A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Emma, Olivia, William, Lily, and Ella. Owen asserted: "Ella is a knight". Emma stated, "Lily is a knight and William is a knight". In Olivia's words: "William is not a knight". William expressed that Owen is a knave if and only if Olivia is a knight. Lily asserted: "Olivia is a knave". As Ella put it, "Lily is a knave and Ella is a knight". So who is a knight and who is a knave?
Owen is a knight, Emma is a knave, Olivia is a knight, William is a knave, Lily is a knave, and Ella is a knight.
(1) Owen is a knight
(2) Emma is a knave
(3) Olivia is a knight
(4) William is a knave
(5) Lily is a knave
(6) Ella is a knight
Assume Owen is a knight. No contradiction is found in their claim that Ella is a knight. Assume Ella is a knight. No contradiction is found in their claim that Lily is a knave and Ella is a knight. Lily cannot be a knight, because this would contradict the claim of Ella that Lily is a knave and Ella is a knight. Assume Lily is a knave. No contradiction is found in their false claim that Olivia is a knave. Assume Olivia is a knight. No contradiction is found in their claim that William is not a knight. William cannot be a knight, because this would contradict the claim of Olivia that William is not a knight. Assume William is a knave. No contradiction is found in their false claim that Owen is a knave if and only if Olivia is a knight. Emma cannot be a knight, because this would contradict the claim of their own that Lily is a knight and William is a knight. Assume Emma is a knave. No contradiction is found in their false claim that Lily is a knight and William is a knight.