Problem 27E

The exercise relates 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 these three people knows the type of person each of other two is. For each of those 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.”

Solution:

Step 1:

In this problem we need to determine who the knave , knight and spy are .

Given : A says that “ I am the knight ” , B says “ A is telling the truth ” and C says “ I am the spy”. Also given that Knight who always tell the truth , knaves who always lie , and spies who can either lie or tell the truth.