Brain Teasers
Logitopia 2
Lisa, Martha, Nora, and Ophelia live in the strange country of Logitopia. This country is inhabited by four races of people: the type A people and type B people who always tell the truth, and the type C people and type D people who always lie. Each of them is of a different race.
Lisa says, "Martha is a type A person." Martha says, "Nora is a type C person." Nora says, "Ophelia is a type D person." Ophelia says, "Lisa is NOT a type B person."
Who is which race?
Lisa says, "Martha is a type A person." Martha says, "Nora is a type C person." Nora says, "Ophelia is a type D person." Ophelia says, "Lisa is NOT a type B person."
Who is which race?
Answer
Lisa is a type D person, Martha is a type B person, Nora is a type C person, and Ophelia is a type A person.Suppose Lisa is a truthteller. This means that Martha is a type A person, which means that Nora is a type C person. Since Lisa is a truthteller who is not a type A person, she is a type B person, which means Ophelia is lying. Since Ophelia is a liar who is not a type C person, she must be a type D person. But since Nora is a type C person, Ophelia cannot be a type D person. So this cannot work.
This means that Lisa is a liar and cannot be a type B person, which means that Ophelia is telling the truth and cannot be a type D person, which means that Nora is lying. Since Lisa and Nora are both lying, Martha and Ophelia must be the two truthtellers, which means that Nora is a type C person and Lisa is a type D person. Since Lisa is lying, Martha cannot be a type A person and must be a type B person, and Ophelia must be a type A person.
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