Logic puzzle. First 10 points for correct answer (w/ correct explanation)...cat=!
Question: Suppose you are on an island where the inhabitants are either knights (who always tell the truth) or knaves (who always lie). Bettie, George, and Cat are there and each is either a knight or a knave. George and Bettie make the following statements:
George: All of us are knaves.
Bettie: Exactly one of us is a knave.
What is Cat?
Answers: Suppose you are on an island where the inhabitants are either knights (who always tell the truth) or knaves (who always lie). Bettie, George, and Cat are there and each is either a knight or a knave. George and Bettie make the following statements:
George: All of us are knaves.
Bettie: Exactly one of us is a knave.
What is Cat?
not all of them are knaves- George says "all of us are knaves" knaves always lie, so George would be lying, and not all of them are knaves. George can't be a knight because he just called himself a knave and that would be lying if he was a knight, and knights never lie.
so George-knave
Bettie says "exactly one of us is a knave" if she is a knave, then 2 of them are knaves. if she is a knave, then she is lying. so that would mean NOT exactly one of them is a knave. but they can't all three be knaves, because of what George said. Also, George is a knave, so there can't be 0 knaves. so if Bettie is lying, then she is a knave. and if she is lying, there must be 2 knaves. those two would be Bettie and George. and the
CAT = KNIGHT
if Bettie is telling the truth, then only one of them is a knave, and that is George. Then Bettie=knight and
CAT = KNIGHT
so...either way the CAT IS A KNIGHT!
George=knave
Bettie=doesn't matter, either knight of knave
Cat =Knight
Georgre = Knaves, he lied
Bettie = Knight, she tells the truth
Bettie says there is only 1 Knave (she is a knight) and George says the all are Knaves, he lies and is the only Knave that Bettie spoke of. This leaves 2 Knights, bettie and Cat, and I Knave George
the cat is a cat. cats can't talk!!!
Ok.
So, George cannot be a knight, because knights do not lie. Therefor he is a knave.
And because knaves lie, that means that not all of them are knaves.
Now, assuming Bettie is a knight, then she is telling the truth about exactly one of them being a knave(George) which makes Cat a knight.
If Bettie is a knave, then she is lying because two of them are knaves(her and George).
But, Cat is still a knight, even in this situation, because George, who is a knave, always lies and he said that all of them are knaves, but only two of them are, so that makes Cat a knight.
I hope I didn't confuse you, and I hope you got what I was trying to say!:)
Edit: Dammit! I wasn't fast enough!!!!!
all are knaves.... no one can or does tell truth all the time! ;P
cat is a knight.
George said : all of us are knaves. he lied. you told us that knaves always lie and If he was a knight he would say so. but since knaves always lie, his lie was in saying that everyone was a knave. only he is the knave.
Bettie, can be either a knave or a knight. If Bettie is a knave, then that she lied by saying there was exactly one when there were two, she and George. But if Bettie is a knight, she would be telling the truth because she and Cat are knights making it exactly one Knave, George.
Cat has to be a knight under both circumstances. Cat has to be a knight if george is lying and bettie isnt. (all of us are not knaves but there is exactly 1 knave)
Cat has to be a knight if they are both lying. (all of us are not naves but more than one of us is a knave.)
whew!