A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Riley, Lucas, Liam, Jackson, and Scarlett. "Liam is not a knight" - Sofia. "Sofia is a knave or Lucas is a knave," Riley declared. Lucas said that If Jackson is a knight then Scarlett is a knight. Liam was heard saying, "Scarlett is a knave". Jackson stated, "If Liam is a knave then Riley is a knight". According to Scarlett, "Lucas is a knave if and only if Sofia is a knight". So who is a knight and who is a knave?
Sofia is a knave, Riley is a knight, Lucas is a knave, Liam is a knight, Jackson is a knight, and Scarlett is a knave.
(1) Sofia is a knave
(2) Riley is a knight
(3) Lucas is a knave
(4) Liam is a knight
(5) Jackson is a knight
(6) Scarlett is a knave
Assume Sofia is a knight. No contradiction is found in their claim that Liam is not a knight. Liam cannot be a knight, because this would contradict the claim of Sofia that Liam is not a knight. Assume Liam is a knave. No contradiction is found in their false claim that Scarlett is a knave. Assume Scarlett is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Sofia is a knight. Lucas cannot be a knight, because this would contradict the claim of Scarlett that Lucas is a knave if and only if Sofia is a knight. Lucas cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knight then Scarlett is a knight. We have exhausted all possibilities for Lucas, so let us go back and reconsider Scarlett. Scarlett cannot be a knave, because this would contradict the false claim of Liam that Scarlett is a knave. We have exhausted all possibilities for Scarlett and Liam, so let us go back and reconsider Sofia. Assume Sofia is a knave. No contradiction is found in their false claim that Liam is not a knight. Assume Liam is a knight. No contradiction is found in their claim that Scarlett is a knave. Scarlett cannot be a knight, because this would contradict the claim of Liam that Scarlett is a knave. Assume Scarlett is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Sofia is a knight. Lucas cannot be a knight, because this would contradict the false claim of Scarlett that Lucas is a knave if and only if Sofia is a knight. Assume Lucas is a knave. No contradiction is found in their false claim that If Jackson is a knight then Scarlett is a knight. Assume Jackson is a knight. No contradiction is found in their claim that If Liam is a knave then Riley is a knight. Assume Riley is a knight. No contradiction is found in their claim that Sofia is a knave or Lucas is a knave.