A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Harper, Michael, Matthew, Avery, Jack, Henry, Owen, and Liam. "Michael is not a knight," Harper claimed. Michael said that Matthew is a knave or Liam is a knight. Matthew noted, "Jack is a knight or Henry is a knave". Avery asserted: "If Owen is a knave then Henry is a knave". "Jack is a knight if and only if Harper is a knight" - Jack. In a statement by Henry: "Harper is a knight or Jack is a knight". In Owen's words: "Henry is not a knight". Liam said, "Avery is a knight and Avery is a knave." So who is a knight and who is a knave?

Harper Michael Matthew Avery Jack Henry Owen Liam

Harper is a knight, Michael is a knave, Matthew is a knight, Avery is a knave, Jack is a knight, Henry is a knight, Owen is a knave, and Liam is a knave.

(1) Harper is a knight
(2) Michael is a knave
(3) Matthew is a knight
(4) Avery is a knave
(5) Jack is a knight
(6) Henry is a knight
(7) Owen is a knave
(8) Liam is a knave

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

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

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

Assume Matthew is a knight. No contradiction is found in their claim that Jack is a knight or Henry is a knave.

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

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

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

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

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

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

Owen cannot be a knave, because this would contradict the claim of Avery that If Owen is a knave then Henry is a knave.

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

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

Owen cannot be a knight, because this would contradict the false claim of Avery that If Owen is a knave then Henry is a knave.

Assume Owen is a knave. No contradiction is found in their false claim that Henry 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 8 inhabitants: Olivia, Riley, William, Henry, Isabella, Charlotte, Evelyn, and Elizabeth. Olivia said that Isabella is a knave. Riley asserted: "Isabella is a knight or Olivia is a knave". William remarked, "If Henry is a knave then Evelyn is a knave". In Henry's words: "Riley is a knave if and only if Henry is a knight". In Isabella's words: "If Henry is a knight then Henry is a knave". According to Charlotte, "If Riley is a knight then Charlotte is a knight". In a statement by Evelyn: "Charlotte is not a knave". According to Elizabeth, "Olivia is a knight and Olivia is a knave". So who is a knight and who is a knave?

Olivia Riley William Henry Isabella Charlotte Evelyn Elizabeth

Olivia is a knight, Riley is a knave, William is a knight, Henry is a knight, Isabella is a knave, Charlotte is a knight, Evelyn is a knight, and Elizabeth is a knave.

(1) Olivia is a knight
(2) Riley is a knave
(3) William is a knight
(4) Henry is a knight
(5) Isabella is a knave
(6) Charlotte is a knight
(7) Evelyn is a knight
(8) Elizabeth is a knave

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

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

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

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

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

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

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

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

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

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

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

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


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, William, Owen, Henry, Abigail, Penelope, Grace, and Chloe. Sophia stated, "Henry is a knave". William remarked, "Owen is not a knight". Owen was heard saying, "Chloe is a knight and Abigail is a knight". Henry said, "Grace is not a knight." According to Abigail, "Chloe is a knight or Penelope is a knight". "Owen is not a knight," Penelope mentioned. According to Grace, "Sophia is a knight or Penelope is a knight". In Chloe's words: "If Owen is a knight then Henry is a knave". So who is a knight and who is a knave?

Sophia William Owen Henry Abigail Penelope Grace Chloe

Sophia is a knight, William is a knave, Owen is a knight, Henry is a knave, Abigail is a knight, Penelope is a knave, Grace is a knight, and Chloe is a knight.

(1) Sophia is a knight
(2) William is a knave
(3) Owen is a knight
(4) Henry is a knave
(5) Abigail is a knight
(6) Penelope is a knave
(7) Grace is a knight
(8) Chloe is a knight

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Owen is a knight. No contradiction is found in their claim that Chloe is a knight and Abigail is a knight.

Assume Abigail is a knight. No contradiction is found in their claim that Chloe is a knight or Penelope is a knight.

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

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

(('lying', 3), ('not', ('telling-truth', 2)), ('and', ('telling-truth', 7), ('telling-truth', 4)), ('not', ('telling-truth', 6)), ('or', ('telling-truth', 7), ('telling-truth', 5)), ('not', ('telling-truth', 2)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('->', ('telling-truth', 2), ('lying', 3)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: James, Joseph, David, Ella, Aria, Benjamin, Matthew, and Penelope. James stated, "Benjamin is a knave if and only if Matthew is a knave". "Aria is a knave if and only if Benjamin is a knave," Joseph declared. David told you that If David is a knight then Penelope is a knight. Ella said that If James is a knight then Aria is a knight. "If Ella is a knight then David is a knight," Aria claimed. Benjamin remarked, "Joseph is a knight or Penelope is a knave". Matthew told you that Ella is a knight and Ella is a knave. Penelope said, "David is a knave or James is a knight." So who is a knight and who is a knave?

James Joseph David Ella Aria Benjamin Matthew Penelope

James is a knight, Joseph is a knave, David is a knight, Ella is a knight, Aria is a knight, Benjamin is a knave, Matthew is a knave, and Penelope is a knight.

(1) James is a knight
(2) Joseph is a knave
(3) David is a knight
(4) Ella is a knight
(5) Aria is a knight
(6) Benjamin is a knave
(7) Matthew is a knave
(8) Penelope is a knight

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Aria cannot be a knave, because this would contradict the claim of Joseph that Aria is a knave if and only if Benjamin is a knave.

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

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

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

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

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

Ella cannot be a knave, because this would contradict the false claim of Aria that If Ella is a knight then David is a knight.

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

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

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

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

Assume Matthew is a knave. No contradiction is found in their false claim that Ella is a knight and Ella 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 8 inhabitants: Jack, Emily, Evelyn, Ella, Scarlett, Jackson, William, and Avery. "Evelyn is not a knight," Jack mentioned. Emily stated, "William is a knight if and only if Jackson is a knight". Evelyn noted, "If Scarlett is a knave then Ella is a knight". According to Ella, "Avery is a knave". In a statement by Scarlett: "William is not a knave". Jackson said, "Evelyn is a knave and Scarlett is a knave." William noted, "Emily is a knave or Scarlett is a knight". Avery told you that Jack is a knave. So who is a knight and who is a knave?

Jack Emily Evelyn Ella Scarlett Jackson William Avery

Jack is a knave, Emily is a knave, Evelyn is a knight, Ella is a knave, Scarlett is a knight, Jackson is a knave, William is a knight, and Avery is a knight.

(1) Jack is a knave
(2) Emily is a knave
(3) Evelyn is a knight
(4) Ella is a knave
(5) Scarlett is a knight
(6) Jackson is a knave
(7) William is a knight
(8) Avery is a knight

Assume Jack 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 Jack that Evelyn is not a knight.

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

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

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

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

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

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

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

Jackson cannot be a knave, because this would contradict the false claim of their own that Evelyn is a knave and Scarlett is a knave.

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

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

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

Assume Jack 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 If Scarlett is a knave then Ella is a knight.

Assume Scarlett 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 Emily is a knave or Scarlett is a knight.

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

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

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

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

Assume Jackson is a knave. No contradiction is found in their false claim that Evelyn is a knave and Scarlett is a knave.

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

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

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

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

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

Assume Avery is a knight. No contradiction is found in their claim that 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 8 inhabitants: Mason, Matthew, Chloe, Aurora, Liam, Michael, Victoria, and Daniel. Mason expressed that Aurora is a knave if and only if Aurora is a knight. "If Chloe is a knave then Chloe is a knight," Matthew claimed. "If Michael is a knight then Matthew is a knight," Chloe mentioned. "Michael is not a knight," Aurora mentioned. Liam expressed that Victoria is a knight or Michael is a knight. Michael was heard saying, "Chloe is a knave and Victoria is a knave". Victoria said, "Matthew is a knave if and only if Michael is a knight." Daniel asserted: "If Michael is a knave then Chloe is a knight". So who is a knight and who is a knave?

Mason Matthew Chloe Aurora Liam Michael Victoria Daniel

Mason is a knave, Matthew is a knight, Chloe is a knight, Aurora is a knight, Liam is a knight, Michael is a knave, Victoria is a knight, and Daniel is a knight.

(1) Mason is a knave
(2) Matthew is a knight
(3) Chloe is a knight
(4) Aurora is a knight
(5) Liam is a knight
(6) Michael is a knave
(7) Victoria is a knight
(8) Daniel is a knight

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

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

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

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

Assume Michael is a knave. No contradiction is found in their false claim that Chloe is a knave and Victoria is a knave.

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

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

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

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

Assume Daniel is a knight. No contradiction is found in their claim that If Michael is a knave then Chloe 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 8 inhabitants: Grace, Liam, Abigail, Mason, Jacob, Henry, Avery, and Isabella. In Grace's words: "Mason is a knight and Isabella is a knight". "If Avery is a knight then Henry is a knight" - Liam. According to Abigail, "Abigail is a knight or Avery is a knight". Mason expressed that Liam is not a knave. Jacob said, "Liam is a knave or Isabella is a knave." Henry commented, "Mason is a knight and Abigail is a knave". Avery noted, "Henry is a knight if and only if Isabella is a knave". As Isabella put it, "Jacob is a knight if and only if Jacob is a knave". So who is a knight and who is a knave?

Grace Liam Abigail Mason Jacob Henry Avery Isabella

Grace is a knave, Liam is a knight, Abigail is a knight, Mason is a knight, Jacob is a knight, Henry is a knave, Avery is a knave, and Isabella is a knave.

(1) Grace is a knave
(2) Liam is a knight
(3) Abigail is a knight
(4) Mason is a knight
(5) Jacob is a knight
(6) Henry is a knave
(7) Avery is a knave
(8) Isabella is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Jacob is a knight. No contradiction is found in their claim that Liam is a knave or Isabella 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 8 inhabitants: Samuel, Amelia, Alexander, Ava, James, Aiden, Michael, and Olivia. "James is a knave if and only if Alexander is a knight," Samuel mentioned. Amelia asserted: "Alexander is a knave and Aiden is a knight". In Alexander's words: "Michael is a knave if and only if Samuel is a knave". Ava told you that If Aiden is a knight then Amelia is a knight. "Alexander is not a knight" - James. Aiden noted, "Olivia is a knave if and only if Ava is a knight". Michael commented, "Ava is a knight and Olivia is a knave". Olivia expressed that Alexander is a knave or James is a knave. So who is a knight and who is a knave?

Samuel Amelia Alexander Ava James Aiden Michael Olivia

Samuel is a knight, Amelia is a knave, Alexander is a knave, Ava is a knight, James is a knight, Aiden is a knave, Michael is a knave, and Olivia is a knight.

(1) Samuel is a knight
(2) Amelia is a knave
(3) Alexander is a knave
(4) Ava is a knight
(5) James is a knight
(6) Aiden is a knave
(7) Michael is a knave
(8) Olivia is a knight

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

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

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

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

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

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

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

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

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

Olivia cannot be a knave, because this would contradict the false claim of Michael that Ava is a knight and Olivia is a knave.

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

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

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

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

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


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Scarlett, Chloe, Elizabeth, Aurora, Amelia, Sophia, Isabella, and Aria. Scarlett commented, "Aria is a knave and Aurora is a knave". Chloe asserted: "Amelia is not a knight". Elizabeth was heard saying, "Isabella is a knave and Sophia is a knave". Aurora noted, "Chloe is a knight and Aria is a knight". "Aurora is a knave," Amelia claimed. Sophia told you that Aurora is not a knight. Isabella commented, "Amelia is a knave and Elizabeth is a knight". Aria remarked, "Sophia is not a knight". So who is a knight and who is a knave?

Scarlett Chloe Elizabeth Aurora Amelia Sophia Isabella Aria

Scarlett is a knight, Chloe is a knave, Elizabeth is a knave, Aurora is a knave, Amelia is a knight, Sophia is a knight, Isabella is a knave, and Aria is a knave.

(1) Scarlett is a knight
(2) Chloe is a knave
(3) Elizabeth is a knave
(4) Aurora is a knave
(5) Amelia is a knight
(6) Sophia is a knight
(7) Isabella is a knave
(8) Aria is a knave

Assume Scarlett is a knight. No contradiction is found in their claim that Aria is a knave and Aurora is a knave.

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

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

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

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

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

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

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

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

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

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

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

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

Assume Elizabeth is a knave. No contradiction is found in their false claim that Isabella is a knave and Sophia is a knave.

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

Assume Isabella is a knave. No contradiction is found in their false claim that Amelia is a knave and Elizabeth 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 8 inhabitants: Mia, Luke, Victoria, Harper, Sophia, Zoey, Lily, and Avery. "Victoria is a knave or Avery is a knave" - Mia. Luke stated, "Harper is a knight or Mia is a knight". Victoria remarked, "Lily is a knight". Harper told you that Zoey is not a knave. Sophia said that Zoey is a knave and Victoria is a knight. "Lily is not a knave" - Zoey. In a statement by Lily: "If Sophia is a knight then Victoria is a knight". As Avery put it, "Zoey is a knave". So who is a knight and who is a knave?

Mia Luke Victoria Harper Sophia Zoey Lily Avery

Mia is a knight, Luke is a knight, Victoria is a knight, Harper is a knight, Sophia is a knave, Zoey is a knight, Lily is a knight, and Avery is a knave.

(1) Mia is a knight
(2) Luke is a knight
(3) Victoria is a knight
(4) Harper is a knight
(5) Sophia is a knave
(6) Zoey is a knight
(7) Lily is a knight
(8) Avery is a knave

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

Assume Victoria 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 If Sophia is a knight then Victoria is a knight.

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

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

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

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

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

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

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

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

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

Assume Harper is a knight. No contradiction is found in their claim that Zoey 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 8 inhabitants: William, Evelyn, Sebastian, Alexander, Matthew, Isabella, Zoey, and Jack. William noted, "Matthew is a knight if and only if Sebastian is a knave". "Jack is a knave or Zoey is a knave" - Evelyn. "Matthew is a knave," Sebastian mentioned. Alexander commented, "Evelyn is not a knave". Matthew noted, "William is a knave or Alexander is a knave". Isabella noted, "Alexander is a knight or William is a knight". Zoey expressed that William is a knight or Evelyn is a knave. "Sebastian is a knight and Evelyn is a knave," Jack mentioned. So who is a knight and who is a knave?

William Evelyn Sebastian Alexander Matthew Isabella Zoey Jack

William is a knight, Evelyn is a knight, Sebastian is a knight, Alexander is a knight, Matthew is a knave, Isabella is a knight, Zoey is a knight, and Jack is a knave.

(1) William is a knight
(2) Evelyn is a knight
(3) Sebastian is a knight
(4) Alexander is a knight
(5) Matthew is a knave
(6) Isabella is a knight
(7) Zoey is a knight
(8) Jack is a knave

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

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

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

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

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

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

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

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

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

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

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

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

Assume Matthew is a knave. No contradiction is found in their false claim that William is a knave or Alexander is a knave.

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

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

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

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

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

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

Assume Isabella is a knight. No contradiction is found in their claim that Alexander is a knight or William 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 8 inhabitants: Aria, Logan, Noah, Liam, Sofia, Emily, Joseph, and Sophia. In Aria's words: "Emily is a knight and Joseph is a knight". As Logan put it, "Aria is a knight or Joseph is a knight". As Noah put it, "Sofia is a knave or Sofia is a knight". Liam told you that Noah is a knight. "Liam is a knave," Sofia mentioned. "Noah is not a knave" - Emily. As Joseph put it, "Emily is a knave and Logan is a knight". Sophia told you that If Logan is a knave then Logan is a knight. So who is a knight and who is a knave?

Aria Logan Noah Liam Sofia Emily Joseph Sophia

Aria is a knave, Logan is a knave, Noah is a knight, Liam is a knight, Sofia is a knave, Emily is a knight, Joseph is a knave, and Sophia is a knave.

(1) Aria is a knave
(2) Logan is a knave
(3) Noah is a knight
(4) Liam is a knight
(5) Sofia is a knave
(6) Emily is a knight
(7) Joseph is a knave
(8) Sophia is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(('and', ('telling-truth', 5), ('telling-truth', 6)), ('or', ('telling-truth', 0), ('telling-truth', 6)), ('or', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 2), ('lying', 3), ('not', ('lying', 2)), ('and', ('lying', 5), ('telling-truth', 1)), ('->', ('lying', 1), ('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 8 inhabitants: Evelyn, Chloe, Joseph, Harper, Aiden, Aria, Riley, and Mia. "Aria is a knave or Mia is a knight" - Evelyn. Chloe expressed that Riley is not a knave. "Harper is not a knave," Joseph claimed. Harper commented, "If Riley is a knight then Mia is a knave". In a statement by Aiden: "Harper is a knight or Mia is a knight". "If Riley is a knight then Harper is a knave," Aria mentioned. Riley noted, "Chloe is a knight and Joseph is a knave". Mia said, "Aria is not a knight." So who is a knight and who is a knave?

Evelyn Chloe Joseph Harper Aiden Aria Riley Mia

Evelyn is a knave, Chloe is a knave, Joseph is a knight, Harper is a knight, Aiden is a knight, Aria is a knight, Riley is a knave, and Mia is a knave.

(1) Evelyn is a knave
(2) Chloe is a knave
(3) Joseph is a knight
(4) Harper is a knight
(5) Aiden is a knight
(6) Aria is a knight
(7) Riley is a knave
(8) Mia is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Mia cannot be a knight, because this would contradict the false claim of Evelyn that Aria is a knave or Mia is a knight.

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

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

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


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Sophia, Henry, Liam, Aiden, Abigail, Jackson, Mia, and Jacob. "Sophia is a knight and Jacob is a knight" - Sophia. Henry said that If Jacob is a knight then Liam is a knave. Liam stated, "Abigail is a knave and Mia is a knight". Aiden asserted: "Henry is a knight if and only if Jackson is a knave". Abigail told you that If Sophia is a knight then Mia is a knight. In Jackson's words: "Sophia is a knave or Aiden is a knight". Mia was heard saying, "Liam is a knight and Abigail is a knave". Jacob was heard saying, "Aiden is not a knave". So who is a knight and who is a knave?

Sophia Henry Liam Aiden Abigail Jackson Mia Jacob

Sophia is a knave, Henry is a knight, Liam is a knave, Aiden is a knave, Abigail is a knight, Jackson is a knight, Mia is a knave, and Jacob is a knave.

(1) Sophia is a knave
(2) Henry is a knight
(3) Liam is a knave
(4) Aiden is a knave
(5) Abigail is a knight
(6) Jackson is a knight
(7) Mia is a knave
(8) Jacob is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

Jackson cannot be a knight, because this would contradict the claim of Aiden that Henry 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 Sophia is a knave or Aiden is a knight.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Jackson is a knight. No contradiction is found in their claim that Sophia is a knave or Aiden is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Olivia, Harper, Aiden, Ella, Michael, Amelia, Benjamin, and Oliver. Olivia stated, "Oliver is a knight". Harper asserted: "Michael is not a knight". In Aiden's words: "Amelia is a knight and Olivia is a knave". In Ella's words: "Harper is a knight or Olivia is a knight". In a statement by Michael: "Aiden is a knave if and only if Oliver is a knight". In Amelia's words: "Ella is not a knight". Benjamin expressed that Ella is a knave and Olivia is a knight. "Oliver is a knight if and only if Aiden is a knight," Oliver claimed. So who is a knight and who is a knave?

Olivia Harper Aiden Ella Michael Amelia Benjamin Oliver

Olivia is a knave, Harper is a knave, Aiden is a knight, Ella is a knave, Michael is a knight, Amelia is a knight, Benjamin is a knave, and Oliver is a knave.

(1) Olivia is a knave
(2) Harper is a knave
(3) Aiden is a knight
(4) Ella is a knave
(5) Michael is a knight
(6) Amelia is a knight
(7) Benjamin is a knave
(8) Oliver is a knave

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

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

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

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

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

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

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

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

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

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

Assume Aiden is a knight. No contradiction is found in their claim that Amelia is a knight and Olivia is a knave.

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

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

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

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

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

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

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

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

(('telling-truth', 7), ('not', ('telling-truth', 4)), ('and', ('telling-truth', 5), ('lying', 0)), ('or', ('telling-truth', 1), ('telling-truth', 0)), ('<=>', ('lying', 2), ('telling-truth', 7)), ('not', ('telling-truth', 3)), ('and', ('lying', 3), ('telling-truth', 0)), ('<=>', ('telling-truth', 7), ('telling-truth', 2)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Alexander, Luke, Henry, Abigail, Elizabeth, Michael, Isabella, and Grace. Alexander said, "Grace is a knight or Isabella is a knave." In a statement by Luke: "Henry is a knight". Henry asserted: "If Grace is a knight then Abigail is a knight". Abigail commented, "Elizabeth is a knave and Henry is a knave". Elizabeth told you that Isabella is a knight. Michael expressed that Luke is a knight if and only if Grace is a knave. Isabella commented, "Michael is a knight or Isabella is a knight". Grace said, "Michael is a knight or Abigail is a knave." So who is a knight and who is a knave?

Alexander Luke Henry Abigail Elizabeth Michael Isabella Grace

Alexander is a knight, Luke is a knave, Henry is a knave, Abigail is a knave, Elizabeth is a knight, Michael is a knight, Isabella is a knight, and Grace is a knight.

(1) Alexander is a knight
(2) Luke is a knave
(3) Henry is a knave
(4) Abigail is a knave
(5) Elizabeth is a knight
(6) Michael is a knight
(7) Isabella is a knight
(8) Grace is a knight

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

Assume Grace is a knight. No contradiction is found in their claim that Michael is a knight or Abigail is a knave.

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

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

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

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

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

Abigail cannot be a knight, because this would contradict the false claim of Henry that If Grace is a knight then Abigail is a knight.

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

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

Assume Isabella is a knight. No contradiction is found in their claim that Michael is a knight or Isabella 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 8 inhabitants: Grace, Zoey, Charlotte, Riley, Evelyn, Michael, Joseph, and James. Grace said that If James is a knight then Charlotte is a knave. As Zoey put it, "Joseph is a knight or James is a knave". Charlotte was heard saying, "Zoey is a knight". As Riley put it, "Zoey is a knight or Michael is a knave". Evelyn expressed that James is not a knave. In a statement by Michael: "Riley is a knave if and only if Charlotte is a knight". Joseph told you that Michael is a knave and James is a knight. James was heard saying, "Zoey is a knight". So who is a knight and who is a knave?

Grace Zoey Charlotte Riley Evelyn Michael Joseph James

Grace is a knave, Zoey is a knight, Charlotte is a knight, Riley is a knight, Evelyn is a knight, Michael is a knave, Joseph is a knight, and James is a knight.

(1) Grace is a knave
(2) Zoey is a knight
(3) Charlotte is a knight
(4) Riley is a knight
(5) Evelyn is a knight
(6) Michael is a knave
(7) Joseph is a knight
(8) James is a knight

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Evelyn is a knight. No contradiction is found in their claim that James 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 8 inhabitants: Riley, Evelyn, Avery, Isabella, Aiden, Ethan, Grace, and Charlotte. In a statement by Riley: "Grace is not a knave". As Evelyn put it, "Isabella is not a knight". Avery told you that Evelyn is not a knight. "If Charlotte is a knight then Ethan is a knave," Isabella declared. Aiden asserted: "Avery is a knave if and only if Charlotte is a knave". Ethan commented, "If Riley is a knave then Grace is a knight". Grace remarked, "Ethan is a knight and Evelyn is a knight". Charlotte stated, "If Ethan is a knight then Ethan is a knave". So who is a knight and who is a knave?

Riley Evelyn Avery Isabella Aiden Ethan Grace Charlotte

Riley is a knave, Evelyn is a knave, Avery is a knight, Isabella is a knight, Aiden is a knight, Ethan is a knave, Grace is a knave, and Charlotte is a knight.

(1) Riley is a knave
(2) Evelyn is a knave
(3) Avery is a knight
(4) Isabella is a knight
(5) Aiden is a knight
(6) Ethan is a knave
(7) Grace is a knave
(8) Charlotte is a knight

Assume Riley 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 Ethan is a knight and Evelyn is a knight.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Aiden is a knight. No contradiction is found in their claim that Avery is a knave if and only if Charlotte 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 8 inhabitants: Liam, William, Penelope, Luke, Sofia, David, Joseph, and Lily. Liam commented, "Luke is not a knight". In a statement by William: "Liam is a knight if and only if David is a knave". Penelope said that Sofia is a knave if and only if Joseph is a knave. "Penelope is a knight and David is a knight," Luke claimed. Sofia was heard saying, "If Penelope is a knight then Lily is a knave". David said, "If Liam is a knave then David is a knight." Joseph said that Sofia is not a knight. "If William is a knave then Joseph is a knave" - Lily. So who is a knight and who is a knave?

Liam William Penelope Luke Sofia David Joseph Lily

Liam is a knight, William is a knave, Penelope is a knave, Luke is a knave, Sofia is a knight, David is a knight, Joseph is a knave, and Lily is a knight.

(1) Liam is a knight
(2) William is a knave
(3) Penelope is a knave
(4) Luke is a knave
(5) Sofia is a knight
(6) David is a knight
(7) Joseph is a knave
(8) Lily is a knight

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

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

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

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

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

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

Assume Lily is a knave. No contradiction is found in their false claim that If William is a knave then Joseph is a knave.

William cannot be a knight, because this would contradict the false claim of Lily that If William is a knave then Joseph is a knave.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Joseph is a knave. No contradiction is found in their false claim that Sofia 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 8 inhabitants: Scarlett, William, Alexander, Jack, James, Jackson, Ella, and Olivia. Scarlett commented, "Jack is a knight or Ella is a knave". According to William, "William is a knight and Ella is a knight". Alexander was heard saying, "Jackson is a knave and James is a knave". In Jack's words: "If Ella is a knight then Jackson is a knave". James commented, "Jack is not a knave". Jackson expressed that William is not a knave. Ella told you that Jack is not a knave. In a statement by Olivia: "James is a knave and William is a knave". So who is a knight and who is a knave?

Scarlett William Alexander Jack James Jackson Ella Olivia

Scarlett is a knight, William is a knave, Alexander is a knave, Jack is a knight, James is a knight, Jackson is a knave, Ella is a knight, and Olivia is a knave.

(1) Scarlett is a knight
(2) William is a knave
(3) Alexander is a knave
(4) Jack is a knight
(5) James is a knight
(6) Jackson is a knave
(7) Ella is a knight
(8) Olivia is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Olivia is a knave. No contradiction is found in their false claim that James is a knave and William 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 8 inhabitants: Grace, Riley, Luke, Matthew, Penelope, Mia, Charlotte, and Lucas. Grace was heard saying, "Charlotte is a knight if and only if Charlotte is a knave". Riley stated, "Penelope is a knave and Lucas is a knave". Luke was heard saying, "Riley is a knave if and only if Lucas is a knight". "Charlotte is not a knight," Matthew declared. "If Luke is a knave then Mia is a knave," Penelope claimed. "Riley is a knight if and only if Matthew is a knave," Mia claimed. Charlotte stated, "Lucas is not a knight". "Charlotte is a knave and Charlotte is a knight," Lucas claimed. So who is a knight and who is a knave?

Grace Riley Luke Matthew Penelope Mia Charlotte Lucas

Grace is a knave, Riley is a knave, Luke is a knave, Matthew is a knave, Penelope is a knight, Mia is a knave, Charlotte is a knight, and Lucas is a knave.

(1) Grace is a knave
(2) Riley is a knave
(3) Luke is a knave
(4) Matthew is a knave
(5) Penelope is a knight
(6) Mia is a knave
(7) Charlotte is a knight
(8) Lucas is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Matthew is a knave. No contradiction is found in their false claim that Charlotte 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 8 inhabitants: Noah, Riley, Joseph, Emma, Michael, Jackson, Lucas, and Harper. As Noah put it, "Michael is a knight". Riley was heard saying, "Harper is a knight if and only if Michael is a knight". In Joseph's words: "Emma is a knave or Emma is a knight". Emma commented, "If Jackson is a knight then Jackson is a knave". "Riley is a knight or Lucas is a knave" - Michael. "Lucas is a knave or Harper is a knave," Jackson claimed. In a statement by Lucas: "Joseph is not a knight". Harper remarked, "Joseph is a knave". So who is a knight and who is a knave?

Noah Riley Joseph Emma Michael Jackson Lucas Harper

Noah is a knight, Riley is a knave, Joseph is a knight, Emma is a knave, Michael is a knight, Jackson is a knight, Lucas is a knave, and Harper is a knave.

(1) Noah is a knight
(2) Riley is a knave
(3) Joseph is a knight
(4) Emma is a knave
(5) Michael is a knight
(6) Jackson is a knight
(7) Lucas is a knave
(8) Harper is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Lucas is a knave. No contradiction is found in their false claim that Joseph 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 8 inhabitants: Michael, Jacob, Joseph, Abigail, Alexander, Ava, Sofia, and Avery. As Michael put it, "Sofia is not a knight". As Jacob put it, "Abigail is a knight or Michael is a knave". "Michael is a knave and Avery is a knave," Joseph declared. Abigail remarked, "Avery is a knave". Alexander noted, "Sofia is a knight or Joseph is a knight". "If Alexander is a knight then Avery is a knight" - Ava. Sofia commented, "Alexander is a knave if and only if Jacob is a knight". In a statement by Avery: "Alexander is a knave or Sofia is a knight". So who is a knight and who is a knave?

Michael Jacob Joseph Abigail Alexander Ava Sofia Avery

Michael is a knight, Jacob is a knave, Joseph is a knave, Abigail is a knave, Alexander is a knave, Ava is a knight, Sofia is a knave, and Avery is a knight.

(1) Michael is a knight
(2) Jacob is a knave
(3) Joseph is a knave
(4) Abigail is a knave
(5) Alexander is a knave
(6) Ava is a knight
(7) Sofia is a knave
(8) Avery is a knight

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

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

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

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

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

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

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

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

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

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

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

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

Abigail cannot be a knight, because this would contradict the false claim of Jacob that Abigail is a knight or Michael is a knave.

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

Assume Ava is a knight. No contradiction is found in their claim that If Alexander is a knight then Avery 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 8 inhabitants: William, Emma, Sebastian, Zoey, Logan, Samuel, Penelope, and Ethan. In William's words: "Samuel is a knight and Sebastian is a knave". Emma said, "Logan is not a knave." "Samuel is a knight if and only if Zoey is a knave," Sebastian declared. "Emma is a knave and William is a knave," Zoey declared. Logan was heard saying, "Sebastian is a knave". As Samuel put it, "Logan is a knave if and only if Ethan is a knight". As Penelope put it, "William is a knight or Emma is a knave". Ethan told you that Penelope is a knight and Emma is a knight. So who is a knight and who is a knave?

William Emma Sebastian Zoey Logan Samuel Penelope Ethan

William is a knave, Emma is a knave, Sebastian is a knight, Zoey is a knight, Logan is a knave, Samuel is a knave, Penelope is a knight, and Ethan is a knave.

(1) William is a knave
(2) Emma is a knave
(3) Sebastian is a knight
(4) Zoey is a knight
(5) Logan is a knave
(6) Samuel is a knave
(7) Penelope is a knight
(8) Ethan is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Zoey is a knave. No contradiction is found in their false claim that Emma is a knave and William is a knave.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Zoey is a knight. No contradiction is found in their claim that Emma is a knave and William is a knave.

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

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

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

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


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 8 inhabitants: Zoey, Avery, Alexander, Sebastian, Noah, Logan, Emma, and Samuel. Zoey remarked, "Noah is a knave and Sebastian is a knave". "Zoey is a knave or Samuel is a knave," Avery claimed. "Zoey is a knight if and only if Sebastian is a knave," Alexander mentioned. Sebastian said that If Avery is a knave then Samuel is a knight. Noah remarked, "Zoey is not a knave". "Alexander is a knave or Avery is a knight," Logan declared. Emma was heard saying, "If Avery is a knave then Samuel is a knave". Samuel remarked, "Emma is a knave". So who is a knight and who is a knave?

Zoey Avery Alexander Sebastian Noah Logan Emma Samuel

Zoey is a knave, Avery is a knight, Alexander is a knight, Sebastian is a knight, Noah is a knave, Logan is a knight, Emma is a knight, and Samuel is a knave.

(1) Zoey is a knave
(2) Avery is a knight
(3) Alexander is a knight
(4) Sebastian is a knight
(5) Noah is a knave
(6) Logan is a knight
(7) Emma is a knight
(8) Samuel is a knave

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

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

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

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

Assume Zoey is a knave. No contradiction is found in their false claim that Noah is a knave and Sebastian is a knave.

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

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

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

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

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

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

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

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

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

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

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

Assume Logan is a knight. No contradiction is found in their claim that Alexander is a knave or Avery 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 8 inhabitants: Grace, Zoey, Elizabeth, Victoria, Joseph, Sebastian, Noah, and Mia. Grace noted, "Elizabeth is a knave and Noah is a knave". Zoey expressed that If Mia is a knight then Victoria is a knight. Elizabeth was heard saying, "Victoria is a knave". Victoria was heard saying, "Joseph is a knight and Grace is a knight". Joseph asserted: "Grace is a knight and Elizabeth is a knight". "Noah is a knight," Sebastian declared. Noah remarked, "Zoey is a knight or Elizabeth is a knight". Mia asserted: "Victoria is not a knight". So who is a knight and who is a knave?

Grace Zoey Elizabeth Victoria Joseph Sebastian Noah Mia

Grace is a knave, Zoey is a knave, Elizabeth is a knight, Victoria is a knave, Joseph is a knave, Sebastian is a knight, Noah is a knight, and Mia is a knight.

(1) Grace is a knave
(2) Zoey is a knave
(3) Elizabeth is a knight
(4) Victoria is a knave
(5) Joseph is a knave
(6) Sebastian is a knight
(7) Noah is a knight
(8) Mia is a knight

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

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

Assume Elizabeth is a knave. No contradiction is found in their false claim that Victoria is a knave.

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

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

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

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

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

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

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

Assume Elizabeth 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 Elizabeth that Victoria is a knave.

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

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

Assume Noah is a knight. No contradiction is found in their claim that Zoey is a knight or Elizabeth is a knight.

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

Mia cannot be a knight, because this would contradict the claim of Zoey that If Mia is a knight then Victoria is a knight.

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

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

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

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

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

(('and', ('lying', 2), ('lying', 6)), ('->', ('telling-truth', 7), ('telling-truth', 3)), ('lying', 3), ('and', ('telling-truth', 4), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('telling-truth', 2)), ('telling-truth', 6), ('or', ('telling-truth', 1), ('telling-truth', 2)), ('not', ('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 8 inhabitants: Ella, Luke, Chloe, Aiden, Harper, Emma, Mason, and Aurora. As Ella put it, "Aiden is a knave and Mason is a knight". Luke was heard saying, "Harper is not a knight". Chloe stated, "Mason is not a knight". "Emma is a knight if and only if Mason is a knave," Aiden declared. In a statement by Harper: "Chloe is not a knight". Emma was heard saying, "Luke is a knave". Mason said, "Chloe is a knave or Ella is a knave." In Aurora's words: "Mason is a knight". So who is a knight and who is a knave?

Ella Luke Chloe Aiden Harper Emma Mason Aurora

Ella is a knight, Luke is a knave, Chloe is a knave, Aiden is a knave, Harper is a knight, Emma is a knight, Mason is a knight, and Aurora is a knight.

(1) Ella is a knight
(2) Luke is a knave
(3) Chloe is a knave
(4) Aiden is a knave
(5) Harper is a knight
(6) Emma is a knight
(7) Mason is a knight
(8) Aurora is a knight

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

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

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

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

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

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

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

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

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

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

Assume Aurora is a knight. No contradiction is found in their claim that Mason 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 8 inhabitants: Lily, Evelyn, Sofia, Aiden, Oliver, Mason, Jack, and Henry. "Aiden is a knight and Henry is a knave," Lily mentioned. Evelyn asserted: "If Evelyn is a knight then Sofia is a knight". Sofia expressed that Lily is a knave or Lily is a knight. Aiden asserted: "Oliver is a knight or Aiden is a knight". Oliver commented, "If Evelyn is a knight then Oliver is a knight". "Sofia is a knight," Mason mentioned. According to Jack, "Oliver is a knight if and only if Evelyn is a knight". Henry stated, "Lily is a knight". So who is a knight and who is a knave?

Lily Evelyn Sofia Aiden Oliver Mason Jack Henry

Lily is a knave, Evelyn is a knight, Sofia is a knight, Aiden is a knave, Oliver is a knave, Mason is a knight, Jack is a knave, and Henry is a knave.

(1) Lily is a knave
(2) Evelyn is a knight
(3) Sofia is a knight
(4) Aiden is a knave
(5) Oliver is a knave
(6) Mason is a knight
(7) Jack is a knave
(8) Henry is a knave

Assume Lily is a knight. No contradiction is found in their claim that Aiden is a knight and Henry is a knave.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(('and', ('telling-truth', 3), ('lying', 7)), ('->', ('telling-truth', 1), ('telling-truth', 2)), ('or', ('lying', 0), ('telling-truth', 0)), ('or', ('telling-truth', 4), ('telling-truth', 3)), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('telling-truth', 2), ('<=>', ('telling-truth', 4), ('telling-truth', 1)), ('telling-truth', 0))