A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Penelope, Olivia, Matthew, Owen, Emily, and Jack. "Jack is a knight if and only if Olivia is a knight," Penelope mentioned. Olivia said, "If Emily is a knave then Penelope is a knave." Matthew said that Matthew is a knight or Emily is a knight. Owen said that Matthew is a knight. According to Emily, "Jack is a knave if and only if Owen is a knight". Jack was heard saying, "Emily is a knave". So who is a knight and who is a knave?
Penelope is a knave, Olivia is a knight, Matthew is a knight, Owen is a knight, Emily is a knight, and Jack is a knave.
(1) Penelope is a knave
(2) Olivia is a knight
(3) Matthew is a knight
(4) Owen is a knight
(5) Emily is a knight
(6) Jack is a knave
Assume Penelope is a knight. No contradiction is found in their claim that Jack is a knight if and only if Olivia is a knight. Assume Jack is a knight. No contradiction is found in their claim that Emily is a knave. Emily cannot be a knight, because this would contradict the claim of Jack that Emily is a knave. Assume Emily is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Owen is a knight. Assume Owen is a knight. No contradiction is found in their claim that Matthew is a knight. Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Emily is a knight. Olivia cannot be a knight, because this would contradict the claim of their own that If Emily is a knave then Penelope is a knave. Olivia cannot be a knave, because this would contradict the claim of Penelope that Jack is a knight if and only if Olivia is a knight. We have exhausted all possibilities for Olivia, so let us go back and reconsider Matthew. Matthew cannot be a knave, because this would contradict the claim of Owen that Matthew is a knight. We have exhausted all possibilities for Matthew, so let us go back and reconsider Owen. Owen cannot be a knave, because this would contradict the false claim of Emily that Jack is a knave if and only if Owen is a knight. We have exhausted all possibilities for Owen and Emily, so let us go back and reconsider Jack. Assume Jack is a knave. No contradiction is found in their false claim that Emily is a knave. Assume Emily is a knight. No contradiction is found in their claim that Jack is a knave if and only if Owen is a knight. Assume Owen is a knight. No contradiction is found in their claim that Matthew is a knight. Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Emily is a knight. Olivia cannot be a knight, because this would contradict the claim of Penelope that Jack is a knight if and only if Olivia is a knight. Olivia cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Penelope is a knave. We have exhausted all possibilities for Olivia, so let us go back and reconsider Matthew. Matthew cannot be a knave, because this would contradict the false claim of their own that Matthew is a knight or Emily is a knight. We have exhausted all possibilities for Matthew, so let us go back and reconsider Owen. Owen cannot be a knave, because this would contradict the claim of Emily that Jack is a knave if and only if Owen is a knight. We have exhausted all possibilities for Owen, so let us go back and reconsider Emily. Emily cannot be a knave, because this would contradict the false claim of Jack that Emily is a knave. We have exhausted all possibilities for Emily and Jack, so let us go back and reconsider Penelope. Assume Penelope is a knave. No contradiction is found in their false claim that Jack is a knight if and only if Olivia is a knight. Assume Jack is a knight. No contradiction is found in their claim that Emily is a knave. Emily cannot be a knight, because this would contradict the claim of Jack that Emily is a knave. Assume Emily is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Owen is a knight. Assume Owen is a knight. No contradiction is found in their claim that Matthew is a knight. Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Emily is a knight. Olivia cannot be a knight, because this would contradict the false claim of Penelope that Jack is a knight if and only if Olivia is a knight. Olivia cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Penelope is a knave. We have exhausted all possibilities for Olivia, so let us go back and reconsider Matthew. Matthew cannot be a knave, because this would contradict the claim of Owen that Matthew is a knight. We have exhausted all possibilities for Matthew, so let us go back and reconsider Owen. Owen cannot be a knave, because this would contradict the false claim of Emily that Jack is a knave if and only if Owen is a knight. We have exhausted all possibilities for Owen and Emily, so let us go back and reconsider Jack. Assume Jack is a knave. No contradiction is found in their false claim that Emily is a knave. Assume Emily is a knight. No contradiction is found in their claim that Jack is a knave if and only if Owen is a knight. Assume Owen is a knight. No contradiction is found in their claim that Matthew is a knight. Assume Matthew is a knight. No contradiction is found in their claim that Matthew is a knight or Emily is a knight. Assume Olivia is a knight. No contradiction is found in their claim that If Emily is a knave then Penelope is a knave.