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SMO 2018 Junior Round 1 Question 4

SMO · SMO 2018 Junior Round 1

Question 4

In a strange island, there are only two types of inhabitants: truth-tellers who only tell the truth and liars who only tell lies. One day, you meet two such inhabitants A and B. A said: “At least one of us is a liar.” B kept silent. Which of the following must be true?
  1. Both A and B are truth-tellers
  2. Both A and B are liars
  3. A is a truth-teller and B is a liar
  4. A is a liar and B is a truth-teller
  5. Not enough information to decide