On an island each person either always tells the truth or always lies. Hugo says: "At least two of the three of us are liars." Marcus says: "Exactly one of the three of us is a liar." Tom says: "Hugo and Marcus are both liars." Which of the following is correct?
Answer and explanation
Correct answer: D. Truth-tellers: Hugo; liars: Marcus and Tom
- 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: Marcus and Tom. Answer: Truth-tellers: Hugo; liars: Marcus and Tom. Why not the others: 'Truth-tellers: Marcus and Tom; liars: Hugo' fails because Tom would be a truth-teller but the statement "Hugo and Marcus are both liars" would then be false; 'Truth-tellers: Hugo and Tom; liars: Marcus' fails because Hugo would be a truth-teller but the statement "at least two of the three of us are liars" would then be false; 'Truth-tellers: Marcus; liars: Hugo and Tom' fails because Hugo would be a liar but the statement "at least two of the three of us are liars" would then be true.
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