A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Liam, Luke, Charlotte, Samuel, and Grace. Victoria remarked, "Charlotte is a knave or Luke is a knight". Liam expressed that If Charlotte is a knave then Victoria is a knight. "If Charlotte is a knave then Grace is a knight," Luke declared. As Charlotte put it, "Luke is a knight". According to Samuel, "Victoria is a knave if and only if Charlotte is a knight". "Charlotte is a knave if and only if Luke is a knave" - Grace. So who is a knight and who is a knave?
Victoria is a knight, Liam is a knight, Luke is a knight, Charlotte is a knight, Samuel is a knave, and Grace is a knight.
(1) Victoria is a knight
(2) Liam is a knight
(3) Luke is a knight
(4) Charlotte is a knight
(5) Samuel is a knave
(6) Grace is a knight
Assume Victoria is a knight. No contradiction is found in their claim that Charlotte is a knave or Luke is a knight. Assume Charlotte is a knight. No contradiction is found in their claim that Luke is a knight. Assume Luke is a knight. No contradiction is found in their claim that If Charlotte is a knave then Grace is a knight. Assume Grace is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Luke is a knave. Assume Liam is a knight. No contradiction is found in their claim that If Charlotte is a knave then Victoria is a knight. Samuel cannot be a knight, because this would contradict the claim of their own that Victoria is a knave if and only if Charlotte is a knight. Assume Samuel is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Charlotte is a knight.