A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Harper, Scarlett, Sebastian, William, and Aurora. Harper asserted: "Aurora is a knave or Scarlett is a knave". Scarlett noted, "Aurora is a knight if and only if Sebastian is a knave". "William is a knight and Harper is a knight," Sebastian claimed. "Harper is a knight," William mentioned. Aurora noted, "William is not a knave". So who is a knight and who is a knave?

Harper Scarlett Sebastian William Aurora

Harper is a knight, Scarlett is a knave, Sebastian is a knight, William is a knight, and Aurora is a knight.

(1) Harper is a knight
(2) Scarlett is a knave
(3) Sebastian is a knight
(4) William is a knight
(5) Aurora is a knight

Assume Harper is a knight. No contradiction is found in their claim that Aurora is a knave or Scarlett is a knave.

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

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

Scarlett cannot be a knight, because this would contradict the claim of Harper that Aurora is a knave or Scarlett is a knave.

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

Assume Sebastian is a knight. No contradiction is found in their claim that William is a knight and Harper 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 5 inhabitants: Abigail, Ava, Luke, Sofia, and Evelyn. Abigail said that If Abigail is a knight then Ava is a knave. "Sofia is a knave and Ava is a knight" - Ava. "Sofia is a knight or Ava is a knave," Luke mentioned. Sofia said, "If Abigail is a knight then Luke is a knight." Evelyn was heard saying, "Luke is a knave if and only if Ava is a knave". So who is a knight and who is a knave?

Abigail is a knight, Ava is a knave, Luke is a knight, Sofia is a knight, and Evelyn is a knave.

(1) Abigail is a knight
(2) Ava is a knave
(3) Luke is a knight
(4) Sofia is a knight
(5) Evelyn is a knave

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

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

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

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

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

Assume Luke is a knight. No contradiction is found in their claim that Sofia is a knight or Ava is a knave.

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

Assume Evelyn is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Ava 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 5 inhabitants: Daniel, Isabella, Sophia, Amelia, and Ava. Daniel said, "Amelia is a knight if and only if Sophia is a knave." As Isabella put it, "Sophia is a knave if and only if Ava is a knight". Sophia stated, "Isabella is not a knave". In Amelia's words: "Ava is a knave or Sophia is a knave". "Sophia is a knight," Ava claimed. So who is a knight and who is a knave?

Daniel is a knight, Isabella is a knave, Sophia is a knave, Amelia is a knight, and Ava is a knave.

(1) Daniel is a knight
(2) Isabella is a knave
(3) Sophia is a knave
(4) Amelia is a knight
(5) Ava is a knave

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

Assume Amelia is a knight. No contradiction is found in their claim that Ava is a knave or Sophia is a knave.

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

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

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

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

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

Assume Sophia is a knave. No contradiction is found in their false claim that Isabella is not a knave.

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

Assume Isabella is a knave. No contradiction is found in their false claim that Sophia 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 5 inhabitants: Amelia, Emily, Alexander, Jacob, and Sophia. Amelia stated, "Alexander is a knave". Emily stated, "Jacob is a knight or Alexander is a knight". "Jacob is a knight or Sophia is a knight," Alexander declared. Jacob said, "Emily is not a knave." Sophia was heard saying, "Jacob is a knave and Emily is a knave". So who is a knight and who is a knave?

Amelia is a knave, Emily is a knight, Alexander is a knight, Jacob is a knight, and Sophia is a knave.

(1) Amelia is a knave
(2) Emily is a knight
(3) Alexander is a knight
(4) Jacob is a knight
(5) Sophia is a knave

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

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

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

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

Assume Jacob 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 claim of their own that Jacob is a knight or Alexander is a knight.

Assume Emily is a knave. No contradiction is found in their false claim that Jacob is a knight or Alexander is a knight.

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

Sophia cannot be a knave, because this would contradict the false claim of their own that Jacob is a knave and Emily is a knave.

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

Assume Amelia is a knave. No contradiction is found in their false claim that Alexander is a knave.

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

Assume Jacob 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 Jacob is a knight or Alexander is a knight.

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

Assume Sophia is a knave. No contradiction is found in their false claim that Jacob is a knave and Emily 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 5 inhabitants: Emily, Jacob, Aiden, Liam, and Grace. Emily remarked, "Aiden is a knight or Jacob is a knight". Jacob was heard saying, "Jacob is a knight and Emily is a knight". In a statement by Aiden: "Liam is a knave and Jacob is a knight". "Aiden is a knight" - Liam. Grace expressed that Jacob is not a knave. So who is a knight and who is a knave?

Emily is a knave, Jacob is a knave, Aiden is a knave, Liam is a knave, and Grace is a knave.

(1) Emily is a knave
(2) Jacob is a knave
(3) Aiden is a knave
(4) Liam is a knave
(5) Grace is a knave

Assume Emily is a knight. No contradiction is found in their claim that Aiden is a knight or Jacob is a knight.

Assume Aiden is a knight. No contradiction is found in their claim that Liam is a knave and Jacob is a knight.

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

Liam 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 Liam, so let us go back and reconsider Aiden.

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

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

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

Jacob cannot be a knight, because this would contradict the false claim of Aiden that Liam is a knave and Jacob is a knight.

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

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

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

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

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

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

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

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

(('or', ('telling-truth', 2), ('telling-truth', 1)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('and', ('lying', 3), ('telling-truth', 1)), ('telling-truth', 2), ('not', ('lying', 1)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: David, Chloe, Aiden, Jack, and Elizabeth. As David put it, "If Jack is a knave then Elizabeth is a knave". "Elizabeth is a knave or David is a knave" - Chloe. Aiden said that Jack is a knave if and only if Jack is a knight. According to Jack, "David is a knave and David is a knight". According to Elizabeth, "If Chloe is a knight then Chloe is a knave". So who is a knight and who is a knave?

David is a knight, Chloe is a knight, Aiden is a knave, Jack is a knave, and Elizabeth is a knave.

(1) David is a knight
(2) Chloe is a knight
(3) Aiden is a knave
(4) Jack is a knave
(5) Elizabeth is a knave

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

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

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

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

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

Assume Chloe is a knight. No contradiction is found in their claim that Elizabeth is a knave or David is a knave.

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

Assume Aiden is a knave. No contradiction is found in their false claim that Jack is a knave if and only if Jack 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 5 inhabitants: James, Chloe, Jack, William, and Ava. As James put it, "If Ava is a knave then Chloe is a knave". In a statement by Chloe: "Ava is a knave or Jack is a knight". "Jack is a knight and Chloe is a knave," Jack mentioned. William commented, "James is a knave or Chloe is a knave". Ava told you that Jack is a knight and Jack is a knave. So who is a knight and who is a knave?

James is a knave, Chloe is a knight, Jack is a knave, William is a knight, and Ava is a knave.

(1) James is a knave
(2) Chloe is a knight
(3) Jack is a knave
(4) William is a knight
(5) Ava is a knave

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

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

Assume Ava is a knave. No contradiction is found in their false claim that Jack is a knight and Jack is a knave.

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

Chloe cannot be a knight, because this would contradict the claim of James that If Ava is a knave then Chloe is a knave.

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

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

Assume Jack is a knave. No contradiction is found in their false claim that Jack is a knight and Chloe is a knave.

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

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

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

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

Chloe cannot be a knave, because this would contradict the false claim of James that If Ava is a knave then Chloe is a knave.

Assume Chloe is a knight. No contradiction is found in their claim that Ava is a knave or Jack is a knight.

Assume William is a knight. No contradiction is found in their claim that James is a knave or Chloe 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 5 inhabitants: James, Lucas, Ava, Mason, and Emily. James asserted: "Emily is a knight and Emily is a knave". Lucas told you that Lucas is a knight if and only if Mason is a knave. Ava expressed that Emily is a knave if and only if Lucas is a knave. According to Mason, "If Lucas is a knight then James is a knight". "Mason is a knave if and only if Lucas is a knight," Emily mentioned. So who is a knight and who is a knave?

James is a knave, Lucas is a knight, Ava is a knight, Mason is a knave, and Emily is a knight.

(1) James is a knave
(2) Lucas is a knight
(3) Ava is a knight
(4) Mason is a knave
(5) Emily is a knight

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

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

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

Assume Mason is a knight. No contradiction is found in their claim that If Lucas is a knight then James is a knight.

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

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

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

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

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

Assume Ava is a knight. No contradiction is found in their claim that Emily is a knave if and only if Lucas 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 5 inhabitants: James, Harper, Ava, Mia, and Scarlett. "If Ava is a knight then Mia is a knight," James claimed. Harper told you that Scarlett is a knight or Ava is a knave. Ava said, "Mia is a knave and Harper is a knave." In a statement by Mia: "Ava is a knight or James is a knave". Scarlett told you that If Scarlett is a knight then Ava is a knave. So who is a knight and who is a knave?

James is a knight, Harper is a knight, Ava is a knave, Mia is a knave, and Scarlett is a knight.

(1) James is a knight
(2) Harper is a knight
(3) Ava is a knave
(4) Mia is a knave
(5) Scarlett is a knight

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

Assume Ava is a knight. No contradiction is found in their claim that Mia is a knave and Harper is a knave.

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

Mia cannot be a knave, because this would contradict the claim of James that If Ava is a knight then Mia is a knight.

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

Assume Ava is a knave. No contradiction is found in their false claim that Mia is a knave and Harper is a knave.

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

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

Assume Harper is a knight. No contradiction is found in their claim that Scarlett is a knight or Ava is a knave.

Assume Scarlett is a knight. No contradiction is found in their claim that If Scarlett is a knight then Ava 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 5 inhabitants: Michael, David, Alexander, Zoey, and Penelope. "Penelope is a knave and Alexander is a knave," Michael claimed. David remarked, "Michael is not a knave". Alexander told you that If Alexander is a knight then Michael is a knave. Zoey was heard saying, "If Alexander is a knave then Michael is a knight". In Penelope's words: "David is a knave if and only if Alexander is a knave". So who is a knight and who is a knave?

Michael is a knave, David is a knave, Alexander is a knight, Zoey is a knight, and Penelope is a knave.

(1) Michael is a knave
(2) David is a knave
(3) Alexander is a knight
(4) Zoey is a knight
(5) Penelope is a knave

Assume Michael is a knight. No contradiction is found in their claim that Penelope is a knave and Alexander is a knave.

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

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

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

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

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

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

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

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

Assume Michael is a knave. No contradiction is found in their false claim that Penelope is a knave and Alexander is a knave.

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

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

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

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

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

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

Assume Zoey is a knight. No contradiction is found in their claim that If Alexander is a knave 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 5 inhabitants: Sebastian, Evelyn, Isabella, Riley, and Liam. Sebastian remarked, "Liam is a knave or Riley is a knight". Evelyn commented, "Riley is a knave and Isabella is a knave". Isabella commented, "If Isabella is a knight then Liam is a knave". Riley asserted: "Isabella is a knight if and only if Evelyn is a knave". Liam noted, "Isabella is a knave and Evelyn is a knight". So who is a knight and who is a knave?

Sebastian is a knight, Evelyn is a knave, Isabella is a knight, Riley is a knight, and Liam is a knave.

(1) Sebastian is a knight
(2) Evelyn is a knave
(3) Isabella is a knight
(4) Riley is a knight
(5) Liam is a knave

Assume Sebastian is a knight. No contradiction is found in their claim that Liam is a knave or Riley is a knight.

Assume Liam is a knight. No contradiction is found in their claim that Isabella is a knave and Evelyn is a knight.

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

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

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

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

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

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

Assume Evelyn is a knave. No contradiction is found in their false claim that Riley is a knave and Isabella is a knave.

Assume Riley is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Evelyn 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 5 inhabitants: Amelia, Mason, Alexander, Emma, and Jackson. Amelia was heard saying, "Alexander is a knight if and only if Jackson is a knave". Mason asserted: "If Alexander is a knight then Emma is a knave". Alexander asserted: "Emma is a knight". As Emma put it, "Alexander is a knight or Jackson is a knight". In Jackson's words: "Amelia is a knight". So who is a knight and who is a knave?

Amelia is a knave, Mason is a knight, Alexander is a knave, Emma is a knave, and Jackson is a knave.

(1) Amelia is a knave
(2) Mason is a knight
(3) Alexander is a knave
(4) Emma is a knave
(5) Jackson is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Jackson cannot be a knight, because this would contradict the false claim of Amelia that Alexander 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 Amelia is a knight.

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

(('<=>', ('telling-truth', 2), ('lying', 4)), ('->', ('telling-truth', 2), ('lying', 3)), ('telling-truth', 3), ('or', ('telling-truth', 2), ('telling-truth', 4)), ('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 5 inhabitants: Sofia, James, Henry, Evelyn, and Jackson. In a statement by Sofia: "Jackson is a knave and James is a knave". In James's words: "Henry is a knight and Evelyn is a knight". "Jackson is not a knave," Henry declared. "Jackson is a knight or Sofia is a knight," Evelyn declared. Jackson commented, "James is a knight and Henry is a knave". So who is a knight and who is a knave?

Sofia is a knight, James is a knave, Henry is a knave, Evelyn is a knight, and Jackson is a knave.

(1) Sofia is a knight
(2) James is a knave
(3) Henry is a knave
(4) Evelyn is a knight
(5) Jackson is a knave

Assume Sofia is a knight. No contradiction is found in their claim that Jackson is a knave and James is a knave.

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

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

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

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

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

Assume Henry is a knave. No contradiction is found in their false claim that Jackson is not a knave.

Assume Evelyn is a knight. No contradiction is found in their claim that Jackson is a knight or Sofia is a knight.

(('and', ('lying', 4), ('lying', 1)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('not', ('lying', 4)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('telling-truth', 1), ('lying', 2)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Victoria, Liam, Penelope, Benjamin, and Zoey. Victoria expressed that Benjamin is a knave and Zoey is a knave. Liam expressed that Zoey is a knight and Benjamin is a knave. In Penelope's words: "Zoey is not a knight". "Penelope is a knight" - Benjamin. "Victoria is a knave or Zoey is a knight," Zoey declared. So who is a knight and who is a knave?

Victoria is a knave, Liam is a knight, Penelope is a knave, Benjamin is a knave, and Zoey is a knight.

(1) Victoria is a knave
(2) Liam is a knight
(3) Penelope is a knave
(4) Benjamin is a knave
(5) Zoey is a knight

Assume Victoria is a knight. No contradiction is found in their claim that Benjamin is a knave and Zoey is a knave.

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

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

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

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

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

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

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

Assume Victoria is a knave. No contradiction is found in their false claim that Benjamin is a knave and Zoey is a knave.

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

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

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

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

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

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

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

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

Assume Liam is a knight. No contradiction is found in their claim that Zoey is a knight and Benjamin 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 5 inhabitants: Riley, Olivia, Alexander, Zoey, and Liam. Riley said, "Alexander is a knave." "Liam is a knight or Zoey is a knight," Olivia mentioned. "Olivia is a knave and Liam is a knight," Alexander declared. Zoey stated, "Liam is a knave if and only if Liam is a knight". According to Liam, "Zoey is a knight or Alexander is a knave". So who is a knight and who is a knave?

Riley is a knight, Olivia is a knight, Alexander is a knave, Zoey is a knave, and Liam is a knight.

(1) Riley is a knight
(2) Olivia is a knight
(3) Alexander is a knave
(4) Zoey is a knave
(5) Liam is a knight

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

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

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

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

Assume Liam is a knight. No contradiction is found in their claim that Zoey is a knight or Alexander is a knave.

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

Assume Zoey is a knave. No contradiction is found in their false claim that Liam is a knave if and only if Liam 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 5 inhabitants: Sofia, Lucas, Evelyn, Avery, and Victoria. Sofia expressed that Avery is not a knave. As Lucas put it, "Sofia is a knight or Evelyn is a knight". "Lucas is a knight if and only if Avery is a knight," Evelyn mentioned. In a statement by Avery: "Victoria is a knave if and only if Evelyn is a knight". In a statement by Victoria: "Victoria is a knight and Evelyn is a knave". So who is a knight and who is a knave?

Sofia is a knight, Lucas is a knight, Evelyn is a knight, Avery is a knight, and Victoria is a knave.

(1) Sofia is a knight
(2) Lucas is a knight
(3) Evelyn is a knight
(4) Avery is a knight
(5) Victoria is a knave

Assume Sofia 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 Victoria is a knave if and only if Evelyn is a knight.

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

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

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

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

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

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

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

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

Assume Lucas is a knight. No contradiction is found in their claim that Sofia is a knight or Evelyn 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 5 inhabitants: Elizabeth, Henry, Ella, Lucas, and David. Elizabeth said, "Henry is a knight." Henry expressed that Elizabeth is a knight if and only if Henry is a knight. According to Ella, "Elizabeth is a knight or Elizabeth is a knave". Lucas asserted: "Elizabeth is a knight or Henry is a knight". David said, "Lucas is a knave." So who is a knight and who is a knave?

Elizabeth is a knight, Henry is a knight, Ella is a knight, Lucas is a knight, and David is a knave.

(1) Elizabeth is a knight
(2) Henry is a knight
(3) Ella is a knight
(4) Lucas is a knight
(5) David is a knave

Assume Elizabeth is a knight. No contradiction is found in their claim that Henry is a knight.

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

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

Assume Lucas is a knight. No contradiction is found in their claim that Elizabeth is a knight or Henry is a knight.

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

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

(('telling-truth', 1), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 0), ('lying', 0)), ('or', ('telling-truth', 0), ('telling-truth', 1)), ('lying', 3))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Penelope, Aria, Ava, Sophia, and Jack. Penelope noted, "If Sophia is a knight then Ava is a knave". In Aria's words: "Sophia is a knight". Ava told you that Penelope is a knight. "Penelope is a knave," Sophia declared. "Aria is a knave and Penelope is a knight," Jack claimed. So who is a knight and who is a knave?

Penelope is a knight, Aria is a knave, Ava is a knight, Sophia is a knave, and Jack is a knight.

(1) Penelope is a knight
(2) Aria is a knave
(3) Ava is a knight
(4) Sophia is a knave
(5) Jack is a knight

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

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

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

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

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

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

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

(('->', ('telling-truth', 3), ('lying', 2)), ('telling-truth', 3), ('telling-truth', 0), ('lying', 0), ('and', ('lying', 1), ('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 5 inhabitants: Owen, Lucas, Michael, Olivia, and Samuel. Owen told you that Michael is a knave. "Samuel is not a knave," Lucas claimed. "Samuel is a knave or Owen is a knight," Michael mentioned. Olivia expressed that Samuel is a knave and Lucas is a knight. "Lucas is a knave and Lucas is a knight," Samuel claimed. So who is a knight and who is a knave?

Owen is a knave, Lucas is a knave, Michael is a knight, Olivia is a knave, and Samuel is a knave.

(1) Owen is a knave
(2) Lucas is a knave
(3) Michael is a knight
(4) Olivia is a knave
(5) Samuel is a knave

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

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

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

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

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

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

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

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

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

Assume Lucas is a knave. No contradiction is found in their false claim that Samuel is not a knave.

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

Assume Olivia is a knave. No contradiction is found in their false claim that Samuel is a knave and Lucas 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 5 inhabitants: Lucas, Penelope, Amelia, Isabella, and Riley. Lucas asserted: "Isabella is a knight if and only if Penelope is a knight". Penelope asserted: "Lucas is a knave or Riley is a knave". Amelia was heard saying, "Riley is a knave if and only if Amelia is a knight". Isabella said that Isabella is a knight. Riley expressed that If Amelia is a knight then Isabella is a knave. So who is a knight and who is a knave?

Lucas is a knight, Penelope is a knight, Amelia is a knight, Isabella is a knight, and Riley is a knave.

(1) Lucas is a knight
(2) Penelope is a knight
(3) Amelia is a knight
(4) Isabella is a knight
(5) Riley is a knave

Assume Lucas is a knight. No contradiction is found in their claim that Isabella is a knight if and only if Penelope is a knight.

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

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

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

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

Assume Amelia is a knight. No contradiction is found in their claim that Riley is a knave if and only if Amelia 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 5 inhabitants: Aurora, Abigail, Isabella, Henry, and Michael. Aurora was heard saying, "Henry is a knave and Abigail is a knight". Abigail was heard saying, "Isabella is a knight". In a statement by Isabella: "Michael is a knave and Michael is a knight". "Aurora is a knight," Henry mentioned. Michael said, "Henry is a knave and Abigail is a knight." So who is a knight and who is a knave?

Aurora is a knave, Abigail is a knave, Isabella is a knave, Henry is a knave, and Michael is a knave.

(1) Aurora is a knave
(2) Abigail is a knave
(3) Isabella is a knave
(4) Henry is a knave
(5) Michael is a knave

Assume Aurora is a knight. No contradiction is found in their claim that Henry is a knave and Abigail is a knight.

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

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

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

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

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

Assume Henry is a knave. No contradiction is found in their false claim that Aurora is a knight.

Abigail cannot be a knight, because this would contradict the false claim of Aurora that Henry is a knave and Abigail is a knight.

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

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

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

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

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

(('and', ('lying', 3), ('telling-truth', 1)), ('telling-truth', 2), ('and', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 0), ('and', ('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 5 inhabitants: Chloe, Joseph, Lucas, Samuel, and Mason. Chloe asserted: "Joseph is a knight and Lucas is a knight". As Joseph put it, "Samuel is not a knight". Lucas said that If Lucas is a knight then Samuel is a knight. "Chloe is a knave," Samuel declared. "Samuel is a knave or Joseph is a knave" - Mason. So who is a knight and who is a knave?

Chloe is a knave, Joseph is a knave, Lucas is a knight, Samuel is a knight, and Mason is a knight.

(1) Chloe is a knave
(2) Joseph is a knave
(3) Lucas is a knight
(4) Samuel is a knight
(5) Mason is a knight

Assume Chloe is a knight. No contradiction is found in their claim that Joseph is a knight and Lucas is a knight.

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

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

Assume Samuel is a knave. No contradiction is found in their false claim that Chloe is a knave.

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

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

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

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

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

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

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

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

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

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

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

Assume Mason is a knight. No contradiction is found in their claim that Samuel is a knave or Joseph 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 5 inhabitants: Lucas, Owen, Oliver, Lily, and Sebastian. In a statement by Lucas: "Oliver is a knight and Sebastian is a knave". Owen stated, "Lily is a knave". Oliver expressed that Lily is a knight. Lily told you that Sebastian is a knight or Lily is a knight. Sebastian was heard saying, "Oliver is a knave". So who is a knight and who is a knave?

Lucas is a knight, Owen is a knave, Oliver is a knight, Lily is a knight, and Sebastian is a knave.

(1) Lucas is a knight
(2) Owen is a knave
(3) Oliver is a knight
(4) Lily is a knight
(5) Sebastian is a knave

Assume Lucas is a knight. No contradiction is found in their claim that Oliver is a knight and Sebastian is a knave.

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

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

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

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

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

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

(('and', ('telling-truth', 2), ('lying', 4)), ('lying', 3), ('telling-truth', 3), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('lying', 2))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Matthew, Luke, William, Jackson, and Daniel. In Matthew's words: "Luke is a knave if and only if Daniel is a knave". Luke told you that Jackson is not a knight. William commented, "Luke is not a knight". In Jackson's words: "Luke is a knave and Luke is a knight". Daniel said that Luke is a knave and Luke is a knight. So who is a knight and who is a knave?

Matthew is a knave, Luke is a knight, William is a knave, Jackson is a knave, and Daniel is a knave.

(1) Matthew is a knave
(2) Luke is a knight
(3) William is a knave
(4) Jackson is a knave
(5) Daniel is a knave

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

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

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

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

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

Daniel cannot be a knave, because this would contradict the claim of Matthew that Luke is a knave if and only if Daniel is a knave.

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

Assume Luke is a knave. No contradiction is found in their false claim that Jackson is not a knight.

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

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

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

Assume Matthew is a knave. No contradiction is found in their false claim that Luke is a knave if and only if Daniel is a knave.

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

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

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

Assume William is a knave. No contradiction is found in their false claim that Luke 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 5 inhabitants: Jack, Luke, Oliver, Penelope, and Jackson. "Jack is a knight if and only if Oliver is a knight," Jack claimed. "Oliver is a knave or Penelope is a knight," Luke mentioned. "Jackson is a knave" - Oliver. Penelope said, "If Jackson is a knave then Oliver is a knight." As Jackson put it, "Penelope is a knight and Jack is a knight". So who is a knight and who is a knave?

Jack is a knave, Luke is a knight, Oliver is a knight, Penelope is a knight, and Jackson is a knave.

(1) Jack is a knave
(2) Luke is a knight
(3) Oliver is a knight
(4) Penelope is a knight
(5) Jackson is a knave

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

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

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

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

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

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

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

Oliver cannot be a knave, because this would contradict the claim of Jack that Jack 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 Jack.

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

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

Assume Luke is a knight. No contradiction is found in their claim that Oliver is a knave or Penelope 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 5 inhabitants: Sophia, Aria, Logan, Victoria, and Elizabeth. As Sophia put it, "Elizabeth is a knight if and only if Victoria is a knight". Aria noted, "Elizabeth is a knave or Aria is a knight". Logan commented, "Sophia is a knight if and only if Sophia is a knave". "Elizabeth is a knave or Aria is a knight," Victoria declared. Elizabeth remarked, "Aria is a knight". So who is a knight and who is a knave?

Sophia is a knight, Aria is a knight, Logan is a knave, Victoria is a knight, and Elizabeth is a knight.

(1) Sophia is a knight
(2) Aria is a knight
(3) Logan is a knave
(4) Victoria is a knight
(5) Elizabeth is a knight

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

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

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

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

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

Assume Logan is a knave. No contradiction is found in their false claim that Sophia is a knight if and only if Sophia 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 5 inhabitants: Sofia, Grace, Jack, Jacob, and Amelia. According to Sofia, "Grace is a knight". "If Grace is a knight then Jacob is a knight," Grace declared. Jack noted, "Sofia is a knave". "Grace is a knight," Jacob declared. "Jacob is a knave if and only if Sofia is a knight," Amelia declared. So who is a knight and who is a knave?

Sofia is a knight, Grace is a knight, Jack is a knave, Jacob is a knight, and Amelia is a knave.

(1) Sofia is a knight
(2) Grace is a knight
(3) Jack is a knave
(4) Jacob is a knight
(5) Amelia is a knave

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

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

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

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

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

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

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

(('telling-truth', 1), ('->', ('telling-truth', 1), ('telling-truth', 3)), ('lying', 0), ('telling-truth', 1), ('<=>', ('lying', 3), ('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 5 inhabitants: Alexander, David, Oliver, Sofia, and Riley. Alexander remarked, "Riley is not a knave". "Riley is a knight and Oliver is a knave," David mentioned. "Riley is a knight" - Oliver. As Sofia put it, "Riley is a knave and Oliver is a knave". "Sofia is a knave if and only if Oliver is a knight," Riley claimed. So who is a knight and who is a knave?

Alexander is a knight, David is a knave, Oliver is a knight, Sofia is a knave, and Riley is a knight.

(1) Alexander is a knight
(2) David is a knave
(3) Oliver is a knight
(4) Sofia is a knave
(5) Riley is a knight

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

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

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

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

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

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

Assume David is a knave. No contradiction is found in their false claim that Riley is a knight and Oliver 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 5 inhabitants: Aurora, Joseph, David, Alexander, and Michael. Aurora noted, "Joseph is a knave and Joseph is a knight". Joseph was heard saying, "Alexander is a knight and Michael is a knave". As David put it, "David is a knight or Alexander is a knave". In a statement by Alexander: "David is not a knave". As Michael put it, "David is a knight or Joseph is a knight". So who is a knight and who is a knave?

Aurora is a knave, Joseph is a knave, David is a knight, Alexander is a knight, and Michael is a knight.

(1) Aurora is a knave
(2) Joseph is a knave
(3) David is a knight
(4) Alexander is a knight
(5) Michael is a knight

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

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

Assume Joseph is a knight. No contradiction is found in their claim that Alexander is a knight and Michael is a knave.

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

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

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

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

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

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

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

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

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

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

Assume Michael is a knight. No contradiction is found in their claim that David is a knight or Joseph 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 5 inhabitants: Liam, Elizabeth, Joseph, Jack, and Jackson. Liam noted, "If Jackson is a knight then Liam is a knight". Elizabeth said that Liam is a knight or Liam is a knave. Joseph told you that Elizabeth is a knight and Jackson is a knave. "Liam is a knight or Elizabeth is a knave," Jack mentioned. In Jackson's words: "Liam is a knight and Elizabeth is a knight". So who is a knight and who is a knave?

Liam is a knight, Elizabeth is a knight, Joseph is a knave, Jack is a knight, and Jackson is a knight.

(1) Liam is a knight
(2) Elizabeth is a knight
(3) Joseph is a knave
(4) Jack is a knight
(5) Jackson is a knight

Assume Liam is a knight. No contradiction is found in their claim that If Jackson is a knight then Liam is a knight.

Assume Jackson is a knight. No contradiction is found in their claim that Liam is a knight and Elizabeth is a knight.

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

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

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

Assume Jack is a knight. No contradiction is found in their claim that Liam is a knight or Elizabeth is a knave.

(('->', ('telling-truth', 4), ('telling-truth', 0)), ('or', ('telling-truth', 0), ('lying', 0)), ('and', ('telling-truth', 1), ('lying', 4)), ('or', ('telling-truth', 0), ('lying', 1)), ('and', ('telling-truth', 0), ('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 5 inhabitants: Liam, James, Benjamin, Abigail, and Harper. "If James is a knight then Harper is a knight," Liam claimed. James expressed that If Benjamin is a knave then Harper is a knave. Benjamin said that Harper is a knight if and only if James is a knight. "Liam is not a knave," Abigail declared. Harper stated, "If Harper is a knight then James is a knave". So who is a knight and who is a knave?

Liam is a knight, James is a knave, Benjamin is a knave, Abigail is a knight, and Harper is a knight.

(1) Liam is a knight
(2) James is a knave
(3) Benjamin is a knave
(4) Abigail is a knight
(5) Harper is a knight

Assume Liam is a knight. No contradiction is found in their claim that If James is a knight then Harper is a knight.

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

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

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

Harper cannot be a knave, because this would contradict the claim of Liam that If James is a knight then Harper is a knight.

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

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

Harper cannot be a knight, because this would contradict the claim of James that If Benjamin is a knave then Harper is a knave.

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

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

Benjamin cannot be a knight, because this would contradict the false claim of James that If Benjamin is a knave then Harper is a knave.

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

Assume Abigail is a knight. No contradiction is found in their claim that Liam 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 5 inhabitants: Daniel, Sofia, Lucas, James, and Victoria. Daniel was heard saying, "Victoria is a knave". In a statement by Sofia: "James is a knight if and only if Daniel is a knight". As Lucas put it, "Victoria is a knave or Victoria is a knight". James said that Victoria is not a knight. Victoria noted, "Victoria is a knight and James is a knight". So who is a knight and who is a knave?

Daniel is a knight, Sofia is a knight, Lucas is a knight, James is a knight, and Victoria is a knave.

(1) Daniel is a knight
(2) Sofia is a knight
(3) Lucas is a knight
(4) James is a knight
(5) Victoria is a knave

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

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

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

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

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

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

(('lying', 4), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('lying', 4), ('telling-truth', 4)), ('not', ('telling-truth', 4)), ('and', ('telling-truth', 4), ('telling-truth', 3)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Aria, Owen, James, Amelia, and Lily. "Amelia is a knight," Aria claimed. In Owen's words: "Owen is a knight and James is a knave". James told you that Lily is not a knave. Amelia told you that James is not a knight. Lily said, "If Owen is a knight then James is a knave." So who is a knight and who is a knave?

Aria is a knave, Owen is a knave, James is a knight, Amelia is a knave, and Lily is a knight.

(1) Aria is a knave
(2) Owen is a knave
(3) James is a knight
(4) Amelia is a knave
(5) Lily is a knight

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

Assume Amelia is a knight. No contradiction is found in their claim that James is not a knight.

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

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

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

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

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

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

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

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

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

Assume Amelia is a knave. No contradiction is found in their false claim that James is not a knight.

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

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

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

Assume Owen is a knave. No contradiction is found in their false claim that Owen is a knight and James 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 5 inhabitants: Ethan, Michael, Ava, Penelope, and Harper. "If Penelope is a knave then Ethan is a knight," Ethan mentioned. Michael expressed that Penelope is a knight if and only if Harper is a knave. "If Ethan is a knight then Michael is a knave," Ava claimed. Penelope was heard saying, "If Penelope is a knight then Ava is a knight". "Penelope is a knight," Harper declared. So who is a knight and who is a knave?

Ethan is a knight, Michael is a knave, Ava is a knight, Penelope is a knight, and Harper is a knight.

(1) Ethan is a knight
(2) Michael is a knave
(3) Ava is a knight
(4) Penelope is a knight
(5) Harper is a knight

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

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

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

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

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

Assume Harper is a knight. No contradiction is found in their claim that Penelope 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 5 inhabitants: Riley, Aurora, James, Grace, and Harper. Riley remarked, "Harper is a knight if and only if Harper is a knave". Aurora told you that Riley is a knave if and only if James is a knight. James commented, "If Riley is a knight then Grace is a knave". Grace said, "Aurora is a knight." Harper stated, "Grace is not a knave". So who is a knight and who is a knave?

Riley is a knave, Aurora is a knight, James is a knight, Grace is a knight, and Harper is a knight.

(1) Riley is a knave
(2) Aurora is a knight
(3) James is a knight
(4) Grace is a knight
(5) Harper is a knight

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

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

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

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

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

Assume James is a knight. No contradiction is found in their claim that If Riley is a knight 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 5 inhabitants: Amelia, Chloe, Elizabeth, Lucas, and Logan. "Chloe is a knave or Elizabeth is a knave," Amelia claimed. Chloe said that Amelia is a knave or Logan is a knight. Elizabeth was heard saying, "Chloe is not a knight". According to Lucas, "Amelia is a knight". Logan commented, "Lucas is a knight". So who is a knight and who is a knave?

Amelia is a knight, Chloe is a knight, Elizabeth is a knave, Lucas is a knight, and Logan is a knight.

(1) Amelia is a knight
(2) Chloe is a knight
(3) Elizabeth is a knave
(4) Lucas is a knight
(5) Logan is a knight

Assume Amelia is a knight. No contradiction is found in their claim that Chloe is a knave or Elizabeth is a knave.

Assume Chloe is a knight. No contradiction is found in their claim that Amelia is a knave or Logan is a knight.

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

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

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

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

(('or', ('lying', 1), ('lying', 2)), ('or', ('lying', 0), ('telling-truth', 4)), ('not', ('telling-truth', 1)), ('telling-truth', 0), ('telling-truth', 3))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Grace, Aria, Evelyn, Mia, and Isabella. Grace noted, "Mia is not a knight". Aria commented, "If Grace is a knight then Isabella is a knight". Evelyn said that Grace is a knave and Isabella is a knave. Mia commented, "Grace is a knight and Aria is a knave". According to Isabella, "Isabella is a knight or Grace is a knight". So who is a knight and who is a knave?

Grace is a knight, Aria is a knight, Evelyn is a knave, Mia is a knave, and Isabella is a knight.

(1) Grace is a knight
(2) Aria is a knight
(3) Evelyn is a knave
(4) Mia is a knave
(5) Isabella is a knight

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

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

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

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

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

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

Assume Evelyn is a knave. No contradiction is found in their false claim that Grace is a knave and Isabella is a knave.

(('not', ('telling-truth', 3)), ('->', ('telling-truth', 0), ('telling-truth', 4)), ('and', ('lying', 0), ('lying', 4)), ('and', ('telling-truth', 0), ('lying', 1)), ('or', ('telling-truth', 4), ('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 5 inhabitants: Chloe, Liam, Zoey, Evelyn, and Grace. According to Chloe, "Evelyn is not a knight". In Liam's words: "Chloe is a knave if and only if Evelyn is a knave". "Liam is a knight," Zoey mentioned. According to Evelyn, "Zoey is a knave or Grace is a knave". "Liam is not a knight," Grace claimed. So who is a knight and who is a knave?

Chloe is a knave, Liam is a knave, Zoey is a knave, Evelyn is a knight, and Grace is a knight.

(1) Chloe is a knave
(2) Liam is a knave
(3) Zoey is a knave
(4) Evelyn is a knight
(5) Grace is a knight

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

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

Assume Evelyn is a knave. No contradiction is found in their false claim that Zoey is a knave or Grace is a knave.

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

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

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

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

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

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

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

Assume Evelyn is a knight. No contradiction is found in their claim that Zoey is a knave or Grace is a knave.

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

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

Assume Grace is a knight. No contradiction is found in their claim that Liam 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 5 inhabitants: Victoria, Scarlett, Oliver, Alexander, and Elizabeth. Victoria was heard saying, "Oliver is not a knight". Scarlett noted, "Elizabeth is a knight and Scarlett is a knight". "Alexander is a knave or Oliver is a knight," Oliver claimed. Alexander remarked, "Scarlett is a knight and Victoria is a knight". Elizabeth remarked, "Scarlett is not a knight". So who is a knight and who is a knave?

Victoria Scarlett Oliver Alexander Elizabeth

Victoria is a knave, Scarlett is a knave, Oliver is a knight, Alexander is a knave, and Elizabeth is a knight.

(1) Victoria is a knave
(2) Scarlett is a knave
(3) Oliver is a knight
(4) Alexander is a knave
(5) Elizabeth is a knight

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Elizabeth is a knight. No contradiction is found in their claim that Scarlett is not a knight.

(('not', ('telling-truth', 2)), ('and', ('telling-truth', 4), ('telling-truth', 1)), ('or', ('lying', 3), ('telling-truth', 2)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('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 5 inhabitants: Oliver, Aiden, Daniel, Matthew, and Ethan. "Ethan is a knave if and only if Ethan is a knight," Oliver mentioned. Aiden said, "Ethan is a knave." Daniel remarked, "Aiden is a knave". According to Matthew, "If Aiden is a knight then Oliver is a knight". Ethan expressed that Aiden is a knave if and only if Matthew is a knave. So who is a knight and who is a knave?

Oliver is a knave, Aiden is a knight, Daniel is a knave, Matthew is a knave, and Ethan is a knave.

(1) Oliver is a knave
(2) Aiden is a knight
(3) Daniel is a knave
(4) Matthew is a knave
(5) Ethan is a knave

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

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

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

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

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

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

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

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

Assume Ethan is a knave. No contradiction is found in their false claim that Aiden is a knave if and only if Matthew is a knave.

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

Matthew cannot be a knight, because this would contradict the claim of their own that If Aiden is a knight then Oliver is a knight.

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

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

Assume Daniel is a knave. No contradiction is found in their false claim that Aiden 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 5 inhabitants: David, Oliver, Amelia, Riley, and Elizabeth. David was heard saying, "Riley is a knave if and only if Riley is a knight". As Oliver put it, "Oliver is a knight and Elizabeth is a knight". Amelia said, "David is a knight." Riley remarked, "Elizabeth is a knight if and only if Oliver is a knave". "David is not a knave" - Elizabeth. So who is a knight and who is a knave?

David is a knave, Oliver is a knave, Amelia is a knave, Riley is a knave, and Elizabeth is a knave.

(1) David is a knave
(2) Oliver is a knave
(3) Amelia is a knave
(4) Riley is a knave
(5) Elizabeth is a knave

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

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

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

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

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

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

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

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

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

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

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

Assume Amelia is a knave. No contradiction is found in their false claim that David 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 5 inhabitants: Ella, Harper, Henry, Jack, and Luke. "If Ella is a knight then Harper is a knight," Ella mentioned. Harper noted, "Jack is a knave or Ella is a knave". Henry commented, "Harper is not a knight". Jack said that Jack is a knight if and only if Ella is a knight. Luke stated, "Henry is a knight or Jack is a knave". So who is a knight and who is a knave?

Ella is a knight, Harper is a knight, Henry is a knave, Jack is a knave, and Luke is a knight.

(1) Ella is a knight
(2) Harper is a knight
(3) Henry is a knave
(4) Jack is a knave
(5) Luke is a knight

Assume Ella is a knight. No contradiction is found in their claim that If Ella is a knight then Harper is a knight.

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

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

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

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

Assume Henry is a knave. No contradiction is found in their false claim that Harper is not a knight.

Assume Luke is a knight. No contradiction is found in their claim that Henry is a knight or Jack 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 5 inhabitants: Mason, Avery, Sofia, Benjamin, and Michael. Mason told you that If Benjamin is a knight then Sofia is a knight. In a statement by Avery: "Michael is a knight and Mason is a knight". Sofia remarked, "Benjamin is a knight if and only if Mason is a knight". In Benjamin's words: "Michael is a knave". Michael was heard saying, "Mason is not a knight". So who is a knight and who is a knave?

Mason is a knight, Avery is a knave, Sofia is a knight, Benjamin is a knight, and Michael is a knave.

(1) Mason is a knight
(2) Avery is a knave
(3) Sofia is a knight
(4) Benjamin is a knight
(5) Michael is a knave

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

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

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

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

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

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

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

(('->', ('telling-truth', 3), ('telling-truth', 2)), ('and', ('telling-truth', 4), ('telling-truth', 0)), ('<=>', ('telling-truth', 3), ('telling-truth', 0)), ('lying', 4), ('not', ('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 5 inhabitants: Mia, Benjamin, Ava, Lily, and Alexander. Mia commented, "Alexander is a knave and Lily is a knave". Benjamin noted, "Lily is a knave and Mia is a knave". Ava commented, "Lily is not a knight". Lily commented, "Benjamin is a knight". Alexander stated, "Ava is a knave". So who is a knight and who is a knave?

Mia is a knight, Benjamin is a knave, Ava is a knight, Lily is a knave, and Alexander is a knave.

(1) Mia is a knight
(2) Benjamin is a knave
(3) Ava is a knight
(4) Lily is a knave
(5) Alexander is a knave

Assume Mia is a knight. No contradiction is found in their claim that Alexander is a knave and Lily is a knave.

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

Assume Alexander is a knave. No contradiction is found in their false claim that Ava is a knave.

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

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

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

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

Assume Benjamin is a knave. No contradiction is found in their false claim that Lily is a knave and Mia 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 5 inhabitants: Isabella, David, Mason, Samuel, and Aiden. Isabella told you that Mason is a knight. David told you that If Aiden is a knight then Mason is a knave. Mason was heard saying, "Isabella is a knave if and only if Aiden is a knight". As Samuel put it, "Mason is a knave". "Samuel is a knave or Aiden is a knight," Aiden claimed. So who is a knight and who is a knave?

Isabella is a knave, David is a knight, Mason is a knave, Samuel is a knight, and Aiden is a knave.

(1) Isabella is a knave
(2) David is a knight
(3) Mason is a knave
(4) Samuel is a knight
(5) Aiden is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume David is a knight. No contradiction is found in their claim that If Aiden is a knight then Mason 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 5 inhabitants: Mia, Ella, Aiden, Mason, and Daniel. Mia expressed that Ella is a knight and Mason is a knave. In a statement by Ella: "Mia is not a knight". Aiden commented, "Mason is a knave or Ella is a knight". In a statement by Mason: "Ella is a knight and Mia is a knave". Daniel said that Ella is not a knight. So who is a knight and who is a knave?

Mia is a knave, Ella is a knight, Aiden is a knight, Mason is a knight, and Daniel is a knave.

(1) Mia is a knave
(2) Ella is a knight
(3) Aiden is a knight
(4) Mason is a knight
(5) Daniel is a knave

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

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

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

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

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

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

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

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

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

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

(('and', ('telling-truth', 1), ('lying', 3)), ('not', ('telling-truth', 0)), ('or', ('lying', 3), ('telling-truth', 1)), ('and', ('telling-truth', 1), ('lying', 0)), ('not', ('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 5 inhabitants: Aria, Sebastian, David, Sophia, and James. "David is a knave or Sebastian is a knight," Aria claimed. In a statement by Sebastian: "Aria is not a knave". David remarked, "James is a knight or Aria is a knight". Sophia expressed that James is not a knight. James was heard saying, "Aria is a knight". So who is a knight and who is a knave?

Aria is a knight, Sebastian is a knight, David is a knight, Sophia is a knave, and James is a knight.

(1) Aria is a knight
(2) Sebastian is a knight
(3) David is a knight
(4) Sophia is a knave
(5) James is a knight

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

Assume David is a knight. No contradiction is found in their claim that James is a knight or Aria is a knight.

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

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

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

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

(('or', ('lying', 2), ('telling-truth', 1)), ('not', ('lying', 0)), ('or', ('telling-truth', 4), ('telling-truth', 0)), ('not', ('telling-truth', 4)), ('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 5 inhabitants: Lucas, Avery, Ethan, Aurora, and Noah. Lucas asserted: "If Ethan is a knight then Avery is a knave". In a statement by Avery: "Noah is a knave and Aurora is a knave". "Avery is not a knight," Ethan claimed. Aurora expressed that Avery is a knight and Ethan is a knave. "If Avery is a knave then Ethan is a knight," Noah claimed. So who is a knight and who is a knave?

Lucas is a knight, Avery is a knave, Ethan is a knight, Aurora is a knave, and Noah is a knight.

(1) Lucas is a knight
(2) Avery is a knave
(3) Ethan is a knight
(4) Aurora is a knave
(5) Noah is a knight

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

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

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

Assume Avery is a knave. No contradiction is found in their false claim that Noah is a knave and Aurora is a knave.

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

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

Assume Aurora is a knave. No contradiction is found in their false claim that Avery is a knight and 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 5 inhabitants: Abigail, Olivia, Logan, Joseph, and Sebastian. Abigail told you that If Sebastian is a knave then Abigail is a knight. "Logan is a knight and Joseph is a knave," Olivia declared. Logan remarked, "If Abigail is a knight then Abigail is a knave". As Joseph put it, "Olivia is a knight". "Olivia is not a knight," Sebastian mentioned. So who is a knight and who is a knave?

Abigail is a knight, Olivia is a knave, Logan is a knave, Joseph is a knave, and Sebastian is a knight.

(1) Abigail is a knight
(2) Olivia is a knave
(3) Logan is a knave
(4) Joseph is a knave
(5) Sebastian is a knight

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

Assume Sebastian 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 Sebastian that Olivia is not a knight.

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

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

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

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

Assume Joseph is a knave. No contradiction is found in their false claim that Olivia 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 5 inhabitants: Owen, Mason, Chloe, Benjamin, and Ella. "Mason is a knave if and only if Owen is a knight," Owen declared. Mason expressed that Chloe is a knight or Owen is a knave. Chloe told you that Benjamin is a knave if and only if Owen is a knave. "Benjamin is a knight" - Benjamin. According to Ella, "If Benjamin is a knave then Chloe is a knave". So who is a knight and who is a knave?

Owen is a knight, Mason is a knave, Chloe is a knave, Benjamin is a knave, and Ella is a knight.

(1) Owen is a knight
(2) Mason is a knave
(3) Chloe is a knave
(4) Benjamin is a knave
(5) Ella is a knight

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

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

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

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

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

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

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

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