A very special island is inhabited by only knights and knaves. Knights always te

Question

A very special island is inhabited by only knights and knaves. Knights always tell the truth, and
knaves always lie. The following 5 scenarios all take place on this special island. In all the scenarios you
are asked to determine who the knights are.

1.You meet three inhabitants: Rex, Bart and Marge. Rex claims, 'Bart is a knave.' Bart says, 'Marge
and I are both knights or both knaves.' Marge claims that Bart is a knave. So who is a knight?
2. You meet three inhabitants: Joe, Zippy and Alice. Joe tells you that Alice is a knave and Zippy is a
knight. Zippy says, 'I am a knight or Joe is a knave.' Alice claims that Zippy is a knave. So who is a
knight?
3. You meet three inhabitants: Abe, Zoey and Zippy. Abe says, 'At least one of the following is true:
that Zippy is a knave or that I am a knight.' Zoey says, 'Abe could claim that I am a knave.' Zippy
claims, 'Neither Abe nor Zoey are knights.' So who is a knight?
4. You meet four inhabitants: Homer, Joe, Zed and Betty. Homer tells you that Zed and Betty are not
the same. Joe says that Zed could claim that Betty is a knave. Zed tells you that either Joe is a knight
or Homer is a knave. Betty says, 'I and Homer are dierent.' So who is a knight?
5. You meet four inhabitants: Sue, Alice, Homer and Ted. Sue tells you that Alice is a knave. Alice tells
you that Ted is a knave. Homer claims, 'Alice is a knight and Ted is a knave.' Ted tells you, 'I and
Homer are dierent.' So who is a knight?

Explanation / Answer

1. If Zed is a knight, then Peggy is a knave If Peggy is a knave, then neither Zed nor Peggy are knights. Contradiction. That means Zed is a knave and Peggy is a knight 2. If Abe is a knight, then he and Bozo are not the same. So Bozo is a knave If bozo is a knave then neither Bozo nor Abe are Knights. Contradiction. If Abe is a knave, then he and Bozo are the same, so Bozo is a knave. If bozo is a knave then neither Bozo nor Abe are Knights. So they are both knaves 3. If Alice is a knave, both statements are false, so Zed is a knight and she is a knave If Zed is a knight then Alice is not a knave. Contradiction If Alice is a knight then Zed is a Knave or She is a knight. Since Zed says that Alice is not a knave, he too must be a knight. They are both Knights. 4. If Carl is a knave, he and Bill must be different, so Bill must be a knight. Bill says that only a knave would say Carl was a knave, so Carl is not a knave. Contradiction If Carl is a knight, he and Bill must be the same, so Bill must be a knight Bill says that only a knave would say Carl was a knave, so Carl is not a knave. They are Both Knights 5. If Alice is a Knight, Rex is a Knave If Rex is a Knave, then Bob is a Knave If Bob is a knave, then neither he nor Alice are knights. Contradiction. If alice is a Knave, then Rex is a Knight. If Rex is a Knight, then Bob is a Knight. If Bob is a Knight, then either he or Alice is a Knight. Rex and Bob are the knights. 6. If Sue is a knight, then Bob is a knight. If Bob is a Knight, then Mel is a knight. If Mel is a knight, then Bob is a knave. Contradiction. If Sue is a Knave, then Bob is a Knave. If Bob is a Knave, then Mel is a Knave. If Mel is a Knave, then Bob would say that he was a knight, so his statement is a lie. So they are all Knaves 7. If Bozo is a knight, then Carl is a knave. If Carl is a knave then Joe must also be a knave. If Joe is a knave, then he and Bozo cannot be different. Contradiction If Bozo is a knave, then Carl is a Knight. If Carl is a knight, then Joe must be a knave. If Joe is a Knave, he and Bozo cannot be different. Carl is the knight. 8. If Mel is a knight, then Sally is a Knave. If Sally is a knave, then either Mel or Bozo is a Knight. Sally is a Knave, So Bozo is Lying, so Bozo must be a knave. If Mel is a Knave, then Sally is a Knave If Sally is a knave, then either Mel or Bozo is a Knight. So Bozo must be a knight. If Bozo is a knight, then Sally and Mel must be knights. Contradiction So, Mel is the knight.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.