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APMOPS 2008 Question 25

APMOPS · APMOPS 2008

Question 25

Islanders are either gentlemen, who always tell the truth, or liars, who always lie. A sailor asks A, “Are you a gentleman or a liar?” He cannot hear A’s answer, so asks B what A said. B replies, “A said that he is a liar.” C immediately shouts, “B is lying!” Consider: I. It is impossible to tell whether A is a gentleman or liar. II. B is a gentleman and C a liar. III. B is a liar and C a gentleman. Which statements are true?
  1. (1) Only I is true.
  2. (2) Only II is true.
  3. (3) Only III is true.
  4. (4) Only I and II are true.
  5. (5) Only I and III are true.