A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Sofia, Owen, Evelyn, Aria, and Grace. Michael said that Owen is a knight and Aria is a knight. Sofia said, "If Michael is a knave then Grace is a knight." "Evelyn is a knave and Grace is a knave" - Owen. Evelyn commented, "Michael is a knight or Sofia is a knave". "Michael is a knight or Grace is a knave," Aria declared. Grace told you that Michael is a knight and Michael is a knave. So who is a knight and who is a knave?
Michael is a knave, Sofia is a knave, Owen is a knave, Evelyn is a knight, Aria is a knight, and Grace is a knave.
(1) Michael is a knave
(2) Sofia is a knave
(3) Owen is a knave
(4) Evelyn is a knight
(5) Aria is a knight
(6) Grace is a knave
Assume Michael is a knight. No contradiction is found in their claim that Owen is a knight and Aria is a knight. Assume Owen is a knight. No contradiction is found in their claim that Evelyn is a knave and Grace is a knave. Evelyn cannot be a knight, because this would contradict the claim of Owen that Evelyn is a knave and Grace is a knave. Evelyn cannot be a knave, because this would contradict the false claim of their own that Michael is a knight or Sofia is a knave. We have exhausted all possibilities for Evelyn, so let us go back and reconsider Owen. Owen cannot be a knave, because this would contradict the claim of Michael that Owen is a knight and Aria is a knight. We have exhausted all possibilities for Owen, so let us go back and reconsider Michael. Assume Michael is a knave. No contradiction is found in their false claim that Owen is a knight and Aria is a knight. Assume Owen is a knight. No contradiction is found in their claim that Evelyn is a knave and Grace is a knave. Evelyn cannot be a knight, because this would contradict the claim of Owen that Evelyn is a knave and Grace is a knave. Assume Evelyn is a knave. No contradiction is found in their false claim that Michael is a knight or Sofia is a knave. Assume Sofia is a knight. No contradiction is found in their claim that If Michael is a knave then Grace is a knight. Grace cannot be a knight, because this would contradict the claim of Owen that Evelyn is a knave and Grace is a knave. Grace cannot be a knave, because this would contradict the claim of Sofia that If Michael is a knave then Grace is a knight. We have exhausted all possibilities for Grace, so let us go back and reconsider Sofia. Sofia cannot be a knave, because this would contradict the false claim of Evelyn that Michael is a knight or Sofia is a knave. We have exhausted all possibilities for Sofia and Evelyn, so let us go back and reconsider Owen. Assume Owen is a knave. No contradiction is found in their false claim that Evelyn is a knave and Grace is a knave. Assume Evelyn is a knight. No contradiction is found in their claim that Michael is a knight or Sofia is a knave. Sofia cannot be a knight, because this would contradict the claim of Evelyn that Michael is a knight or Sofia is a knave. Assume Sofia is a knave. No contradiction is found in their false claim that If Michael is a knave then Grace is a knight. Grace cannot be a knight, because this would contradict the false claim of Sofia that If Michael is a knave then Grace is a knight. Assume Grace is a knave. No contradiction is found in their false claim that Michael is a knight and Michael is a knave. Assume Aria is a knight. No contradiction is found in their claim that Michael is a knight or Grace is a knave.