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Please show all steps. Thanks. Suppose that on an island there are three types o

ID: 2901285 • Letter: P

Question

Please show all steps. Thanks.

Suppose that on an island there are three types of people, knights, knaves, and normal. Knights always tell the truth, knave always lie, and normal sometimes tell the truth and sometimes lie. Detectives question three inhabitants of the island-Amy, Brenda, and Claire-as part of the investigation of a crime. The detectives knew that one of three committed the crime, but which one? They also know that the criminal was a knight, and that the other two were not. Additionally the detectives recorded these statements: Amy: "I am innocent." Brenda: "What Amy says is true." Claire: "Brenda is not normal." After analyzing their information, the detectives positively identified the guilty party. Who was it? (explain)

Explanation / Answer

only one of them is a knight => 3 cases possible

case 1: Amy is knight

Amy 's statement is "I am innocent " => she is innocent but we know that knight commited the crime => Amy commited the crime => amy is lying contradicting the hypothesis => amy is not a knight

case 2: Claire is knight

if claire is knight then claire's statement is true

=>
brenda is not normal, but we already know that brenda is not a knight (since we assumed claire is knight)

=>

brenda is a knave

=>

the statement "what amy says is true" is false

=>

amy is lying

=>

"I am innocent" is false => amy is the criminal but we assumed claire is the criminal (since claire is the knight ) contradicting the hypothesis

=>

Claire is not a knight

=>
Brenda is the knight => Brenda is the criminal

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