Liar Puzzle

Annie says Becky is lying
Becky says Carol is lying
Carol says both Annie and Becky are lying

Who is lying, and who is telling the truth?

  1. If Carol is telling the truth, then Annie (and Becky) is lying. In that case, Becky is not lying (opposite of what Annie, the ‘liar’ said). This is a contradiction. Therefore, Carol is lying.
  2. Since Carol is lying, the person who identified that correctly, Becky, must be telling the truth
  3. If Becky is telling the truth, the first statement is incorrect. Therefore, the person who made the first statement, Annie, is also lying.