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