Winter Term 2000
The World According to Mathematics
Smullyan. The problems concern the island of knights and knaves. On this island, some of the
inhabitants, called knights, always tell the truth, while others, called knaves, always lie. You are
a tourist on the island and you stop to talk to some of the inhabitants.
knave?”A answers, but he mumbles and you can’t hear what he says. You ask B, “What did
A say?”B replies, “A said that he is a knave.”C then says, “Don’t believe B, he is lying!”
What are B and C?
A, “How many knights are among you?” but again you can’t make out his reply. So you ask
B, “What did A say?” and B replies, “A said there is one knight among us.”Again C says,
“Don’t believe B, he is lying!”Again, what are B and C?
us is a knave.”What are A and B?
hear them remark:
A: All of us are knaves.
B: Exactly one of us is a knight.
What are A, B, and C?
A: All of us are knaves.
B: Exactly one of us is a knave.
What can you say about A, B, and C?
same type.” (i.e. both knights or both knaves)What is C?