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 “A is the spy.”

Short answer

A is a knight B is a spy C is a knave.

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

Given: one knight, one knave and one spy.

Knight: always tells the truth

Knave: always lies

Spy: lies or tells the truth

A = " am not the spy".

B = " not the spy".

C = A is the spy".

A Cannot be the knave, because then A is lying and thus A should be the spy.

B Cannot be the knave, because then B is lying and thus B should be the spy.

Thus C is then the only person than can be the knave.

C is the knave, thus C is lying and thus A cannot be the spy. The only remaining position for A is then the knight, while B then has to be the spy.