A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Mia, Henry, Zoey, Matthew, and Jacob. "Matthew is a knight" - Sophia. In a statement by Mia: "Jacob is a knave and Matthew is a knight". Henry said that Jacob is a knight or Matthew is a knight. Zoey expressed that Mia is a knave if and only if Matthew is a knight. Matthew said, "Zoey is a knight if and only if Sophia is a knave." Jacob remarked, "Matthew is a knave and Henry is a knave". So who is a knight and who is a knave?
Sophia is a knight, Mia is a knight, Henry is a knight, Zoey is a knave, Matthew is a knight, and Jacob is a knave.
(1) Sophia is a knight
(2) Mia is a knight
(3) Henry is a knight
(4) Zoey is a knave
(5) Matthew is a knight
(6) Jacob is a knave
Assume Sophia 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 Zoey is a knight if and only if Sophia is a knave. Zoey cannot be a knight, because this would contradict the claim of Matthew that Zoey is a knight if and only if Sophia is a knave. Assume Zoey is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Matthew is a knight. Assume Mia is a knight. No contradiction is found in their claim that Jacob is a knave and Matthew is a knight. Jacob cannot be a knight, because this would contradict the claim of Mia that Jacob is a knave and Matthew is a knight. Assume Jacob is a knave. No contradiction is found in their false claim that Matthew is a knave and Henry is a knave. Assume Henry is a knight. No contradiction is found in their claim that Jacob is a knight or Matthew is a knight.