A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Mia, Oliver, Avery, Michael, and Olivia. Daniel noted, "Olivia is a knave if and only if Olivia is a knight". "Michael is a knave if and only if Olivia is a knave," Mia mentioned. "Olivia is a knave," Oliver claimed. "Mia is a knave" - Avery. Michael said, "Oliver is a knight." Olivia asserted: "Avery is a knave". So who is a knight and who is a knave?
Daniel is a knave, Mia is a knave, Oliver is a knight, Avery is a knight, Michael is a knight, and Olivia is a knave.
(1) Daniel is a knave
(2) Mia is a knave
(3) Oliver is a knight
(4) Avery is a knight
(5) Michael is a knight
(6) Olivia is a knave
Daniel cannot be a knight, because this would contradict the claim of their own that Olivia is a knave if and only if Olivia is a knight. Assume Daniel is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Olivia is a knight. Assume Olivia is a knight. No contradiction is found in their claim that Avery is a knave. Avery cannot be a knight, because this would contradict the claim of Olivia that Avery is a knave. Assume Avery is a knave. No contradiction is found in their false claim that Mia is a knave. Assume Mia is a knight. No contradiction is found in their claim that Michael is a knave if and only if Olivia is a knave. Assume Michael is a knight. No contradiction is found in their claim that Oliver is a knight. Oliver cannot be a knight, because this would contradict the claim of their own that Olivia is a knave. Oliver cannot be a knave, because this would contradict the claim of Michael that Oliver is a knight. We have exhausted all possibilities for Oliver, so let us go back and reconsider Michael. Michael cannot be a knave, because this would contradict the claim of Mia that Michael is a knave if and only if Olivia is a knave. We have exhausted all possibilities for Michael, so let us go back and reconsider Mia. Mia cannot be a knave, because this would contradict the false claim of Avery that Mia is a knave. We have exhausted all possibilities for Mia and Avery, so let us go back and reconsider Olivia. Assume Olivia is a knave. No contradiction is found in their false claim that Avery is a knave. Assume Avery is a knight. No contradiction is found in their claim that Mia is a knave. Mia cannot be a knight, because this would contradict the claim of Avery that Mia is a knave. Assume Mia is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Olivia is a knave. Assume Michael is a knight. No contradiction is found in their claim that Oliver is a knight. Assume Oliver is a knight. No contradiction is found in their claim that Olivia is a knave.