A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Victoria, Lucas, James, Jackson, Ava, and Aurora. Victoria told you that Jackson is a knight and Ava is a knave. Lucas asserted: "Victoria is a knave if and only if Ava is a knight". James asserted: "If Ava is a knave then Lucas is a knave". "James is a knight and Victoria is a knight" - Jackson. In Ava's words: "James is a knight if and only if Jackson is a knight". As Aurora put it, "Ava is a knight if and only if James is a knave". So who is a knight and who is a knave?
Victoria is a knave, Lucas is a knave, James is a knight, Jackson is a knave, Ava is a knave, and Aurora is a knight.
(1) Victoria is a knave
(2) Lucas is a knave
(3) James is a knight
(4) Jackson is a knave
(5) Ava is a knave
(6) Aurora is a knight
Assume Victoria is a knight. No contradiction is found in their claim that Jackson is a knight and Ava is a knave. Assume Jackson is a knight. No contradiction is found in their claim that James is a knight and Victoria is a knight. Assume James is a knight. No contradiction is found in their claim that If Ava is a knave then Lucas is a knave. Ava cannot be a knight, because this would contradict the claim of Victoria that Jackson is a knight and Ava is a knave. Ava cannot be a knave, because this would contradict the false claim of their own that James is a knight if and only if Jackson is a knight. We have exhausted all possibilities for Ava, so let us go back and reconsider James. James cannot be a knave, because this would contradict the claim of Jackson that James is a knight and Victoria is a knight. We have exhausted all possibilities for James, so let us go back and reconsider Jackson. Jackson cannot be a knave, because this would contradict the claim of Victoria that Jackson is a knight and Ava is a knave. We have exhausted all possibilities for Jackson, so let us go back and reconsider Victoria. Assume Victoria is a knave. No contradiction is found in their false claim that Jackson is a knight and Ava is a knave. Jackson cannot be a knight, because this would contradict the claim of their own that James is a knight and Victoria is a knight. Assume Jackson is a knave. No contradiction is found in their false claim that James is a knight and Victoria is a knight. Assume James is a knight. No contradiction is found in their claim that If Ava is a knave then Lucas is a knave. Ava cannot be a knight, because this would contradict the claim of their own that James is a knight if and only if Jackson is a knight. Assume Ava is a knave. No contradiction is found in their false claim that James is a knight if and only if Jackson is a knight. Lucas cannot be a knight, because this would contradict the claim of their own that Victoria is a knave if and only if Ava is a knight. Assume Lucas is a knave. No contradiction is found in their false claim that Victoria is a knave if and only if Ava is a knight. Assume Aurora is a knight. No contradiction is found in their claim that Ava is a knight if and only if James is a knave.