Logic puzzle. First 10 points for correct answer (w/ correct explanation)...cat=... gets no points.?

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

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!!!!!

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!

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

all are knaves.... no one can or does tell truth all the time! ;P

the cat is a cat. cats can't talk!!!