1

Mathematics 5
Winter Term 2000
The World According to Mathematics

Dwight Lahr and Josh Laison

Friday Discussion: Week #2

These problems are taken from a book called “What is the Name of This Book?” by Raymond
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.

1.

You meet three inhabitants of the island, A, B, and C. You ask A, “Are you a knight or a
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?

2.

You travel a little farther and meet another three inhabitants, A, B, and C. This time you ask
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?

3.

A little farther on in your travels you meet two people, A and B. A tells you, “At least one of
us is a knave.”What are A and B?

4.

Suppose A had said, “Either I am a knave or B is a knight.”What are A and B?

5.Again there are three people, A, B, and C, each of whom is either a knight or a knave. You
hear them remark:
A: All of us are knaves.
B: Exactly one of us is a knight.
What are A, B, and C?

6.Suppose instead A and B say the following:
A: All of us are knaves.
B: Exactly one of us is a knave.
What can you say about A, B, and C?

7.

Suppose A says, “I am a knave, and B is not a knave.”What are A and B?

8.

Again there are three inhabitants. A says “B is a knave,” and B says, “A and C are of the
same type.” (i.e. both knights or both knaves)What is C?