A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Jack, Victoria, Olivia, Emma, and Sofia. James noted, "Sofia is a knave or Victoria is a knave". Jack stated, "Emma is a knight if and only if Sofia is a knight". In a statement by Victoria: "James is a knight if and only if Emma is a knave". "Jack is a knight" - Olivia. Emma remarked, "Victoria is a knight and Sofia is a knight". Sofia expressed that Olivia is a knight and Victoria is a knave. So who is a knight and who is a knave?
James is a knight, Jack is a knight, Victoria is a knight, Olivia is a knight, Emma is a knave, and Sofia is a knave.
(1) James is a knight
(2) Jack is a knight
(3) Victoria is a knight
(4) Olivia is a knight
(5) Emma is a knave
(6) Sofia is a knave
Assume James is a knight. No contradiction is found in their claim that Sofia is a knave or Victoria is a knave. Assume Sofia is a knight. No contradiction is found in their claim that Olivia is a knight and Victoria is a knave. Assume Olivia is a knight. No contradiction is found in their claim that Jack is a knight. Assume Jack is a knight. No contradiction is found in their claim that Emma is a knight if and only if Sofia is a knight. Assume Emma is a knight. No contradiction is found in their claim that Victoria is a knight and Sofia is a knight. Victoria cannot be a knight, because this would contradict the claim of James that Sofia is a knave or Victoria is a knave. Victoria cannot be a knave, because this would contradict the claim of Emma that Victoria is a knight and Sofia is a knight. We have exhausted all possibilities for Victoria, so let us go back and reconsider Emma. Emma cannot be a knave, because this would contradict the claim of Jack that Emma is a knight if and only if Sofia is a knight. We have exhausted all possibilities for Emma, so let us go back and reconsider Jack. Jack cannot be a knave, because this would contradict the claim of Olivia that Jack is a knight. We have exhausted all possibilities for Jack, so let us go back and reconsider Olivia. Olivia cannot be a knave, because this would contradict the claim of Sofia that Olivia is a knight and Victoria is a knave. We have exhausted all possibilities for Olivia, so let us go back and reconsider Sofia. Assume Sofia is a knave. No contradiction is found in their false claim that Olivia is a knight and Victoria is a knave. Assume Olivia is a knight. No contradiction is found in their claim that Jack is a knight. Assume Jack is a knight. No contradiction is found in their claim that Emma is a knight if and only if Sofia is a knight. Emma cannot be a knight, because this would contradict the claim of Jack that Emma is a knight if and only if Sofia is a knight. Assume Emma is a knave. No contradiction is found in their false claim that Victoria is a knight and Sofia is a knight. Assume Victoria is a knight. No contradiction is found in their claim that James is a knight if and only if Emma is a knave.