A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Lily, Mia, Oliver, Ava, Evelyn, Alexander, and Ella. "Ella is a knave and Ella is a knight," Lily mentioned. Mia said, "Oliver is a knight." "If Evelyn is a knave then Ella is a knight," Oliver declared. "If Mia is a knave then Oliver is a knave" - Ava. Evelyn remarked, "Lily is not a knight". According to Alexander, "Ella is not a knave". "If Lily is a knight then Evelyn is a knave," Ella claimed. So who is a knight and who is a knave?

Lily Mia Oliver Ava Evelyn Alexander Ella

Lily is a knave, Mia is a knight, Oliver is a knight, Ava is a knight, Evelyn is a knight, Alexander is a knight, and Ella is a knight.

(1) Lily is a knave
(2) Mia is a knight
(3) Oliver is a knight
(4) Ava is a knight
(5) Evelyn is a knight
(6) Alexander is a knight
(7) Ella is a knight

Lily cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Ella is a knight.

Assume Lily is a knave. No contradiction is found in their false claim that Ella is a knave and Ella is a knight.

Assume Ella is a knight. No contradiction is found in their claim that If Lily is a knight then Evelyn is a knave.

Assume Evelyn is a knight. No contradiction is found in their claim that Lily is not a knight.

Assume Mia is a knight. No contradiction is found in their claim that Oliver is a knight.

Assume Oliver is a knight. No contradiction is found in their claim that If Evelyn is a knave then Ella is a knight.

Assume Ava is a knight. No contradiction is found in their claim that If Mia is a knave then Oliver is a knave.

Assume Alexander is a knight. No contradiction is found in their claim that Ella is not a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Jack, Joseph, Liam, Noah, Luke, Victoria, and Ella. Jack remarked, "Victoria is a knight if and only if Liam is a knave". Joseph asserted: "Liam is a knave and Noah is a knight". "Noah is a knave and Luke is a knave," Liam declared. Noah noted, "Ella is a knight if and only if Ella is a knave". According to Luke, "Liam is a knave". Victoria remarked, "Ella is not a knave". In Ella's words: "Victoria is a knave or Jack is a knave". So who is a knight and who is a knave?

Jack Joseph Liam Noah Luke Victoria Ella

Jack is a knave, Joseph is a knave, Liam is a knight, Noah is a knave, Luke is a knave, Victoria is a knight, and Ella is a knight.

(1) Jack is a knave
(2) Joseph is a knave
(3) Liam is a knight
(4) Noah is a knave
(5) Luke is a knave
(6) Victoria is a knight
(7) Ella is a knight

Let's think step by step, by considering whether each person is lying and if that leads to contradiction.

Assume Jack is a knight. No contradiction is found in their claim that Victoria is a knight if and only if Liam is a knave.

Assume Victoria is a knight. No contradiction is found in their claim that Ella is not a knave.

Ella cannot be a knight, because this would contradict the claim of their own that Victoria is a knave or Jack is a knave.

Ella cannot be a knave, because this would contradict the claim of Victoria that Ella is not a knave.

We have exhausted all possibilities for Ella, so let us go back and reconsider Victoria.

Assume Victoria is a knave. No contradiction is found in their false claim that Ella is not a knave.

Ella cannot be a knight, because this would contradict the false claim of Victoria that Ella is not a knave.

Ella cannot be a knave, because this would contradict the false claim of their own that Victoria is a knave or Jack is a knave.

We have exhausted all possibilities for Ella and Victoria, so let us go back and reconsider Jack.

Assume Jack is a knave. No contradiction is found in their false claim that Victoria is a knight if and only if Liam is a knave.

Assume Ella is a knight. No contradiction is found in their claim that Victoria is a knave or Jack is a knave.

Assume Liam is a knight. No contradiction is found in their claim that Noah is a knave and Luke is a knave.

Noah cannot be a knight, because this would contradict the claim of Liam that Noah is a knave and Luke is a knave.

Assume Noah is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Ella is a knave.

Luke cannot be a knight, because this would contradict the claim of Liam that Noah is a knave and Luke is a knave.

Assume Luke is a knave. No contradiction is found in their false claim that Liam is a knave.

Joseph cannot be a knight, because this would contradict the claim of their own that Liam is a knave and Noah is a knight.

Assume Joseph is a knave. No contradiction is found in their false claim that Liam is a knave and Noah is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Riley, Joseph, Noah, Liam, Oliver, Jack, and David. Riley commented, "David is a knight". Joseph was heard saying, "Riley is a knight if and only if David is a knight". Noah said that If David is a knight then Jack is a knight. "Noah is a knight" - Liam. "Joseph is not a knave" - Oliver. Jack was heard saying, "Oliver is not a knight". "Oliver is not a knave," David declared. So who is a knight and who is a knave?

Riley Joseph Noah Liam Oliver Jack David

Riley is a knight, Joseph is a knight, Noah is a knave, Liam is a knave, Oliver is a knight, Jack is a knave, and David is a knight.

(1) Riley is a knight
(2) Joseph is a knight
(3) Noah is a knave
(4) Liam is a knave
(5) Oliver is a knight
(6) Jack is a knave
(7) David is a knight

Assume Riley is a knight. No contradiction is found in their claim that David is a knight.

Assume David is a knight. No contradiction is found in their claim that Oliver is not a knave.

Assume Oliver is a knight. No contradiction is found in their claim that Joseph is not a knave.

Assume Joseph is a knight. No contradiction is found in their claim that Riley is a knight if and only if David is a knight.

Assume Noah is a knight. No contradiction is found in their claim that If David is a knight then Jack is a knight.

Jack cannot be a knight, because this would contradict the claim of their own that Oliver is not a knight.

Jack cannot be a knave, because this would contradict the claim of Noah that If David is a knight then Jack is a knight.

We have exhausted all possibilities for Jack, so let us go back and reconsider Noah.

Assume Noah is a knave. No contradiction is found in their false claim that If David is a knight then Jack is a knight.

Jack cannot be a knight, because this would contradict the false claim of Noah that If David is a knight then Jack is a knight.

Assume Jack is a knave. No contradiction is found in their false claim that Oliver is not a knight.

Liam cannot be a knight, because this would contradict the claim of their own that Noah is a knight.

Assume Liam is a knave. No contradiction is found in their false claim that Noah is a knight.

(('telling-truth', 6), ('<=>', ('telling-truth', 0), ('telling-truth', 6)), ('->', ('telling-truth', 6), ('telling-truth', 5)), ('telling-truth', 2), ('not', ('lying', 1)), ('not', ('telling-truth', 4)), ('not', ('lying', 4)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Harper, Michael, Benjamin, Elizabeth, Lily, Jacob, and Evelyn. Harper was heard saying, "Michael is a knight if and only if Evelyn is a knight". Michael stated, "Lily is a knave if and only if Harper is a knave". Benjamin said that Jacob is a knight. Elizabeth told you that Harper is a knight if and only if Elizabeth is a knight. Lily remarked, "If Michael is a knight then Lily is a knight". "Lily is not a knight," Jacob claimed. Evelyn said that Elizabeth is a knave and Lily is a knight. So who is a knight and who is a knave?

Harper Michael Benjamin Elizabeth Lily Jacob Evelyn

Harper is a knight, Michael is a knight, Benjamin is a knave, Elizabeth is a knave, Lily is a knight, Jacob is a knave, and Evelyn is a knight.

(1) Harper is a knight
(2) Michael is a knight
(3) Benjamin is a knave
(4) Elizabeth is a knave
(5) Lily is a knight
(6) Jacob is a knave
(7) Evelyn is a knight

Assume Harper is a knight. No contradiction is found in their claim that Michael is a knight if and only if Evelyn is a knight.

Assume Michael is a knight. No contradiction is found in their claim that Lily is a knave if and only if Harper is a knave.

Assume Lily is a knight. No contradiction is found in their claim that If Michael is a knight then Lily is a knight.

Assume Evelyn is a knight. No contradiction is found in their claim that Elizabeth is a knave and Lily is a knight.

Elizabeth cannot be a knight, because this would contradict the claim of Evelyn that Elizabeth is a knave and Lily is a knight.

Assume Elizabeth is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Elizabeth is a knight.

Assume Benjamin is a knight. No contradiction is found in their claim that Jacob is a knight.

Jacob cannot be a knight, because this would contradict the claim of their own that Lily is not a knight.

Jacob cannot be a knave, because this would contradict the claim of Benjamin that Jacob is a knight.

We have exhausted all possibilities for Jacob, so let us go back and reconsider Benjamin.

Assume Benjamin is a knave. No contradiction is found in their false claim that Jacob is a knight.

Jacob cannot be a knight, because this would contradict the false claim of Benjamin that Jacob is a knight.

Assume Jacob is a knave. No contradiction is found in their false claim that Lily is not a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Aiden, Zoey, Mia, Matthew, Benjamin, Aurora, and Elizabeth. Aiden stated, "If Zoey is a knight then Mia is a knight". Zoey asserted: "Benjamin is a knave or Matthew is a knight". Mia expressed that Zoey is a knight or Benjamin is a knave. Matthew asserted: "Zoey is a knight or Aiden is a knight". Benjamin remarked, "Aurora is a knave if and only if Elizabeth is a knave". Aurora was heard saying, "If Benjamin is a knight then Mia is a knight". Elizabeth said that If Benjamin is a knave then Matthew is a knight. So who is a knight and who is a knave?

Aiden Zoey Mia Matthew Benjamin Aurora Elizabeth

Aiden is a knight, Zoey is a knight, Mia is a knight, Matthew is a knight, Benjamin is a knight, Aurora is a knight, and Elizabeth is a knight.

(1) Aiden is a knight
(2) Zoey is a knight
(3) Mia is a knight
(4) Matthew is a knight
(5) Benjamin is a knight
(6) Aurora is a knight
(7) Elizabeth is a knight

Assume Aiden is a knight. No contradiction is found in their claim that If Zoey is a knight then Mia is a knight.

Assume Zoey is a knight. No contradiction is found in their claim that Benjamin is a knave or Matthew is a knight.

Assume Benjamin is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Elizabeth is a knave.

Assume Aurora is a knight. No contradiction is found in their claim that If Benjamin is a knight then Mia is a knight.

Assume Mia is a knight. No contradiction is found in their claim that Zoey is a knight or Benjamin is a knave.

Assume Elizabeth is a knight. No contradiction is found in their claim that If Benjamin is a knave then Matthew is a knight.

Assume Matthew is a knight. No contradiction is found in their claim that Zoey is a knight or Aiden is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Sofia, Scarlett, Chloe, Abigail, Ethan, Emma, and Owen. Sofia told you that Chloe is a knight if and only if Owen is a knight. Scarlett expressed that Scarlett is a knight and Emma is a knight. According to Chloe, "Emma is a knight or Scarlett is a knave". Abigail said that If Abigail is a knight then Sofia is a knave. Ethan was heard saying, "Sofia is not a knight". Emma told you that Scarlett is a knight and Abigail is a knave. In Owen's words: "Scarlett is a knight". So who is a knight and who is a knave?

Sofia Scarlett Chloe Abigail Ethan Emma Owen

Sofia is a knave, Scarlett is a knave, Chloe is a knight, Abigail is a knight, Ethan is a knight, Emma is a knave, and Owen is a knave.

(1) Sofia is a knave
(2) Scarlett is a knave
(3) Chloe is a knight
(4) Abigail is a knight
(5) Ethan is a knight
(6) Emma is a knave
(7) Owen is a knave

Assume Sofia is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Owen is a knight.

Assume Chloe is a knight. No contradiction is found in their claim that Emma is a knight or Scarlett is a knave.

Assume Emma is a knight. No contradiction is found in their claim that Scarlett is a knight and Abigail is a knave.

Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight and Emma is a knight.

Abigail cannot be a knight, because this would contradict the claim of their own that If Abigail is a knight then Sofia is a knave.

Abigail cannot be a knave, because this would contradict the false claim of their own that If Abigail is a knight then Sofia is a knave.

We have exhausted all possibilities for Abigail, so let us go back and reconsider Scarlett.

Scarlett cannot be a knave, because this would contradict the claim of Emma that Scarlett is a knight and Abigail is a knave.

We have exhausted all possibilities for Scarlett, so let us go back and reconsider Emma.

Assume Emma is a knave. No contradiction is found in their false claim that Scarlett is a knight and Abigail is a knave.

Scarlett cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Emma is a knight.

Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight and Emma is a knight.

We have exhausted all possibilities for Abigail, Scarlett, and Emma, so let us go back and reconsider Chloe.

Assume Chloe is a knave. No contradiction is found in their false claim that Emma is a knight or Scarlett is a knave.

Emma cannot be a knight, because this would contradict the false claim of Chloe that Emma is a knight or Scarlett is a knave.

Scarlett cannot be a knave, because this would contradict the false claim of Chloe that Emma is a knight or Scarlett is a knave.

We have exhausted all possibilities for Scarlett, Emma, and Chloe, so let us go back and reconsider Sofia.

Assume Sofia is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Owen is a knight.

Abigail cannot be a knight, because this would contradict the claim of Emma that Scarlett is a knight and Abigail is a knave.

Assume Abigail is a knight. No contradiction is found in their claim that If Abigail is a knight then Sofia is a knave.

Owen cannot be a knight, because this would contradict the false claim of Sofia that Chloe is a knight if and only if Owen is a knight.

Assume Owen is a knave. No contradiction is found in their false claim that Scarlett is a knight.

Assume Ethan is a knight. No contradiction is found in their claim that Sofia is not a knight.

(('<=>', ('telling-truth', 2), ('telling-truth', 6)), ('and', ('telling-truth', 1), ('telling-truth', 5)), ('or', ('telling-truth', 5), ('lying', 1)), ('->', ('telling-truth', 3), ('lying', 0)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 3)), ('telling-truth', 1))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Abigail, David, Amelia, Mia, Logan, Daniel, and Sophia. "Mia is a knight," Abigail claimed. David asserted: "Abigail is a knave". Amelia told you that Mia is a knave. Mia remarked, "Mia is a knight and Daniel is a knight". Logan told you that Daniel is a knave or David is a knave. Daniel remarked, "Abigail is a knave or Sophia is a knight". According to Sophia, "Abigail is a knight if and only if Daniel is a knave". So who is a knight and who is a knave?

Abigail David Amelia Mia Logan Daniel Sophia

Abigail is a knave, David is a knight, Amelia is a knight, Mia is a knave, Logan is a knave, Daniel is a knight, and Sophia is a knight.

(1) Abigail is a knave
(2) David is a knight
(3) Amelia is a knight
(4) Mia is a knave
(5) Logan is a knave
(6) Daniel is a knight
(7) Sophia is a knight

Assume Abigail is a knight. No contradiction is found in their claim that Mia is a knight.

Assume Mia is a knight. No contradiction is found in their claim that Mia is a knight and Daniel is a knight.

Assume Daniel is a knight. No contradiction is found in their claim that Abigail is a knave or Sophia is a knight.

Sophia cannot be a knight, because this would contradict the claim of their own that Abigail is a knight if and only if Daniel is a knave.

Sophia cannot be a knave, because this would contradict the claim of Daniel that Abigail is a knave or Sophia is a knight.

We have exhausted all possibilities for Sophia, so let us go back and reconsider Daniel.

Daniel cannot be a knave, because this would contradict the claim of Mia that Mia is a knight and Daniel is a knight.

We have exhausted all possibilities for Daniel, so let us go back and reconsider Mia.

Mia cannot be a knave, because this would contradict the claim of Abigail that Mia is a knight.

We have exhausted all possibilities for Mia, so let us go back and reconsider Abigail.

Assume Abigail is a knave. No contradiction is found in their false claim that Mia is a knight.

Mia cannot be a knight, because this would contradict the false claim of Abigail that Mia is a knight.

Assume Mia is a knave. No contradiction is found in their false claim that Mia is a knight and Daniel is a knight.

Assume Sophia is a knight. No contradiction is found in their claim that Abigail is a knight if and only if Daniel is a knave.

Assume David is a knight. No contradiction is found in their claim that Abigail is a knave.

Assume Amelia is a knight. No contradiction is found in their claim that Mia is a knave.

Logan cannot be a knight, because this would contradict the claim of their own that Daniel is a knave or David is a knave.

Assume Logan is a knave. No contradiction is found in their false claim that Daniel is a knave or David is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Logan, Grace, Henry, Michael, Ethan, Riley, and Isabella. According to Logan, "Riley is not a knight". Grace asserted: "If Logan is a knight then Henry is a knight". "Henry is a knight if and only if Grace is a knight," Henry declared. Michael told you that Riley is a knight if and only if Henry is a knight. As Ethan put it, "If Grace is a knight then Logan is a knight". Riley commented, "Michael is not a knight". Isabella expressed that If Riley is a knight then Michael is a knave. So who is a knight and who is a knave?

Logan Grace Henry Michael Ethan Riley Isabella

Logan is a knave, Grace is a knight, Henry is a knave, Michael is a knave, Ethan is a knave, Riley is a knight, and Isabella is a knight.

(1) Logan is a knave
(2) Grace is a knight
(3) Henry is a knave
(4) Michael is a knave
(5) Ethan is a knave
(6) Riley is a knight
(7) Isabella is a knight

Assume Logan is a knight. No contradiction is found in their claim that Riley is not a knight.

Riley cannot be a knight, because this would contradict the claim of Logan that Riley is not a knight.

Assume Riley is a knave. No contradiction is found in their false claim that Michael is not a knight.

Assume Michael is a knight. No contradiction is found in their claim that Riley is a knight if and only if Henry is a knight.

Henry cannot be a knight, because this would contradict the claim of Michael that Riley is a knight if and only if Henry is a knight.

Assume Henry is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Grace is a knight.

Grace cannot be a knight, because this would contradict the claim of their own that If Logan is a knight then Henry is a knight.

Grace cannot be a knave, because this would contradict the false claim of Henry that Henry is a knight if and only if Grace is a knight.

We have exhausted all possibilities for Grace and Henry, so let us go back and reconsider Michael.

Michael cannot be a knave, because this would contradict the false claim of Riley that Michael is not a knight.

We have exhausted all possibilities for Michael and Riley, so let us go back and reconsider Logan.

Assume Logan is a knave. No contradiction is found in their false claim that Riley is not a knight.

Assume Riley is a knight. No contradiction is found in their claim that Michael is not a knight.

Michael cannot be a knight, because this would contradict the claim of Riley that Michael is not a knight.

Assume Michael is a knave. No contradiction is found in their false claim that Riley is a knight if and only if Henry is a knight.

Henry cannot be a knight, because this would contradict the false claim of Michael that Riley is a knight if and only if Henry is a knight.

Assume Grace is a knight. No contradiction is found in their claim that If Logan is a knight then Henry is a knight.

Ethan cannot be a knight, because this would contradict the claim of their own that If Grace is a knight then Logan is a knight.

Assume Ethan is a knave. No contradiction is found in their false claim that If Grace is a knight then Logan is a knight.

Assume Isabella is a knight. No contradiction is found in their claim that If Riley is a knight then Michael is a knave.

(('not', ('telling-truth', 5)), ('->', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 2), ('telling-truth', 1)), ('<=>', ('telling-truth', 5), ('telling-truth', 2)), ('->', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('telling-truth', 3)), ('->', ('telling-truth', 5), ('lying', 3)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Ava, Avery, Luke, Aurora, Sebastian, Grace, and Liam. In a statement by Ava: "If Grace is a knave then Liam is a knight". Avery said, "Ava is a knight or Sebastian is a knight." Luke stated, "Grace is a knave and Luke is a knight". Aurora told you that If Luke is a knight then Luke is a knave. Sebastian was heard saying, "Ava is a knave and Liam is a knave". According to Grace, "If Avery is a knave then Aurora is a knight". Liam expressed that Liam is a knight or Ava is a knight. So who is a knight and who is a knave?

Ava Avery Luke Aurora Sebastian Grace Liam

Ava is a knight, Avery is a knight, Luke is a knave, Aurora is a knight, Sebastian is a knave, Grace is a knight, and Liam is a knight.

(1) Ava is a knight
(2) Avery is a knight
(3) Luke is a knave
(4) Aurora is a knight
(5) Sebastian is a knave
(6) Grace is a knight
(7) Liam is a knight

Assume Ava is a knight. No contradiction is found in their claim that If Grace is a knave then Liam is a knight.

Assume Grace is a knight. No contradiction is found in their claim that If Avery is a knave then Aurora is a knight.

Assume Avery is a knight. No contradiction is found in their claim that Ava is a knight or Sebastian is a knight.

Sebastian cannot be a knight, because this would contradict the claim of their own that Ava is a knave and Liam is a knave.

Assume Sebastian is a knave. No contradiction is found in their false claim that Ava is a knave and Liam is a knave.

Assume Liam is a knight. No contradiction is found in their claim that Liam is a knight or Ava is a knight.

Assume Aurora is a knight. No contradiction is found in their claim that If Luke is a knight then Luke is a knave.

Luke cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Luke is a knight.

Assume Luke is a knave. No contradiction is found in their false claim that Grace is a knave and Luke is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Evelyn, Liam, Sophia, Emily, Alexander, Logan, and Matthew. According to Evelyn, "Emily is a knave". According to Liam, "Matthew is a knave". Sophia was heard saying, "Logan is a knave or Evelyn is a knave". "Evelyn is a knight if and only if Matthew is a knave," Emily claimed. In a statement by Alexander: "Evelyn is a knight if and only if Sophia is a knight". "Sophia is not a knave," Logan declared. "Alexander is a knave or Sophia is a knave" - Matthew. So who is a knight and who is a knave?

Evelyn Liam Sophia Emily Alexander Logan Matthew

Evelyn is a knave, Liam is a knave, Sophia is a knight, Emily is a knight, Alexander is a knave, Logan is a knight, and Matthew is a knight.

(1) Evelyn is a knave
(2) Liam is a knave
(3) Sophia is a knight
(4) Emily is a knight
(5) Alexander is a knave
(6) Logan is a knight
(7) Matthew is a knight

Assume Evelyn is a knight. No contradiction is found in their claim that Emily is a knave.

Emily cannot be a knight, because this would contradict the claim of Evelyn that Emily is a knave.

Assume Emily is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Matthew is a knave.

Assume Matthew is a knight. No contradiction is found in their claim that Alexander is a knave or Sophia is a knave.

Assume Alexander is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Sophia is a knight.

Sophia cannot be a knight, because this would contradict the claim of Matthew that Alexander is a knave or Sophia is a knave.

Sophia cannot be a knave, because this would contradict the claim of Alexander that Evelyn is a knight if and only if Sophia is a knight.

We have exhausted all possibilities for Sophia, so let us go back and reconsider Alexander.

Assume Alexander is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Sophia is a knight.

Sophia cannot be a knight, because this would contradict the false claim of Alexander that Evelyn is a knight if and only if Sophia is a knight.

Assume Sophia is a knave. No contradiction is found in their false claim that Logan is a knave or Evelyn is a knave.

Logan cannot be a knight, because this would contradict the claim of their own that Sophia is not a knave.

Logan cannot be a knave, because this would contradict the false claim of Sophia that Logan is a knave or Evelyn is a knave.

We have exhausted all possibilities for Logan, Sophia, and Alexander, so let us go back and reconsider Matthew.

Matthew cannot be a knave, because this would contradict the false claim of Emily that Evelyn is a knight if and only if Matthew is a knave.

We have exhausted all possibilities for Matthew and Emily, so let us go back and reconsider Evelyn.

Assume Evelyn is a knave. No contradiction is found in their false claim that Emily is a knave.

Assume Emily is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Matthew is a knave.

Sophia cannot be a knight, because this would contradict the claim of Alexander that Evelyn is a knight if and only if Sophia is a knight.

Sophia cannot be a knave, because this would contradict the false claim of their own that Logan is a knave or Evelyn is a knave.

Assume Sophia is a knight. No contradiction is found in their claim that Logan is a knave or Evelyn is a knave.

Assume Logan is a knight. No contradiction is found in their claim that Sophia is not a knave.

Liam cannot be a knight, because this would contradict the claim of their own that Matthew is a knave.

Assume Liam is a knave. No contradiction is found in their false claim that Matthew is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Daniel, Logan, Noah, Joseph, Victoria, Elizabeth, and Aiden. Daniel told you that Victoria is a knave and Joseph is a knave. "Aiden is a knave or Victoria is a knave," Logan declared. Noah said, "Elizabeth is a knight and Joseph is a knave." As Joseph put it, "Victoria is a knight or Aiden is a knave". Victoria said, "Aiden is a knight or Joseph is a knight." Elizabeth noted, "Victoria is a knave or Aiden is a knight". Aiden was heard saying, "If Joseph is a knight then Victoria is a knight". So who is a knight and who is a knave?

Daniel Logan Noah Joseph Victoria Elizabeth Aiden

Daniel is a knave, Logan is a knave, Noah is a knave, Joseph is a knight, Victoria is a knight, Elizabeth is a knight, and Aiden is a knight.

(1) Daniel is a knave
(2) Logan is a knave
(3) Noah is a knave
(4) Joseph is a knight
(5) Victoria is a knight
(6) Elizabeth is a knight
(7) Aiden is a knight

Assume Daniel is a knight. No contradiction is found in their claim that Victoria is a knave and Joseph is a knave.

Victoria cannot be a knight, because this would contradict the claim of Daniel that Victoria is a knave and Joseph is a knave.

Assume Victoria is a knave. No contradiction is found in their false claim that Aiden is a knight or Joseph is a knight.

Aiden cannot be a knight, because this would contradict the false claim of Victoria that Aiden is a knight or Joseph is a knight.

Assume Aiden is a knave. No contradiction is found in their false claim that If Joseph is a knight then Victoria is a knight.

Joseph cannot be a knight, because this would contradict the claim of Daniel that Victoria is a knave and Joseph is a knave.

Joseph cannot be a knave, because this would contradict the false claim of their own that Victoria is a knight or Aiden is a knave.

We have exhausted all possibilities for Joseph, Aiden, and Victoria, so let us go back and reconsider Daniel.

Assume Daniel is a knave. No contradiction is found in their false claim that Victoria is a knave and Joseph is a knave.

Assume Victoria is a knight. No contradiction is found in their claim that Aiden is a knight or Joseph is a knight.

Assume Aiden is a knight. No contradiction is found in their claim that If Joseph is a knight then Victoria is a knight.

Assume Joseph is a knight. No contradiction is found in their claim that Victoria is a knight or Aiden is a knave.

Logan cannot be a knight, because this would contradict the claim of their own that Aiden is a knave or Victoria is a knave.

Assume Logan is a knave. No contradiction is found in their false claim that Aiden is a knave or Victoria is a knave.

Noah cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Joseph is a knave.

Assume Noah is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Joseph is a knave.

Assume Elizabeth is a knight. No contradiction is found in their claim that Victoria is a knave or Aiden is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Aiden, Luke, Michael, Charlotte, Ella, Daniel, and Grace. "Michael is not a knave" - Aiden. Luke noted, "Ella is a knave or Daniel is a knight". Michael remarked, "Ella is a knave and Luke is a knight". "Ella is a knight," Charlotte mentioned. Ella told you that Luke is a knight if and only if Aiden is a knave. Daniel expressed that Luke is a knave. Grace commented, "Michael is not a knight". So who is a knight and who is a knave?

Aiden Luke Michael Charlotte Ella Daniel Grace

Aiden is a knight, Luke is a knight, Michael is a knight, Charlotte is a knave, Ella is a knave, Daniel is a knave, and Grace is a knave.

(1) Aiden is a knight
(2) Luke is a knight
(3) Michael is a knight
(4) Charlotte is a knave
(5) Ella is a knave
(6) Daniel is a knave
(7) Grace is a knave

Assume Aiden is a knight. No contradiction is found in their claim that Michael is not a knave.

Assume Michael is a knight. No contradiction is found in their claim that Ella is a knave and Luke is a knight.

Ella cannot be a knight, because this would contradict the claim of Michael that Ella is a knave and Luke is a knight.

Assume Ella is a knave. No contradiction is found in their false claim that Luke is a knight if and only if Aiden is a knave.

Assume Luke is a knight. No contradiction is found in their claim that Ella is a knave or Daniel is a knight.

Daniel cannot be a knight, because this would contradict the claim of their own that Luke is a knave.

Assume Daniel is a knave. No contradiction is found in their false claim that Luke is a knave.

Charlotte cannot be a knight, because this would contradict the claim of their own that Ella is a knight.

Assume Charlotte is a knave. No contradiction is found in their false claim that Ella is a knight.

Grace cannot be a knight, because this would contradict the claim of their own that Michael is not a knight.

Assume Grace is a knave. No contradiction is found in their false claim that Michael is not a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Samuel, Ethan, Riley, Lucas, Sofia, Penelope, and Owen. Samuel commented, "Ethan is a knight". In a statement by Ethan: "Owen is not a knight". Riley stated, "Penelope is a knave if and only if Penelope is a knight". Lucas told you that Samuel is a knight. Sofia remarked, "Samuel is not a knave". As Penelope put it, "If Penelope is a knight then Samuel is a knight". Owen asserted: "Riley is not a knave". So who is a knight and who is a knave?

Samuel Ethan Riley Lucas Sofia Penelope Owen

Samuel is a knight, Ethan is a knight, Riley is a knave, Lucas is a knight, Sofia is a knight, Penelope is a knight, and Owen is a knave.

(1) Samuel is a knight
(2) Ethan is a knight
(3) Riley is a knave
(4) Lucas is a knight
(5) Sofia is a knight
(6) Penelope is a knight
(7) Owen is a knave

Assume Samuel is a knight. No contradiction is found in their claim that Ethan is a knight.

Assume Ethan is a knight. No contradiction is found in their claim that Owen is not a knight.

Owen cannot be a knight, because this would contradict the claim of Ethan that Owen is not a knight.

Assume Owen is a knave. No contradiction is found in their false claim that Riley is not a knave.

Riley cannot be a knight, because this would contradict the claim of their own that Penelope is a knave if and only if Penelope is a knight.

Assume Riley is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if Penelope is a knight.

Assume Penelope is a knight. No contradiction is found in their claim that If Penelope is a knight then Samuel is a knight.

Assume Lucas is a knight. No contradiction is found in their claim that Samuel is a knight.

Assume Sofia is a knight. No contradiction is found in their claim that Samuel is not a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Oliver, Olivia, Penelope, Avery, Michael, Samuel, and Liam. Oliver told you that Avery is not a knave. "Liam is a knave or Oliver is a knight" - Olivia. Penelope said that Liam is a knave. Avery said that Oliver is a knight if and only if Samuel is a knave. Michael told you that Penelope is not a knave. Samuel noted, "If Penelope is a knight then Oliver is a knave". According to Liam, "Michael is a knave if and only if Michael is a knight". So who is a knight and who is a knave?

Oliver Olivia Penelope Avery Michael Samuel Liam

Oliver is a knight, Olivia is a knight, Penelope is a knight, Avery is a knight, Michael is a knight, Samuel is a knave, and Liam is a knave.

(1) Oliver is a knight
(2) Olivia is a knight
(3) Penelope is a knight
(4) Avery is a knight
(5) Michael is a knight
(6) Samuel is a knave
(7) Liam is a knave

Assume Oliver is a knight. No contradiction is found in their claim that Avery is not a knave.

Assume Avery is a knight. No contradiction is found in their claim that Oliver is a knight if and only if Samuel is a knave.

Samuel cannot be a knight, because this would contradict the claim of Avery that Oliver is a knight if and only if Samuel is a knave.

Assume Samuel is a knave. No contradiction is found in their false claim that If Penelope is a knight then Oliver is a knave.

Assume Penelope is a knight. No contradiction is found in their claim that Liam is a knave.

Liam cannot be a knight, because this would contradict the claim of Penelope that Liam is a knave.

Assume Liam is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Michael is a knight.

Assume Michael is a knight. No contradiction is found in their claim that Penelope is not a knave.

Assume Olivia is a knight. No contradiction is found in their claim that Liam is a knave or Oliver is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Daniel, Sofia, Henry, William, Samuel, Isabella, and Benjamin. Daniel stated, "If Samuel is a knight then Sofia is a knight". Sofia said, "Benjamin is a knight or Isabella is a knave." As Henry put it, "William is a knight if and only if Daniel is a knight". In a statement by William: "Benjamin is a knight and Henry is a knave". Samuel asserted: "Sofia is a knight if and only if Daniel is a knave". Isabella asserted: "If Samuel is a knave then Sofia is a knave". Benjamin stated, "Daniel is a knave and Sofia is a knight". So who is a knight and who is a knave?

Daniel Sofia Henry William Samuel Isabella Benjamin

Daniel is a knight, Sofia is a knight, Henry is a knave, William is a knave, Samuel is a knave, Isabella is a knave, and Benjamin is a knave.

(1) Daniel is a knight
(2) Sofia is a knight
(3) Henry is a knave
(4) William is a knave
(5) Samuel is a knave
(6) Isabella is a knave
(7) Benjamin is a knave

Assume Daniel is a knight. No contradiction is found in their claim that If Samuel is a knight then Sofia is a knight.

Assume Samuel is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Daniel is a knave.

Sofia cannot be a knight, because this would contradict the claim of Samuel that Sofia is a knight if and only if Daniel is a knave.

Sofia cannot be a knave, because this would contradict the claim of Daniel that If Samuel is a knight then Sofia is a knight.

We have exhausted all possibilities for Sofia, so let us go back and reconsider Samuel.

Assume Samuel is a knave. No contradiction is found in their false claim that Sofia is a knight if and only if Daniel is a knave.

Assume Sofia is a knight. No contradiction is found in their claim that Benjamin is a knight or Isabella is a knave.

Benjamin cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Sofia is a knight.

Assume Benjamin is a knave. No contradiction is found in their false claim that Daniel is a knave and Sofia is a knight.

Isabella cannot be a knight, because this would contradict the claim of Sofia that Benjamin is a knight or Isabella is a knave.

Assume Isabella is a knave. No contradiction is found in their false claim that If Samuel is a knave then Sofia is a knave.

Assume Henry is a knight. No contradiction is found in their claim that William is a knight if and only if Daniel is a knight.

William cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Henry is a knave.

William cannot be a knave, because this would contradict the claim of Henry that William is a knight if and only if Daniel is a knight.

We have exhausted all possibilities for William, so let us go back and reconsider Henry.

Assume Henry is a knave. No contradiction is found in their false claim that William is a knight if and only if Daniel is a knight.

William cannot be a knight, because this would contradict the false claim of Henry that William is a knight if and only if Daniel is a knight.

Assume William is a knave. No contradiction is found in their false claim that Benjamin is a knight and Henry is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Sofia, Joseph, Mia, Aria, Oliver, Victoria, and Emily. "Oliver is a knight and Aria is a knight," Sofia claimed. Joseph commented, "Emily is not a knave". Mia remarked, "Aria is a knave and Joseph is a knave". As Aria put it, "Mia is a knight and Emily is a knave". In a statement by Oliver: "If Emily is a knave then Victoria is a knight". Victoria asserted: "Sofia is a knight or Mia is a knight". Emily said, "If Sofia is a knave then Emily is a knight." So who is a knight and who is a knave?

Sofia Joseph Mia Aria Oliver Victoria Emily

Sofia is a knave, Joseph is a knight, Mia is a knave, Aria is a knave, Oliver is a knight, Victoria is a knave, and Emily is a knight.

(1) Sofia is a knave
(2) Joseph is a knight
(3) Mia is a knave
(4) Aria is a knave
(5) Oliver is a knight
(6) Victoria is a knave
(7) Emily is a knight

Assume Sofia is a knight. No contradiction is found in their claim that Oliver is a knight and Aria is a knight.

Assume Oliver is a knight. No contradiction is found in their claim that If Emily is a knave then Victoria is a knight.

Assume Emily is a knight. No contradiction is found in their claim that If Sofia is a knave then Emily is a knight.

Assume Victoria is a knight. No contradiction is found in their claim that Sofia is a knight or Mia is a knight.

Assume Mia is a knight. No contradiction is found in their claim that Aria is a knave and Joseph is a knave.

Aria cannot be a knight, because this would contradict the claim of Mia that Aria is a knave and Joseph is a knave.

Aria cannot be a knave, because this would contradict the claim of Sofia that Oliver is a knight and Aria is a knight.

We have exhausted all possibilities for Aria, so let us go back and reconsider Mia.

Assume Mia is a knave. No contradiction is found in their false claim that Aria is a knave and Joseph is a knave.

Aria cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Emily is a knave.

We have exhausted all possibilities for Aria and Mia, so let us go back and reconsider Victoria.

Victoria cannot be a knave, because this would contradict the false claim of their own that Sofia is a knight or Mia is a knight.

We have exhausted all possibilities for Victoria, so let us go back and reconsider Emily.

Emily cannot be a knave, because this would contradict the false claim of their own that If Sofia is a knave then Emily is a knight.

We have exhausted all possibilities for Emily, so let us go back and reconsider Oliver.

Oliver cannot be a knave, because this would contradict the claim of Sofia that Oliver is a knight and Aria is a knight.

We have exhausted all possibilities for Oliver, so let us go back and reconsider Sofia.

Assume Sofia is a knave. No contradiction is found in their false claim that Oliver is a knight and Aria is a knight.

Aria cannot be a knight, because this would contradict the false claim of Sofia that Oliver is a knight and Aria is a knight.

Assume Aria is a knave. No contradiction is found in their false claim that Mia is a knight and Emily is a knave.

Joseph cannot be a knight, because this would contradict the claim of Mia that Aria is a knave and Joseph is a knave.

Joseph cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave.

We have exhausted all possibilities for Joseph and Aria, so let us go back and reconsider Mia.

Mia cannot be a knave, because this would contradict the claim of Victoria that Sofia is a knight or Mia is a knight.

We have exhausted all possibilities for Mia, so let us go back and reconsider Victoria.

Assume Victoria is a knave. No contradiction is found in their false claim that Sofia is a knight or Mia is a knight.

Mia cannot be a knight, because this would contradict the false claim of Victoria that Sofia is a knight or Mia is a knight.

Assume Joseph is a knight. No contradiction is found in their claim that Emily is not a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Grace, Samuel, Chloe, Zoey, Charlotte, James, and Aria. In Grace's words: "If Charlotte is a knave then Samuel is a knight". As Samuel put it, "Zoey is a knight or Charlotte is a knight". Chloe asserted: "Zoey is a knave". Zoey commented, "James is a knight". "Grace is a knight or Aria is a knave," Charlotte mentioned. James stated, "Aria is a knave". Aria expressed that Grace is a knight. So who is a knight and who is a knave?

Grace Samuel Chloe Zoey Charlotte James Aria

Grace is a knight, Samuel is a knight, Chloe is a knight, Zoey is a knave, Charlotte is a knight, James is a knave, and Aria is a knight.

(1) Grace is a knight
(2) Samuel is a knight
(3) Chloe is a knight
(4) Zoey is a knave
(5) Charlotte is a knight
(6) James is a knave
(7) Aria is a knight

Assume Grace is a knight. No contradiction is found in their claim that If Charlotte is a knave then Samuel is a knight.

Assume Charlotte is a knight. No contradiction is found in their claim that Grace is a knight or Aria is a knave.

Assume Aria is a knight. No contradiction is found in their claim that Grace is a knight.

Assume Samuel is a knight. No contradiction is found in their claim that Zoey is a knight or Charlotte is a knight.

Assume Zoey is a knight. No contradiction is found in their claim that James is a knight.

James cannot be a knight, because this would contradict the claim of their own that Aria is a knave.

James cannot be a knave, because this would contradict the claim of Zoey that James is a knight.

We have exhausted all possibilities for James, so let us go back and reconsider Zoey.

Assume Zoey is a knave. No contradiction is found in their false claim that James is a knight.

James cannot be a knight, because this would contradict the false claim of Zoey that James is a knight.

Assume James is a knave. No contradiction is found in their false claim that Aria is a knave.

Assume Chloe is a knight. No contradiction is found in their claim that Zoey is a knave.

(('->', ('lying', 4), ('telling-truth', 1)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('lying', 3), ('telling-truth', 5), ('or', ('telling-truth', 0), ('lying', 6)), ('lying', 6), ('telling-truth', 0))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Emily, Daniel, Charlotte, Alexander, Mia, Jackson, and Jacob. "If Alexander is a knave then Mia is a knight," Emily declared. "Mia is a knight and Charlotte is a knight," Daniel declared. According to Charlotte, "If Daniel is a knight then Emily is a knave". Alexander noted, "Emily is not a knave". Mia said, "Alexander is not a knave." According to Jackson, "Jacob is not a knight". "Jacob is a knight and Daniel is a knight," Jacob declared. So who is a knight and who is a knave?

Emily Daniel Charlotte Alexander Mia Jackson Jacob

Emily is a knave, Daniel is a knave, Charlotte is a knight, Alexander is a knave, Mia is a knave, Jackson is a knight, and Jacob is a knave.

(1) Emily is a knave
(2) Daniel is a knave
(3) Charlotte is a knight
(4) Alexander is a knave
(5) Mia is a knave
(6) Jackson is a knight
(7) Jacob is a knave

Assume Emily is a knight. No contradiction is found in their claim that If Alexander is a knave then Mia is a knight.

Assume Alexander is a knight. No contradiction is found in their claim that Emily is not a knave.

Assume Mia is a knight. No contradiction is found in their claim that Alexander is not a knave.

Assume Daniel is a knight. No contradiction is found in their claim that Mia is a knight and Charlotte is a knight.

Charlotte cannot be a knight, because this would contradict the claim of their own that If Daniel is a knight then Emily is a knave.

Charlotte cannot be a knave, because this would contradict the claim of Daniel that Mia is a knight and Charlotte is a knight.

We have exhausted all possibilities for Charlotte, so let us go back and reconsider Daniel.

Assume Daniel is a knave. No contradiction is found in their false claim that Mia is a knight and Charlotte is a knight.

Charlotte cannot be a knight, because this would contradict the false claim of Daniel that Mia is a knight and Charlotte is a knight.

Charlotte cannot be a knave, because this would contradict the false claim of their own that If Daniel is a knight then Emily is a knave.

We have exhausted all possibilities for Charlotte and Daniel, so let us go back and reconsider Mia.

Mia cannot be a knave, because this would contradict the false claim of their own that Alexander is not a knave.

We have exhausted all possibilities for Mia, so let us go back and reconsider Alexander.

Alexander cannot be a knave, because this would contradict the false claim of their own that Emily is not a knave.

We have exhausted all possibilities for Alexander, so let us go back and reconsider Emily.

Assume Emily is a knave. No contradiction is found in their false claim that If Alexander is a knave then Mia is a knight.

Alexander cannot be a knight, because this would contradict the false claim of Emily that If Alexander is a knave then Mia is a knight.

Assume Alexander is a knave. No contradiction is found in their false claim that Emily is not a knave.

Mia cannot be a knight, because this would contradict the false claim of Emily that If Alexander is a knave then Mia is a knight.

Assume Mia is a knave. No contradiction is found in their false claim that Alexander is not a knave.

Daniel cannot be a knight, because this would contradict the claim of their own that Mia is a knight and Charlotte is a knight.

Assume Charlotte is a knight. No contradiction is found in their claim that If Daniel is a knight then Emily is a knave.

Assume Jackson is a knight. No contradiction is found in their claim that Jacob is not a knight.

Jacob cannot be a knight, because this would contradict the claim of Jackson that Jacob is not a knight.

Assume Jacob is a knave. No contradiction is found in their false claim that Jacob is a knight and Daniel is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Sebastian, William, Mia, Scarlett, Victoria, Lily, and Aria. Sebastian expressed that William is a knight. William expressed that Scarlett is a knight and Sebastian is a knave. Mia told you that Mia is a knight if and only if Sebastian is a knave. "Mia is a knave" - Scarlett. Victoria expressed that Mia is a knight or Victoria is a knight. Lily was heard saying, "William is a knight if and only if William is a knave". "Mia is not a knight," Aria claimed. So who is a knight and who is a knave?

Sebastian William Mia Scarlett Victoria Lily Aria

Sebastian is a knave, William is a knave, Mia is a knight, Scarlett is a knave, Victoria is a knight, Lily is a knave, and Aria is a knave.

(1) Sebastian is a knave
(2) William is a knave
(3) Mia is a knight
(4) Scarlett is a knave
(5) Victoria is a knight
(6) Lily is a knave
(7) Aria is a knave

Assume Sebastian is a knight. No contradiction is found in their claim that William is a knight.

William cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Sebastian is a knave.

William cannot be a knave, because this would contradict the claim of Sebastian that William is a knight.

We have exhausted all possibilities for William, so let us go back and reconsider Sebastian.

Assume Sebastian is a knave. No contradiction is found in their false claim that William is a knight.

William cannot be a knight, because this would contradict the false claim of Sebastian that William is a knight.

Assume William is a knave. No contradiction is found in their false claim that Scarlett is a knight and Sebastian is a knave.

Scarlett cannot be a knight, because this would contradict the false claim of William that Scarlett is a knight and Sebastian is a knave.

Assume Scarlett is a knave. No contradiction is found in their false claim that Mia is a knave.

Assume Mia is a knight. No contradiction is found in their claim that Mia is a knight if and only if Sebastian is a knave.

Assume Victoria is a knight. No contradiction is found in their claim that Mia is a knight or Victoria is a knight.

Lily cannot be a knight, because this would contradict the claim of their own that William is a knight if and only if William is a knave.

Assume Lily is a knave. No contradiction is found in their false claim that William is a knight if and only if William is a knave.

Aria cannot be a knight, because this would contradict the claim of their own that Mia is not a knight.

Assume Aria is a knave. No contradiction is found in their false claim that Mia is not a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Jack, Oliver, Aria, Emma, Charlotte, Jackson, and Sebastian. Jack said, "Charlotte is a knight if and only if Jackson is a knave." Oliver commented, "Jackson is a knight". Aria stated, "Emma is a knave or Sebastian is a knave". In a statement by Emma: "If Sebastian is a knave then Jack is a knave". "Jackson is a knight and Emma is a knight," Charlotte mentioned. Jackson commented, "Emma is a knave and Oliver is a knave". Sebastian was heard saying, "Jackson is a knight if and only if Jackson is a knave". So who is a knight and who is a knave?

Jack Oliver Aria Emma Charlotte Jackson Sebastian

Jack is a knave, Oliver is a knave, Aria is a knight, Emma is a knight, Charlotte is a knave, Jackson is a knave, and Sebastian is a knave.

(1) Jack is a knave
(2) Oliver is a knave
(3) Aria is a knight
(4) Emma is a knight
(5) Charlotte is a knave
(6) Jackson is a knave
(7) Sebastian is a knave

Assume Jack is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Jackson is a knave.

Assume Charlotte is a knight. No contradiction is found in their claim that Jackson is a knight and Emma is a knight.

Jackson cannot be a knight, because this would contradict the claim of Jack that Charlotte is a knight if and only if Jackson is a knave.

Jackson cannot be a knave, because this would contradict the claim of Charlotte that Jackson is a knight and Emma is a knight.

We have exhausted all possibilities for Jackson, so let us go back and reconsider Charlotte.

Assume Charlotte is a knave. No contradiction is found in their false claim that Jackson is a knight and Emma is a knight.

Assume Jackson is a knight. No contradiction is found in their claim that Emma is a knave and Oliver is a knave.

Emma cannot be a knight, because this would contradict the false claim of Charlotte that Jackson is a knight and Emma is a knight.

Assume Emma is a knave. No contradiction is found in their false claim that If Sebastian is a knave then Jack is a knave.

Sebastian cannot be a knight, because this would contradict the false claim of Emma that If Sebastian is a knave then Jack is a knave.

Assume Sebastian is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Jackson is a knave.

Oliver cannot be a knight, because this would contradict the claim of Jackson that Emma is a knave and Oliver is a knave.

Oliver cannot be a knave, because this would contradict the false claim of their own that Jackson is a knight.

We have exhausted all possibilities for Oliver, Sebastian, and Emma, so let us go back and reconsider Jackson.

Jackson cannot be a knave, because this would contradict the claim of Jack that Charlotte is a knight if and only if Jackson is a knave.

We have exhausted all possibilities for Jackson and Charlotte, so let us go back and reconsider Jack.

Assume Jack is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Jackson is a knave.

Emma cannot be a knight, because this would contradict the claim of Jackson that Emma is a knave and Oliver is a knave.

Emma cannot be a knave, because this would contradict the false claim of their own that If Sebastian is a knave then Jack is a knave.

We have exhausted all possibilities for Emma, so let us go back and reconsider Jackson.

Jackson cannot be a knave, because this would contradict the false claim of Jack that Charlotte is a knight if and only if Jackson is a knave.

Jackson cannot be a knight, because this would contradict the false claim of Jack that Charlotte is a knight if and only if Jackson is a knave.

Assume Jackson is a knave. No contradiction is found in their false claim that Emma is a knave and Oliver is a knave.

Assume Emma is a knight. No contradiction is found in their claim that If Sebastian is a knave then Jack is a knave.

Sebastian cannot be a knight, because this would contradict the claim of their own that Jackson is a knight if and only if Jackson is a knave.

Oliver cannot be a knight, because this would contradict the claim of their own that Jackson is a knight.

Assume Oliver is a knave. No contradiction is found in their false claim that Jackson is a knight.

Assume Aria is a knight. No contradiction is found in their claim that Emma is a knave or Sebastian is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Joseph, Chloe, Noah, Daniel, Jacob, Oliver, and Jack. "Jack is a knave," Joseph declared. As Chloe put it, "Noah is a knave or Oliver is a knave". In Noah's words: "Jack is a knight if and only if Joseph is a knave". Daniel told you that Noah is a knave or Noah is a knight. "Daniel is a knave or Noah is a knave," Jacob mentioned. Oliver commented, "Noah is a knave and Jacob is a knight". "Joseph is a knight or Jack is a knight," Jack declared. So who is a knight and who is a knave?

Joseph Chloe Noah Daniel Jacob Oliver Jack

Joseph is a knave, Chloe is a knight, Noah is a knight, Daniel is a knight, Jacob is a knave, Oliver is a knave, and Jack is a knight.

(1) Joseph is a knave
(2) Chloe is a knight
(3) Noah is a knight
(4) Daniel is a knight
(5) Jacob is a knave
(6) Oliver is a knave
(7) Jack is a knight

Assume Joseph is a knight. No contradiction is found in their claim that Jack is a knave.

Jack cannot be a knight, because this would contradict the claim of Joseph that Jack is a knave.

Jack cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight or Jack is a knight.

We have exhausted all possibilities for Jack, so let us go back and reconsider Joseph.

Assume Joseph is a knave. No contradiction is found in their false claim that Jack is a knave.

Assume Jack is a knight. No contradiction is found in their claim that Joseph is a knight or Jack is a knight.

Assume Chloe is a knight. No contradiction is found in their claim that Noah is a knave or Oliver is a knave.

Assume Noah is a knight. No contradiction is found in their claim that Jack is a knight if and only if Joseph is a knave.

Oliver cannot be a knight, because this would contradict the claim of Chloe that Noah is a knave or Oliver is a knave.

Assume Oliver is a knave. No contradiction is found in their false claim that Noah is a knave and Jacob is a knight.

Assume Jacob is a knight. No contradiction is found in their claim that Daniel is a knave or Noah is a knave.

Daniel cannot be a knight, because this would contradict the claim of Jacob that Daniel is a knave or Noah is a knave.

Daniel cannot be a knave, because this would contradict the false claim of their own that Noah is a knave or Noah is a knight.

We have exhausted all possibilities for Daniel, so let us go back and reconsider Jacob.

Assume Jacob is a knave. No contradiction is found in their false claim that Daniel is a knave or Noah is a knave.

Assume Daniel is a knight. No contradiction is found in their claim that Noah is a knave or Noah is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Ethan, Mason, Jacob, Aiden, Samuel, Jack, and Emma. Ethan said that Mason is a knave. In a statement by Mason: "Emma is a knave". According to Jacob, "If Ethan is a knave then Jack is a knave". In Aiden's words: "Samuel is a knave if and only if Emma is a knight". Samuel noted, "Aiden is a knight". In a statement by Jack: "Jacob is a knave and Samuel is a knave". According to Emma, "Mason is a knave or Aiden is a knave". So who is a knight and who is a knave?

Ethan Mason Jacob Aiden Samuel Jack Emma

Ethan is a knave, Mason is a knight, Jacob is a knight, Aiden is a knight, Samuel is a knight, Jack is a knave, and Emma is a knave.

(1) Ethan is a knave
(2) Mason is a knight
(3) Jacob is a knight
(4) Aiden is a knight
(5) Samuel is a knight
(6) Jack is a knave
(7) Emma is a knave

Assume Ethan is a knight. No contradiction is found in their claim that Mason is a knave.

Mason cannot be a knight, because this would contradict the claim of Ethan that Mason is a knave.

Assume Mason is a knave. No contradiction is found in their false claim that Emma is a knave.

Assume Emma is a knight. No contradiction is found in their claim that Mason is a knave or Aiden is a knave.

Assume Aiden is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Emma is a knight.

Samuel cannot be a knight, because this would contradict the claim of Aiden that Samuel is a knave if and only if Emma is a knight.

Samuel cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight.

We have exhausted all possibilities for Samuel, so let us go back and reconsider Aiden.

Assume Aiden is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Emma is a knight.

Samuel cannot be a knight, because this would contradict the claim of their own that Aiden is a knight.

Samuel cannot be a knave, because this would contradict the false claim of Aiden that Samuel is a knave if and only if Emma is a knight.

We have exhausted all possibilities for Samuel and Aiden, so let us go back and reconsider Emma.

Emma cannot be a knave, because this would contradict the false claim of Mason that Emma is a knave.

We have exhausted all possibilities for Emma and Mason, so let us go back and reconsider Ethan.

Assume Ethan is a knave. No contradiction is found in their false claim that Mason is a knave.

Assume Mason is a knight. No contradiction is found in their claim that Emma is a knave.

Emma cannot be a knight, because this would contradict the claim of Mason that Emma is a knave.

Assume Emma is a knave. No contradiction is found in their false claim that Mason is a knave or Aiden is a knave.

Assume Samuel is a knight. No contradiction is found in their claim that Aiden is a knight.

Assume Jacob is a knight. No contradiction is found in their claim that If Ethan is a knave then Jack is a knave.

Jack cannot be a knight, because this would contradict the claim of Jacob that If Ethan is a knave then Jack is a knave.

Assume Jack is a knave. No contradiction is found in their false claim that Jacob is a knave and Samuel is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Chloe, Grace, Olivia, Aria, Lucas, David, and Jack. In Chloe's words: "David is not a knight". Grace noted, "Chloe is a knight if and only if Lucas is a knave". Olivia told you that Grace is a knave. Aria said, "Jack is a knave and Lucas is a knight." Lucas asserted: "Aria is not a knave". In David's words: "Olivia is not a knight". In Jack's words: "If Chloe is a knave then Grace is a knave". So who is a knight and who is a knave?

Chloe Grace Olivia Aria Lucas David Jack

Chloe is a knave, Grace is a knight, Olivia is a knave, Aria is a knight, Lucas is a knight, David is a knight, and Jack is a knave.

(1) Chloe is a knave
(2) Grace is a knight
(3) Olivia is a knave
(4) Aria is a knight
(5) Lucas is a knight
(6) David is a knight
(7) Jack is a knave

Assume Chloe is a knight. No contradiction is found in their claim that David is not a knight.

David cannot be a knight, because this would contradict the claim of Chloe that David is not a knight.

Assume David is a knave. No contradiction is found in their false claim that Olivia is not a knight.

Assume Olivia is a knight. No contradiction is found in their claim that Grace is a knave.

Grace cannot be a knight, because this would contradict the claim of Olivia that Grace is a knave.

Assume Grace is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Lucas is a knave.

Assume Lucas is a knight. No contradiction is found in their claim that Aria is not a knave.

Assume Aria is a knight. No contradiction is found in their claim that Jack is a knave and Lucas is a knight.

Jack cannot be a knight, because this would contradict the claim of Aria that Jack is a knave and Lucas is a knight.

Jack cannot be a knave, because this would contradict the false claim of their own that If Chloe is a knave then Grace is a knave.

We have exhausted all possibilities for Jack, so let us go back and reconsider Aria.

Aria cannot be a knave, because this would contradict the claim of Lucas that Aria is not a knave.

We have exhausted all possibilities for Aria, so let us go back and reconsider Lucas.

Lucas cannot be a knave, because this would contradict the false claim of Grace that Chloe is a knight if and only if Lucas is a knave.

We have exhausted all possibilities for Lucas and Grace, so let us go back and reconsider Olivia.

Olivia cannot be a knave, because this would contradict the false claim of David that Olivia is not a knight.

We have exhausted all possibilities for Olivia and David, so let us go back and reconsider Chloe.

Assume Chloe is a knave. No contradiction is found in their false claim that David is not a knight.

Assume David is a knight. No contradiction is found in their claim that Olivia is not a knight.

Olivia cannot be a knight, because this would contradict the claim of David that Olivia is not a knight.

Assume Olivia is a knave. No contradiction is found in their false claim that Grace is a knave.

Assume Grace is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Lucas is a knave.

Assume Jack is a knave. No contradiction is found in their false claim that If Chloe is a knave then Grace is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Jackson, Olivia, Sophia, Logan, Chloe, Emma, and Aria. Jackson asserted: "Emma is a knave". Olivia stated, "If Chloe is a knight then Logan is a knave". In a statement by Sophia: "Emma is not a knave". "Jackson is a knave," Logan claimed. As Chloe put it, "Emma is not a knight". "Olivia is a knight," Emma claimed. Aria stated, "If Chloe is a knave then Olivia is a knave". So who is a knight and who is a knave?

Jackson Olivia Sophia Logan Chloe Emma Aria

Jackson is a knave, Olivia is a knight, Sophia is a knight, Logan is a knight, Chloe is a knave, Emma is a knight, and Aria is a knave.

(1) Jackson is a knave
(2) Olivia is a knight
(3) Sophia is a knight
(4) Logan is a knight
(5) Chloe is a knave
(6) Emma is a knight
(7) Aria is a knave

Assume Jackson is a knight. No contradiction is found in their claim that Emma is a knave.

Emma cannot be a knight, because this would contradict the claim of Jackson that Emma is a knave.

Assume Emma is a knave. No contradiction is found in their false claim that Olivia is a knight.

Olivia cannot be a knight, because this would contradict the false claim of Emma that Olivia is a knight.

Assume Olivia is a knave. No contradiction is found in their false claim that If Chloe is a knight then Logan is a knave.

Assume Chloe is a knight. No contradiction is found in their claim that Emma is not a knight.

Logan cannot be a knight, because this would contradict the claim of their own that Jackson is a knave.

Logan cannot be a knave, because this would contradict the false claim of Olivia that If Chloe is a knight then Logan is a knave.

We have exhausted all possibilities for Logan, so let us go back and reconsider Chloe.

Chloe cannot be a knave, because this would contradict the false claim of Olivia that If Chloe is a knight then Logan is a knave.

We have exhausted all possibilities for Chloe, Olivia, and Emma, so let us go back and reconsider Jackson.

Assume Jackson is a knave. No contradiction is found in their false claim that Emma is a knave.

Assume Emma is a knight. No contradiction is found in their claim that Olivia is a knight.

Assume Olivia is a knight. No contradiction is found in their claim that If Chloe is a knight then Logan is a knave.

Chloe cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.

Assume Chloe is a knave. No contradiction is found in their false claim that Emma is not a knight.

Assume Logan is a knight. No contradiction is found in their claim that Jackson is a knave.

Assume Sophia is a knight. No contradiction is found in their claim that Emma is not a knave.

Aria cannot be a knight, because this would contradict the claim of their own that If Chloe is a knave then Olivia is a knave.

Assume Aria is a knave. No contradiction is found in their false claim that If Chloe is a knave then Olivia is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Lucas, Charlotte, Sofia, Benjamin, Oliver, Ethan, and Riley. Lucas was heard saying, "Sofia is a knave". "Charlotte is a knight if and only if Oliver is a knight," Charlotte declared. Sofia commented, "Riley is a knight". In a statement by Benjamin: "Riley is a knave and Sofia is a knight". Oliver commented, "Lucas is not a knight". "Charlotte is a knight or Oliver is a knave," Ethan claimed. In Riley's words: "Ethan is not a knight". So who is a knight and who is a knave?

Lucas Charlotte Sofia Benjamin Oliver Ethan Riley

Lucas is a knave, Charlotte is a knave, Sofia is a knight, Benjamin is a knave, Oliver is a knight, Ethan is a knave, and Riley is a knight.

(1) Lucas is a knave
(2) Charlotte is a knave
(3) Sofia is a knight
(4) Benjamin is a knave
(5) Oliver is a knight
(6) Ethan is a knave
(7) Riley is a knight

Assume Lucas is a knight. No contradiction is found in their claim that Sofia is a knave.

Sofia cannot be a knight, because this would contradict the claim of Lucas that Sofia is a knave.

Assume Sofia is a knave. No contradiction is found in their false claim that Riley is a knight.

Riley cannot be a knight, because this would contradict the false claim of Sofia that Riley is a knight.

Assume Riley is a knave. No contradiction is found in their false claim that Ethan is not a knight.

Assume Ethan is a knight. No contradiction is found in their claim that Charlotte is a knight or Oliver is a knave.

Assume Charlotte is a knight. No contradiction is found in their claim that Charlotte is a knight if and only if Oliver is a knight.

Oliver cannot be a knight, because this would contradict the claim of their own that Lucas is not a knight.

Oliver cannot be a knave, because this would contradict the claim of Charlotte that Charlotte is a knight if and only if Oliver is a knight.

We have exhausted all possibilities for Oliver, so let us go back and reconsider Charlotte.

Assume Charlotte is a knave. No contradiction is found in their false claim that Charlotte is a knight if and only if Oliver is a knight.

Oliver cannot be a knave, because this would contradict the false claim of Charlotte that Charlotte is a knight if and only if Oliver is a knight.

We have exhausted all possibilities for Oliver and Charlotte, so let us go back and reconsider Ethan.

Ethan cannot be a knave, because this would contradict the false claim of Riley that Ethan is not a knight.

We have exhausted all possibilities for Ethan, Riley, and Sofia, so let us go back and reconsider Lucas.

Assume Lucas is a knave. No contradiction is found in their false claim that Sofia is a knave.

Assume Sofia is a knight. No contradiction is found in their claim that Riley is a knight.

Assume Riley is a knight. No contradiction is found in their claim that Ethan is not a knight.

Ethan cannot be a knight, because this would contradict the claim of Riley that Ethan is not a knight.

Assume Ethan is a knave. No contradiction is found in their false claim that Charlotte is a knight or Oliver is a knave.

Charlotte cannot be a knight, because this would contradict the false claim of Ethan that Charlotte is a knight or Oliver is a knave.

Assume Oliver is a knight. No contradiction is found in their claim that Lucas is not a knight.

Benjamin cannot be a knight, because this would contradict the claim of their own that Riley is a knave and Sofia is a knight.

Assume Benjamin is a knave. No contradiction is found in their false claim that Riley is a knave and Sofia is a knight.

(('lying', 2), ('<=>', ('telling-truth', 1), ('telling-truth', 4)), ('telling-truth', 6), ('and', ('lying', 6), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('or', ('telling-truth', 1), ('lying', 4)), ('not', ('telling-truth', 5)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Scarlett, Charlotte, Emily, Sophia, Noah, Harper, and Penelope. "If Penelope is a knight then Sophia is a knight," Scarlett declared. Charlotte told you that Noah is a knight and Harper is a knight. Emily was heard saying, "Scarlett is a knight and Noah is a knight". According to Sophia, "Sophia is a knight if and only if Harper is a knave". Noah stated, "Noah is a knight if and only if Scarlett is a knave". "If Noah is a knight then Penelope is a knave" - Harper. Penelope expressed that Sophia is a knave if and only if Harper is a knave. So who is a knight and who is a knave?

Scarlett Charlotte Emily Sophia Noah Harper Penelope

Scarlett is a knave, Charlotte is a knave, Emily is a knave, Sophia is a knave, Noah is a knight, Harper is a knave, and Penelope is a knight.

(1) Scarlett is a knave
(2) Charlotte is a knave
(3) Emily is a knave
(4) Sophia is a knave
(5) Noah is a knight
(6) Harper is a knave
(7) Penelope is a knight

Assume Scarlett is a knight. No contradiction is found in their claim that If Penelope is a knight then Sophia is a knight.

Assume Penelope is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Harper is a knave.

Assume Sophia is a knight. No contradiction is found in their claim that Sophia is a knight if and only if Harper is a knave.

Harper cannot be a knight, because this would contradict the claim of Sophia that Sophia is a knight if and only if Harper is a knave.

Harper cannot be a knave, because this would contradict the claim of Penelope that Sophia is a knave if and only if Harper is a knave.

We have exhausted all possibilities for Harper, so let us go back and reconsider Sophia.

Sophia cannot be a knave, because this would contradict the claim of Scarlett that If Penelope is a knight then Sophia is a knight.

We have exhausted all possibilities for Sophia, so let us go back and reconsider Penelope.

Assume Penelope is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Harper is a knave.

Harper cannot be a knave, because this would contradict the false claim of their own that If Noah is a knight then Penelope is a knave.

Assume Sophia is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Harper is a knave.

Harper cannot be a knight, because this would contradict the false claim of Sophia that Sophia is a knight if and only if Harper is a knave.

We have exhausted all possibilities for Harper, Sophia, and Penelope, so let us go back and reconsider Scarlett.

Assume Scarlett is a knave. No contradiction is found in their false claim that If Penelope is a knight then Sophia is a knight.

Sophia cannot be a knight, because this would contradict the false claim of Scarlett that If Penelope is a knight then Sophia is a knight.

Assume Harper is a knave. No contradiction is found in their false claim that If Noah is a knight then Penelope is a knave.

Assume Noah is a knight. No contradiction is found in their claim that Noah is a knight if and only if Scarlett is a knave.

Charlotte cannot be a knight, because this would contradict the claim of their own that Noah is a knight and Harper is a knight.

Assume Charlotte is a knave. No contradiction is found in their false claim that Noah is a knight and Harper is a knight.

Emily cannot be a knight, because this would contradict the claim of their own that Scarlett is a knight and Noah is a knight.

Assume Emily is a knave. No contradiction is found in their false claim that Scarlett is a knight and Noah is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Isabella, Liam, Owen, Grace, Ethan, Michael, and Sophia. Isabella told you that Michael is a knight and Michael is a knave. Liam noted, "Ethan is a knight or Michael is a knight". "If Grace is a knave then Ethan is a knight," Owen mentioned. According to Grace, "If Isabella is a knave then Ethan is a knave". "Liam is a knight" - Ethan. "Grace is a knave if and only if Isabella is a knight," Michael declared. "Ethan is a knave," Sophia claimed. So who is a knight and who is a knave?

Isabella Liam Owen Grace Ethan Michael Sophia

Isabella is a knave, Liam is a knight, Owen is a knight, Grace is a knave, Ethan is a knight, Michael is a knave, and Sophia is a knave.

(1) Isabella is a knave
(2) Liam is a knight
(3) Owen is a knight
(4) Grace is a knave
(5) Ethan is a knight
(6) Michael is a knave
(7) Sophia is a knave

Isabella cannot be a knight, because this would contradict the claim of their own that Michael is a knight and Michael is a knave.

Assume Isabella is a knave. No contradiction is found in their false claim that Michael is a knight and Michael is a knave.

Assume Michael is a knight. No contradiction is found in their claim that Grace is a knave if and only if Isabella is a knight.

Assume Grace is a knight. No contradiction is found in their claim that If Isabella is a knave then Ethan is a knave.

Ethan cannot be a knight, because this would contradict the claim of Grace that If Isabella is a knave then Ethan is a knave.

Assume Ethan is a knave. No contradiction is found in their false claim that Liam is a knight.

Liam cannot be a knight, because this would contradict the false claim of Ethan that Liam is a knight.

Liam cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight or Michael is a knight.

We have exhausted all possibilities for Liam and Ethan, so let us go back and reconsider Grace.

Grace cannot be a knave, because this would contradict the claim of Michael that Grace is a knave if and only if Isabella is a knight.

We have exhausted all possibilities for Grace, so let us go back and reconsider Michael.

Assume Michael is a knave. No contradiction is found in their false claim that Grace is a knave if and only if Isabella is a knight.

Grace cannot be a knight, because this would contradict the false claim of Michael that Grace is a knave if and only if Isabella is a knight.

Assume Grace is a knave. No contradiction is found in their false claim that If Isabella is a knave then Ethan is a knave.

Assume Ethan is a knight. No contradiction is found in their claim that Liam is a knight.

Assume Liam is a knight. No contradiction is found in their claim that Ethan is a knight or Michael is a knight.

Assume Owen is a knight. No contradiction is found in their claim that If Grace is a knave then Ethan is a knight.

Sophia cannot be a knight, because this would contradict the claim of their own that Ethan is a knave.

Assume Sophia is a knave. No contradiction is found in their false claim that Ethan is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Lucas, Ella, Noah, Penelope, Emily, Mia, and William. Lucas remarked, "William is a knave or Mia is a knight". Ella told you that Mia is a knight and William is a knave. Noah was heard saying, "Ella is a knight if and only if Penelope is a knave". Penelope said that If Emily is a knave then Mia is a knight. Emily remarked, "Noah is a knave and Penelope is a knight". "Ella is not a knave," Mia mentioned. William said, "Emily is not a knave." So who is a knight and who is a knave?

Lucas Ella Noah Penelope Emily Mia William

Lucas is a knight, Ella is a knave, Noah is a knave, Penelope is a knave, Emily is a knave, Mia is a knave, and William is a knave.

(1) Lucas is a knight
(2) Ella is a knave
(3) Noah is a knave
(4) Penelope is a knave
(5) Emily is a knave
(6) Mia is a knave
(7) William is a knave

Assume Lucas is a knight. No contradiction is found in their claim that William is a knave or Mia is a knight.

Assume William is a knight. No contradiction is found in their claim that Emily is not a knave.

Assume Emily is a knight. No contradiction is found in their claim that Noah is a knave and Penelope is a knight.

Noah cannot be a knight, because this would contradict the claim of Emily that Noah is a knave and Penelope is a knight.

Assume Noah is a knave. No contradiction is found in their false claim that Ella is a knight if and only if Penelope is a knave.

Ella cannot be a knight, because this would contradict the claim of their own that Mia is a knight and William is a knave.

Assume Ella is a knave. No contradiction is found in their false claim that Mia is a knight and William is a knave.

Mia cannot be a knight, because this would contradict the claim of their own that Ella is not a knave.

Mia cannot be a knave, because this would contradict the claim of Lucas that William is a knave or Mia is a knight.

We have exhausted all possibilities for Mia, Ella, and Noah, so let us go back and reconsider Emily.

Emily cannot be a knave, because this would contradict the claim of William that Emily is not a knave.

We have exhausted all possibilities for Emily, so let us go back and reconsider William.

Assume William is a knave. No contradiction is found in their false claim that Emily is not a knave.

Emily cannot be a knight, because this would contradict the false claim of William that Emily is not a knave.

Assume Emily is a knave. No contradiction is found in their false claim that Noah is a knave and Penelope is a knight.

Assume Noah is a knight. No contradiction is found in their claim that Ella is a knight if and only if Penelope is a knave.

Assume Ella is a knight. No contradiction is found in their claim that Mia is a knight and William is a knave.

Assume Mia is a knight. No contradiction is found in their claim that Ella is not a knave.

Penelope cannot be a knight, because this would contradict the claim of Noah that Ella is a knight if and only if Penelope is a knave.

Penelope cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Mia is a knight.

We have exhausted all possibilities for Penelope, so let us go back and reconsider Mia.

Mia cannot be a knave, because this would contradict the claim of Ella that Mia is a knight and William is a knave.

We have exhausted all possibilities for Mia, so let us go back and reconsider Ella.

Mia cannot be a knight, because this would contradict the false claim of Ella that Mia is a knight and William is a knave.

Assume Mia is a knave. No contradiction is found in their false claim that Ella is not a knave.

Penelope cannot be a knight, because this would contradict the claim of their own that If Emily is a knave then Mia is a knight.

Penelope cannot be a knave, because this would contradict the claim of Noah that Ella is a knight if and only if Penelope is a knave.

We have exhausted all possibilities for Penelope, Mia, and Ella, so let us go back and reconsider Noah.

Penelope cannot be a knight, because this would contradict the false claim of Emily that Noah is a knave and Penelope is a knight.

Penelope cannot be a knave, because this would contradict the false claim of Noah that Ella is a knight if and only if Penelope is a knave.

Penelope cannot be a knight, because this would contradict the false claim of Noah that Ella is a knight if and only if Penelope is a knave.

Assume Penelope is a knave. No contradiction is found in their false claim that If Emily is a knave then Mia is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Owen, Olivia, William, Emma, Samuel, Aiden, and James. "Samuel is a knave if and only if Owen is a knight," Owen mentioned. In Olivia's words: "James is a knave". William stated, "James is a knave if and only if Owen is a knave". Emma told you that William is a knave or Emma is a knight. Samuel said, "James is a knight and Emma is a knight." Aiden commented, "Emma is a knave". As James put it, "Owen is a knave or Samuel is a knave". So who is a knight and who is a knave?

Owen Olivia William Emma Samuel Aiden James

Owen is a knight, Olivia is a knave, William is a knight, Emma is a knave, Samuel is a knave, Aiden is a knight, and James is a knight.

(1) Owen is a knight
(2) Olivia is a knave
(3) William is a knight
(4) Emma is a knave
(5) Samuel is a knave
(6) Aiden is a knight
(7) James is a knight

Assume Owen is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Owen is a knight.

Samuel cannot be a knight, because this would contradict the claim of Owen that Samuel is a knave if and only if Owen is a knight.

Assume Samuel is a knave. No contradiction is found in their false claim that James is a knight and Emma is a knight.

Assume James is a knight. No contradiction is found in their claim that Owen is a knave or Samuel is a knave.

Emma cannot be a knight, because this would contradict the false claim of Samuel that James is a knight and Emma is a knight.

Assume Emma is a knave. No contradiction is found in their false claim that William is a knave or Emma is a knight.

Assume William is a knight. No contradiction is found in their claim that James is a knave if and only if Owen is a knave.

Olivia cannot be a knight, because this would contradict the claim of their own that James is a knave.

Assume Olivia is a knave. No contradiction is found in their false claim that James is a knave.

Assume Aiden is a knight. No contradiction is found in their claim that Emma is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Jackson, Michael, Emily, David, William, Sophia, and Harper. Jackson said that Michael is a knave and Michael is a knight. "William is a knight or Emily is a knight," Michael mentioned. Emily expressed that David is a knight and Harper is a knave. David asserted: "Jackson is a knave if and only if Emily is a knave". William was heard saying, "David is a knave if and only if Sophia is a knave". Sophia said that If Sophia is a knight then Michael is a knight. In a statement by Harper: "William is a knight". So who is a knight and who is a knave?

Jackson Michael Emily David William Sophia Harper

Jackson is a knave, Michael is a knight, Emily is a knave, David is a knight, William is a knight, Sophia is a knight, and Harper is a knight.

(1) Jackson is a knave
(2) Michael is a knight
(3) Emily is a knave
(4) David is a knight
(5) William is a knight
(6) Sophia is a knight
(7) Harper is a knight

Jackson cannot be a knight, because this would contradict the claim of their own that Michael is a knave and Michael is a knight.

Assume Jackson is a knave. No contradiction is found in their false claim that Michael is a knave and Michael is a knight.

Assume Michael is a knight. No contradiction is found in their claim that William is a knight or Emily is a knight.

Assume William is a knight. No contradiction is found in their claim that David is a knave if and only if Sophia is a knave.

Assume David is a knight. No contradiction is found in their claim that Jackson is a knave if and only if Emily is a knave.

Emily cannot be a knight, because this would contradict the claim of David that Jackson is a knave if and only if Emily is a knave.

Assume Emily is a knave. No contradiction is found in their false claim that David is a knight and Harper is a knave.

Assume Harper is a knight. No contradiction is found in their claim that William is a knight.

Assume Sophia is a knight. No contradiction is found in their claim that If Sophia is a knight then Michael is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Owen, Ava, Mason, Benjamin, Riley, Sofia, and Evelyn. "Mason is a knave," Owen mentioned. Ava told you that Mason is a knight if and only if Owen is a knave. According to Mason, "If Riley is a knave then Evelyn is a knight". "If Owen is a knight then Benjamin is a knight," Benjamin mentioned. Riley told you that Benjamin is a knight or Owen is a knave. Sofia stated, "Benjamin is a knave if and only if Ava is a knight". In a statement by Evelyn: "Owen is a knight". So who is a knight and who is a knave?

Owen Ava Mason Benjamin Riley Sofia Evelyn

Owen is a knave, Ava is a knight, Mason is a knight, Benjamin is a knight, Riley is a knight, Sofia is a knave, and Evelyn is a knave.

(1) Owen is a knave
(2) Ava is a knight
(3) Mason is a knight
(4) Benjamin is a knight
(5) Riley is a knight
(6) Sofia is a knave
(7) Evelyn is a knave

Assume Owen is a knight. No contradiction is found in their claim that Mason is a knave.

Mason cannot be a knight, because this would contradict the claim of Owen that Mason is a knave.

Assume Mason is a knave. No contradiction is found in their false claim that If Riley is a knave then Evelyn is a knight.

Riley cannot be a knight, because this would contradict the false claim of Mason that If Riley is a knave then Evelyn is a knight.

Assume Riley is a knave. No contradiction is found in their false claim that Benjamin is a knight or Owen is a knave.

Benjamin cannot be a knight, because this would contradict the false claim of Riley that Benjamin is a knight or Owen is a knave.

Assume Benjamin is a knave. No contradiction is found in their false claim that If Owen is a knight then Benjamin is a knight.

Evelyn cannot be a knight, because this would contradict the false claim of Mason that If Riley is a knave then Evelyn is a knight.

Evelyn cannot be a knave, because this would contradict the false claim of their own that Owen is a knight.

We have exhausted all possibilities for Evelyn, Benjamin, Riley, and Mason, so let us go back and reconsider Owen.

Assume Owen is a knave. No contradiction is found in their false claim that Mason is a knave.

Assume Mason is a knight. No contradiction is found in their claim that If Riley is a knave then Evelyn is a knight.

Assume Riley is a knight. No contradiction is found in their claim that Benjamin is a knight or Owen is a knave.

Assume Benjamin is a knight. No contradiction is found in their claim that If Owen is a knight then Benjamin is a knight.

Evelyn cannot be a knight, because this would contradict the claim of their own that Owen is a knight.

Assume Evelyn is a knave. No contradiction is found in their false claim that Owen is a knight.

Assume Ava is a knight. No contradiction is found in their claim that Mason is a knight if and only if Owen is a knave.

Sofia cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave if and only if Ava is a knight.

Assume Sofia is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Ava is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Charlotte, Aria, Lucas, Harper, Riley, Grace, and Ella. "Harper is a knight if and only if Grace is a knave," Charlotte mentioned. As Aria put it, "If Riley is a knight then Riley is a knave". Lucas said, "Riley is a knave or Charlotte is a knight." "Charlotte is a knave," Harper declared. Riley stated, "Charlotte is not a knave". As Grace put it, "Harper is a knight and Ella is a knight". In Ella's words: "Charlotte is a knight or Riley is a knave". So who is a knight and who is a knave?

Charlotte Aria Lucas Harper Riley Grace Ella

Charlotte is a knave, Aria is a knight, Lucas is a knight, Harper is a knight, Riley is a knave, Grace is a knight, and Ella is a knight.

(1) Charlotte is a knave
(2) Aria is a knight
(3) Lucas is a knight
(4) Harper is a knight
(5) Riley is a knave
(6) Grace is a knight
(7) Ella is a knight

Assume Charlotte is a knight. No contradiction is found in their claim that Harper is a knight if and only if Grace is a knave.

Harper cannot be a knight, because this would contradict the claim of their own that Charlotte is a knave.

Assume Harper is a knave. No contradiction is found in their false claim that Charlotte is a knave.

Grace cannot be a knight, because this would contradict the claim of their own that Harper is a knight and Ella is a knight.

Grace cannot be a knave, because this would contradict the claim of Charlotte that Harper is a knight if and only if Grace is a knave.

We have exhausted all possibilities for Grace and Harper, so let us go back and reconsider Charlotte.

Assume Charlotte is a knave. No contradiction is found in their false claim that Harper is a knight if and only if Grace is a knave.

Assume Harper is a knight. No contradiction is found in their claim that Charlotte is a knave.

Assume Grace is a knight. No contradiction is found in their claim that Harper is a knight and Ella is a knight.

Assume Ella is a knight. No contradiction is found in their claim that Charlotte is a knight or Riley is a knave.

Riley cannot be a knight, because this would contradict the claim of their own that Charlotte is not a knave.

Assume Riley is a knave. No contradiction is found in their false claim that Charlotte is not a knave.

Assume Aria is a knight. No contradiction is found in their claim that If Riley is a knight then Riley is a knave.

Assume Lucas is a knight. No contradiction is found in their claim that Riley is a knave or Charlotte is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Luke, Zoey, Matthew, Emma, Abigail, Sebastian, and Benjamin. In a statement by Luke: "Abigail is a knight". Zoey expressed that Benjamin is a knight or Emma is a knave. Matthew said, "Abigail is a knave and Benjamin is a knave." Emma commented, "Zoey is a knave or Luke is a knight". Abigail said that Benjamin is a knave if and only if Luke is a knight. Sebastian said that Zoey is a knave if and only if Abigail is a knave. Benjamin asserted: "Sebastian is a knight if and only if Benjamin is a knight". So who is a knight and who is a knave?

Luke Zoey Matthew Emma Abigail Sebastian Benjamin

Luke is a knave, Zoey is a knave, Matthew is a knight, Emma is a knight, Abigail is a knave, Sebastian is a knight, and Benjamin is a knave.

(1) Luke is a knave
(2) Zoey is a knave
(3) Matthew is a knight
(4) Emma is a knight
(5) Abigail is a knave
(6) Sebastian is a knight
(7) Benjamin is a knave

Assume Luke is a knight. No contradiction is found in their claim that Abigail is a knight.

Assume Abigail is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Luke is a knight.

Benjamin cannot be a knight, because this would contradict the claim of Abigail that Benjamin is a knave if and only if Luke is a knight.

Assume Benjamin is a knave. No contradiction is found in their false claim that Sebastian is a knight if and only if Benjamin is a knight.

Assume Sebastian is a knight. No contradiction is found in their claim that Zoey is a knave if and only if Abigail is a knave.

Assume Zoey is a knight. No contradiction is found in their claim that Benjamin is a knight or Emma is a knave.

Emma cannot be a knight, because this would contradict the claim of Zoey that Benjamin is a knight or Emma is a knave.

Emma cannot be a knave, because this would contradict the false claim of their own that Zoey is a knave or Luke is a knight.

We have exhausted all possibilities for Emma, so let us go back and reconsider Zoey.

Zoey cannot be a knave, because this would contradict the claim of Sebastian that Zoey is a knave if and only if Abigail is a knave.

We have exhausted all possibilities for Zoey, so let us go back and reconsider Sebastian.

Sebastian cannot be a knave, because this would contradict the false claim of Benjamin that Sebastian is a knight if and only if Benjamin is a knight.

We have exhausted all possibilities for Sebastian and Benjamin, so let us go back and reconsider Abigail.

Abigail cannot be a knave, because this would contradict the claim of Luke that Abigail is a knight.

We have exhausted all possibilities for Abigail, so let us go back and reconsider Luke.

Assume Luke is a knave. No contradiction is found in their false claim that Abigail is a knight.

Abigail cannot be a knight, because this would contradict the false claim of Luke that Abigail is a knight.

Assume Abigail is a knave. No contradiction is found in their false claim that Benjamin is a knave if and only if Luke is a knight.

Benjamin cannot be a knight, because this would contradict the false claim of Abigail that Benjamin is a knave if and only if Luke is a knight.

Zoey cannot be a knight, because this would contradict the claim of Sebastian that Zoey is a knave if and only if Abigail is a knave.

Assume Zoey is a knave. No contradiction is found in their false claim that Benjamin is a knight or Emma is a knave.

Assume Emma is a knight. No contradiction is found in their claim that Zoey is a knave or Luke is a knight.

Assume Matthew is a knight. No contradiction is found in their claim that Abigail is a knave and Benjamin is a knave.