A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Michael, Riley, Elizabeth, Scarlett, and Sebastian. Isabella said, "Riley is a knight if and only if Sebastian is a knight." Michael commented, "Elizabeth is a knave if and only if Michael is a knight". "If Sebastian is a knight then Michael is a knight" - Riley. In a statement by Elizabeth: "Isabella is a knight and Michael is a knight". Scarlett told you that Sebastian is not a knight. "Isabella is not a knight" - Sebastian. So who is a knight and who is a knave?
Isabella is a knave, Michael is a knave, Riley is a knave, Elizabeth is a knave, Scarlett is a knave, and Sebastian is a knight.
(1) Isabella is a knave
(2) Michael is a knave
(3) Riley is a knave
(4) Elizabeth is a knave
(5) Scarlett is a knave
(6) Sebastian is a knight
Assume Isabella is a knight. No contradiction is found in their claim that Riley is a knight if and only if Sebastian is a knight. Assume Riley is a knight. No contradiction is found in their claim that If Sebastian is a knight then Michael is a knight. Sebastian cannot be a knight, because this would contradict the claim of their own that Isabella is not a knight. Sebastian cannot be a knave, because this would contradict the claim of Isabella that Riley is a knight if and only if Sebastian is a knight. We have exhausted all possibilities for Sebastian, so let us go back and reconsider Riley. Assume Riley is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Michael is a knight. Sebastian cannot be a knight, because this would contradict the claim of Isabella that Riley is a knight if and only if Sebastian is a knight. Sebastian cannot be a knave, because this would contradict the false claim of Riley that If Sebastian is a knight then Michael is a knight. We have exhausted all possibilities for Sebastian and Riley, so let us go back and reconsider Isabella. Assume Isabella is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Sebastian is a knight. Assume Riley is a knight. No contradiction is found in their claim that If Sebastian is a knight then Michael is a knight. Sebastian cannot be a knight, because this would contradict the false claim of Isabella that Riley is a knight if and only if Sebastian is a knight. Sebastian cannot be a knave, because this would contradict the false claim of their own that Isabella is not a knight. We have exhausted all possibilities for Sebastian, so let us go back and reconsider Riley. Assume Riley is a knave. No contradiction is found in their false claim that If Sebastian is a knight then Michael is a knight. Assume Sebastian is a knight. No contradiction is found in their claim that Isabella is not a knight. Michael cannot be a knight, because this would contradict the false claim of Riley that If Sebastian is a knight then Michael is a knight. Assume Michael is a knave. No contradiction is found in their false claim that Elizabeth is a knave if and only if Michael is a knight. Elizabeth cannot be a knight, because this would contradict the false claim of Michael that Elizabeth is a knave if and only if Michael is a knight. Assume Elizabeth is a knave. No contradiction is found in their false claim that Isabella is a knight and Michael is a knight. Scarlett cannot be a knight, because this would contradict the claim of their own that Sebastian is not a knight. Assume Scarlett is a knave. No contradiction is found in their false claim that Sebastian is not a knight.