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