A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Samuel, Jackson, William, Penelope, Evelyn, and Matthew. Samuel stated, "Penelope is a knight". "If Penelope is a knight then Evelyn is a knight," Jackson mentioned. William asserted: "Jackson is a knave if and only if Jackson is a knight". Penelope expressed that William is a knave or Matthew is a knight. In Evelyn's words: "Matthew is a knave". Matthew stated, "Samuel is a knight". So who is a knight and who is a knave?
Samuel is a knight, Jackson is a knave, William is a knave, Penelope is a knight, Evelyn is a knave, and Matthew is a knight.
(1) Samuel is a knight
(2) Jackson is a knave
(3) William is a knave
(4) Penelope is a knight
(5) Evelyn is a knave
(6) Matthew is a knight
Assume Samuel is a knight. No contradiction is found in their claim that Penelope is a knight. Assume Penelope is a knight. No contradiction is found in their claim that William is a knave or Matthew is a knight. William cannot be a knight, because this would contradict the claim of their own that Jackson is a knave if and only if Jackson is a knight. Assume William is a knave. No contradiction is found in their false claim that Jackson is a knave if and only if Jackson is a knight. Assume Jackson is a knight. No contradiction is found in their claim that If Penelope is a knight then Evelyn is a knight. Assume Evelyn is a knight. No contradiction is found in their claim that Matthew is a knave. Matthew cannot be a knight, because this would contradict the claim of Evelyn that Matthew is a knave. Matthew cannot be a knave, because this would contradict the false claim of their own that Samuel is a knight. We have exhausted all possibilities for Matthew, so let us go back and reconsider Evelyn. Evelyn cannot be a knave, because this would contradict the claim of Jackson that If Penelope is a knight then Evelyn is a knight. We have exhausted all possibilities for Evelyn, so let us go back and reconsider Jackson. Assume Jackson is a knave. No contradiction is found in their false claim that If Penelope is a knight then Evelyn is a knight. Evelyn cannot be a knight, because this would contradict the false claim of Jackson that If Penelope is a knight then Evelyn is a knight. Assume Evelyn is a knave. No contradiction is found in their false claim that Matthew is a knave. Assume Matthew is a knight. No contradiction is found in their claim that Samuel is a knight.