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 knave,” B says “I am the knave,” and C says “I am the knave.”

Short answer

There is no solution.

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,

says, “I am knave”, B says, “I am Knave” and C says, “I am the knave”.

Then,

A knave cannot tell the truth and the knave cannot say that “I am the Knave”.

None of the three peoples are the Knaves.

Thus, there is no possible solution.