Knight and knaves and distant planet puzzle

[K Sengupta]

A distant planet is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie.

Eight inhabitants of the planet: Marge, Mel, Betty, Bob, Bill, Carl, Zeke and Alice are busy at a conversation, when a visitor from a neighboring planet stops by and asks each of the eight inhabitants their respective identities. They say:

Marge: “It's not the case that Bob is a knave.”

Mel: “Bill is a knave.”

Betty: “Carl and Zeke are knights.”

Bob: “Neither Mel nor Bill are knaves.”

Bill: “Only a knave would say that Carl is a knave.”

Carl: “I know that Alice is a knave and Zeke is a knight.”

Zeke: “Of Carl and I, exactly one is a knight.”

Alice: “Zeke and Marge are both knights.”

Determine the type of each of the inhabitants from the abovementioned statements.

 

[D H]

Spoiler

Mel is a knight; all of the rest of are knaves.

This assumes that knaves can tell the truth so long as they do so in a compound statement and so long as the compound statement is false.

 

[CRGreathouse]

Spoiler

From Zeke's statement, we deduce that Carl is a knave. Then from Bill's statement we deduce that Bill is also a knave. Thus Bob is a knave and Mel is a knight. Thus Marge and Betty are knaves. Thus Alice and Zeke are also knaves.

It's a pretty easy puzzle.

 

[davee123]

Just a persnickity bit-- I don't like the way Carl's statement is phrased. It's arguable as to whether or not he's making a compound statement "X and Y", or two separate statements "X" and "Y". Assuming the former, everything's peachy. But assuming the latter, it's impossible. I know it's a sticky point of grammar, but the current phrasing translates to:

Carl: “I know that Alice is a knave and I know that Zeke is a knight.”

I would recommend changing it to:

Carl: “I know that Alice is a knave and Zeke is a knight.”

DaveE

 

[D H]

Just a persnickity bit-- I don't like the way Carl's statement is phrased. It's arguable as to whether or not he's making a compound statement "X and Y", or two separate statements "X" and "Y". Assuming the former, everything's peachy. But assuming the latter, it's impossible.

I had the same persnickity problem with Carl's statement.

 

[K Sengupta]

I would recommend changing it to:

Carl: “I know that Alice is a knave and Zeke is a knight.”

DaveE

I confirm having made the requisite amendment in the original post in conformity with the foregoing.