A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: William, Aria, Mason, Isabella, Jackson, and Riley. In a statement by William: "Isabella is a knight and Aria is a knave". Aria stated, "If William is a knight then Riley is a knave". As Mason put it, "Jackson is not a knave". Isabella remarked, "Mason is a knave if and only if Riley is a knave". Jackson noted, "William is a knight and Mason is a knight". "William is a knave or Mason is a knave," Riley declared. So who is a knight and who is a knave?
William is a knave, Aria is a knight, Mason is a knave, Isabella is a knave, Jackson is a knave, and Riley is a knight.
(1) William is a knave
(2) Aria is a knight
(3) Mason is a knave
(4) Isabella is a knave
(5) Jackson is a knave
(6) Riley is a knight
Assume William is a knight. No contradiction is found in their claim that Isabella is a knight and Aria is a knave. Assume Isabella is a knight. No contradiction is found in their claim that Mason is a knave if and only if Riley is a knave. Assume Mason is a knight. No contradiction is found in their claim that Jackson is not a knave. Assume Jackson is a knight. No contradiction is found in their claim that William is a knight and Mason is a knight. Riley cannot be a knight, because this would contradict the claim of their own that William is a knave or Mason is a knave. Riley cannot be a knave, because this would contradict the claim of Isabella that Mason is a knave if and only if Riley is a knave. We have exhausted all possibilities for Riley, so let us go back and reconsider Jackson. Jackson cannot be a knave, because this would contradict the claim of Mason that Jackson is not a knave. We have exhausted all possibilities for Jackson, so let us go back and reconsider Mason. Assume Mason is a knave. No contradiction is found in their false claim that Jackson is not a knave. Jackson cannot be a knight, because this would contradict the false claim of Mason that Jackson is not a knave. Assume Jackson is a knave. No contradiction is found in their false claim that William is a knight and Mason is a knight. Riley cannot be a knight, because this would contradict the claim of Isabella that Mason is a knave if and only if Riley is a knave. Riley cannot be a knave, because this would contradict the false claim of their own that William is a knave or Mason is a knave. We have exhausted all possibilities for Riley, Jackson, and Mason, so let us go back and reconsider Isabella. Isabella cannot be a knave, because this would contradict the claim of William that Isabella is a knight and Aria is a knave. We have exhausted all possibilities for Isabella, so let us go back and reconsider William. Assume William is a knave. No contradiction is found in their false claim that Isabella is a knight and Aria is a knave. Assume Isabella is a knight. No contradiction is found in their claim that Mason is a knave if and only if Riley is a knave. Assume Mason is a knight. No contradiction is found in their claim that Jackson is not a knave. Jackson cannot be a knight, because this would contradict the claim of their own that William is a knight and Mason is a knight. Jackson cannot be a knave, because this would contradict the claim of Mason that Jackson is not a knave. We have exhausted all possibilities for Jackson, so let us go back and reconsider Mason. Assume Mason is a knave. No contradiction is found in their false claim that Jackson is not a knave. Jackson cannot be a knight, because this would contradict the false claim of Mason that Jackson is not a knave. Assume Jackson is a knave. No contradiction is found in their false claim that William is a knight and Mason is a knight. Riley cannot be a knight, because this would contradict the claim of Isabella that Mason is a knave if and only if Riley is a knave. Riley cannot be a knave, because this would contradict the false claim of their own that William is a knave or Mason is a knave. We have exhausted all possibilities for Riley, Jackson, and Mason, so let us go back and reconsider Isabella. Assume Isabella is a knave. No contradiction is found in their false claim that Mason is a knave if and only if Riley is a knave. Assume Mason is a knight. No contradiction is found in their claim that Jackson is not a knave. Jackson cannot be a knight, because this would contradict the claim of their own that William is a knight and Mason is a knight. Jackson cannot be a knave, because this would contradict the claim of Mason that Jackson is not a knave. We have exhausted all possibilities for Jackson, so let us go back and reconsider Mason. Assume Mason is a knave. No contradiction is found in their false claim that Jackson is not a knave. Jackson cannot be a knight, because this would contradict the false claim of Mason that Jackson is not a knave. Assume Jackson is a knave. No contradiction is found in their false claim that William is a knight and Mason is a knight. Assume Riley is a knight. No contradiction is found in their claim that William is a knave or Mason is a knave. Assume Aria is a knight. No contradiction is found in their claim that If William is a knight then Riley is a knave.