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