A very special island is inhabited only by knights and liars. Knights always tell the truth, and liars always lie.
Nine inhabitants of the island: Mel, Bart, Sue, Betty, Rex, Zeke, Sally, Zoey and Homer are busy at a conversation. A visitor from a neighboring island stops by and asks each of the nine inhabitants their respective identities. They say:
- Mel: "Only a liar would say that Sally is a liar."
- Bart: "Rex is a liar."
- Sue: "Mel and Homer are liars."
- Betty: "I know that I am a knight and Sally is a liar."
- Rex : "Betty and I are both knights."
- Zeke: "At least one of the following is true: that Sally is a knight or that Sue is a knight."
- Sally:"It's false that Betty is a liar."
- Zoey: "It's not the case that Sue is a liar."
- Homer: "Betty is a liar or Zeke is a liar."
Determine the type of each of the inhabitants from the abovementioned statements.
a) Assume Betty is a knight. then Sally is a liar (based on Betty's statement). But then Sally's lying statement implies Betty is a liar, which is a contradiction. Therefore, Betty is not a knight. Everything else follows quickly from this.
b) Since Betty is a proven liar, Rex's and Sally's statements are false, and Homer's is true.
c) Since Sally is a proven liar, Mel's statement is false.
d) Since Rex is a proven liar, Bart's statement is true.
e) Since Homer is a proven knight, Sue's statement is false.
f) Since Rex is a proven liar, Zoey's statement is false.
g) Since Sally and Sue are both proven liars, Zeke's statement is false.
So the only knights are Bart and Homer, just as Charlie's computer deduced.