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 Sullying [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 not the spy,” B says “I am not the spy,” and C says “I am not the spy.”

Short answer

A says “I am not the spy,” B says “I am not the spy,” and C says “I am not the spy. “None are possible in this statement.

Step-by-step solution

Tips

There are inhabitants of an island on which there are three kinds of people:

• Knights who always tell the truth
• Knaves who always lie
• Spies who can either lie or tell the truth.

The truth value for given Statement

A says "I am not the spy," B says "I am not the spy," and C says "I am not the spy." There is no solution because the knave is the only one speaking the truth when he says that he is not the spy. Because knaves always lie this causes a contradiction.