On an island each person either always tells the truth or always lies. Femi says: "Exactly one of the three of us is a liar." Hugo says: "Femi is a liar." Priya says: "Hugo and I are the same type." Which of the following is correct?
Answer and explanation
Correct answer: B. Truth-tellers: Hugo; liars: Femi and Priya
- Step 1: Try each possible assignment of truth-teller or liar and check every statement against it. Step 2. Only one assignment makes all three people consistent, which is: Truth-tellers: Hugo; liars: Femi and Priya. Answer: Truth-tellers: Hugo; liars: Femi and Priya. Why not the others: 'Truth-tellers: Priya; liars: Femi and Hugo' fails because Hugo would be a liar but the statement "Femi is a liar" would then be true; 'Truth-tellers: Femi and Priya; liars: Hugo' fails because Priya would be a truth-teller but the statement "Hugo and I are the same type" would then be false; 'Truth-tellers: Hugo and Priya; liars: Femi' fails because Femi would be a liar but the statement "exactly one of the three of us is a liar" would then be true.
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