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