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