A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Amelia, Samuel, Matthew, Emily, Liam, and Jackson. Amelia said, "If Samuel is a knight then Matthew is a knave." "Amelia is a knave" - Samuel. As Matthew put it, "Samuel is not a knight". Emily said that If Samuel is a knave then Samuel is a knight. Liam asserted: "Emily is not a knave". Jackson said that Matthew is a knave if and only if Emily is a knave. So who is a knight and who is a knave?
Amelia is a knight, Samuel is a knave, Matthew is a knight, Emily is a knave, Liam is a knave, and Jackson is a knave.
(1) Amelia is a knight
(2) Samuel is a knave
(3) Matthew is a knight
(4) Emily is a knave
(5) Liam is a knave
(6) Jackson is a knave
Assume Amelia is a knight. No contradiction is found in their claim that If Samuel is a knight then Matthew is a knave. Samuel cannot be a knight, because this would contradict the claim of their own that Amelia is a knave. Assume Samuel is a knave. No contradiction is found in their false claim that Amelia is a knave. Assume Matthew is a knight. No contradiction is found in their claim that Samuel is not a knight. Emily cannot be a knight, because this would contradict the claim of their own that If Samuel is a knave then Samuel is a knight. Assume Emily is a knave. No contradiction is found in their false claim that If Samuel is a knave then Samuel is a knight. Liam cannot be a knight, because this would contradict the claim of their own that Emily is not a knave. Assume Liam is a knave. No contradiction is found in their false claim that Emily is not a knave. Jackson cannot be a knight, because this would contradict the claim of their own that Matthew is a knave if and only if Emily is a knave. Assume Jackson is a knave. No contradiction is found in their false claim that Matthew is a knave if and only if Emily is a knave.