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The exercise relates to inhabitants of an
Chapter 1, Problem 27E(choose chapter or problem)
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.”
Questions & Answers
QUESTION:
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.”
ANSWER:
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.