Question

A says “We are both knaves” and B says nothing. Exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by Smullyan [Sm78]) who can either lie or tell the truth. You encounter three people, A, B, and C. You know one of these people is a knight, one is a knave, and one is a spy. Each of the three people knows the type of person each of other two is. For each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. When there is no unique solution, list all possible solutions or state that there are no solutions.

A says “I am the knight,” B says “A is telling the truth,” and C says “I am the spy.”

Short answer

The unique solution is, A is the knight, B is the spy and C is the knave.

Step-by-step solution

Introduction

In response to such directions, truth-tellersfrequently supply more comprehensive information in order to show their innocence. Liars, on the other hand, want to keep their mistakes hidden.

Explanation

From the given data,

Consider the three people A, B and C .

One is a knight, the other is a knave, and the third is a spy.

Spies who can either lie or tell the truth, knights who always tell the truth, knaveswho always lie, and knights who always tell the truth.

We know B isn't the knight because if he was, his claim that A is speaking the truth would imply two knights, which isn't feasible.

Because he claims to be the spy, C is clearly not the knight. A is the knight as a result.

B must be the spy since he was speaking the truth. C is the knave, who claims to be the spy despite the fact that he is not.

Thus, A is the knight, B is the spy and C is the knave.