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 8 scenarios all take place on this special island. In all the scenarios you
are asked to determine who the knights are.

1. You meet two inhabitants: Zed and Peggy. Zed says that Peggy is a knave. Peggy tells you, 'Either
Zed is a knight or I am a knight.' So who is a knight?
2. You meet two inhabitants: Abe and Bozo. Abe says, 'I and Bozo are not the same.' Bozo tells you, 'I
am a knight or Abe is a knight.' So who is a knight?
3. You meet two inhabitants: Alice and Zed. Alice tells you, 'At least one of the following is true: that
Zed is a knave or that I am a knight.' Zed says, 'It's not the case that Alice is a knave.' So who is a
knight?
4. You meet two inhabitants: Carl and Bill. Carl says, 'I and Bill are both knights or both knaves.' Bill
claims, 'Only a knave would say that Carl is a knave.' So who is a knight?
5. You meet three inhabitants: Alice, Rex and Bob. Alice tells you that Rex is a knave. Rex tells you
that it's false that Bob is a knave. Bob claims, 'I am a knight or Alice is a knight.' So who is a knight?
6.You meet three inhabitants: Sue, Bob and Mel. Sue tells you that only a knave would say that Bob is
a knave. Bob claims that it's false that Mel is a knave. Mel tells you, 'Bob would tell you that I am
a knave.' So who is a knight?
7. You meet three inhabitants: Bozo, Carl and Joe. Bozo says that Carl is a knave. Carl tells you, 'Of
Joe and I, exactly one is a knight.' Joe claims, 'Bozo and I are dierent.' So who is a knight?
8. You meet three inhabitants: Mel, Sally and Bozo. Mel tells you, 'Sally and I are not the same.' Sally
tells you that Mel and Bozo are knaves. Bozo claims, 'Neither Sally nor Mel are knaves.' 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.

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