(Adapted from [Sm78]) Suppose that on an island there are three types of people, knights, knaves, and normals (also known as spies). Knights always tell the truth, knaves always lie, and normals sometimes lie and sometimes tell the truth. Detectives questioned three inhabitants of the island—Amy, Brenda. and Claire—as part of the investigation of a crime. The detectives knew that one of the three committed the crime, but not which one. They also knew that the criminal was a knight, and that the other two were nol. Additionally, the detectives recorded these statements: Amy: "I am innocent." Brenda: "What Amy says is true." Claire: " Brenda is not a normal." After analyzing their information, the detectives positively identified the guilty party. Who was it?
Solution: Step-1: In this problem we need to determine who is the criminal (knight). Given : Amy says that “ I am innocent ” , Brenda says “ what Amy says is true ”, and Claire says “ Brenda is not a normal ”. Also given that Knight who always tell the truth , knaves who always lie , and spies who can either lie or tell the truth.Step-2: After analyzing their information, the detectives positively identified that Brenda was the criminal. Because , If Amy is a knight then there is a no relation between Brenda and Claire. If Brenda is a knight then Amy is a spy. If C is a knight then there is a no relation between Amy and Claire. Therefore , Brenda be a knight.