the Boston Post issue of June 8, 1931, with nobles never lying and hunters never telling the truth.

Some years later, Goodman heard about the fork in the road variant; having scruples about counterfactuals, he devised a non-subjunctive, non-contrary-to-fact question that can be asked.