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

1. You meet five inhabitants: Bob, Zoey, Peggy, Betty and Abe. Bob says, 'Either Abe is a knave or I
am a knight.' Zoey tells you that it's false that Peggy is a knave. Peggy tells you that Betty and Abe
are both knights or both knaves. Betty claims that Bob and Abe are not the same. Abe tells you,
'Zoey would tell you that Bob is a knight.' So who is a knight?
2. You meet six inhabitants: Rex, Marge, Zed, Bob, Homer and Bill. Rex says, 'Homer and Marge are
knaves.' Marge claims that it's false that Bill is a knave. Zed tells you that only a knave would say
that Rex is a knave. Bob says that at least one of the following is true: that Rex is a knight or that
Zed is a knave. Homer claims that either Marge is a knight or Bill is a knight. Bill tells you, 'Rex
could claim that I am a knave.' So who is a knight?
3. You meet six inhabitants: Rex, Dave, Zeke, Sally, Zoey and Bart. Rex says, 'Sally and Dave are
knaves.' Dave claims that it's not the case that Zoey is a knave. Zeke says, 'I am a knight or Rex is
a knave.' Sally tells you that at least one of the following is true: that Dave is a knave or that Zeke
is a knight. Zoey tells you, 'Rex could say that Bart is a knave.' Bart says, 'Zeke would tell you that
Rex is a knave.' So who is a knight?
4. You meet eight inhabitants: Sue, Bob, Mel, Ted, Alice, Marge, Zeke and Carl. Sue tells you that Carl
is a knight or Zeke is a knight. Bob tells you, 'At least one of the following is true: that Ted is a
knight or that Zeke is a knight.' Mel says that Marge is a knave. Ted claims that Carl and Alice are
both knights or both knaves. Alice claims, 'Only a knave would say that Bob is a knave.' Marge tells
you that Carl could claim that Alice is a knave. Zeke tells you, 'Either Marge is a knave or Ted is a
knave.' Carl claims, 'I and Marge are not the same.' 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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