# Logic puzzle - truthtellers and liars

I have a question about an island of knights and knaves where knights always speak the truth and knaves always lie.

Now, if A says 'I am a knave and B is a knight' and B says nothing, then is A a knave and B a knave?

• If $A$ is a knight then the statement isn't true,but knights never lie hence $A$ isn't a knight.Now if $A$ is a knave then she's lying hence the statement is false so $B$ is not a knight hence it's a knave. – kingW3 Feb 23 '15 at 8:42
• This should be asked on Puzzling SE? – AvZ Feb 23 '15 at 8:44
• So, my answer is correct? :) – fredsjdhh Feb 23 '15 at 8:45
• I was also wondering if it might ever be possible to eliminate all four possible combinations in problems of this sort. – fredsjdhh Feb 23 '15 at 8:47
• @fredsjdhh If you successfully eliminate all four possible combinations (of A and B being a knight or a knave), then you've proven that the story you've been told is inconsistent, so that story cannot be true. – MarnixKlooster ReinstateMonica Feb 27 '15 at 16:23

Suppose $A$ tells the truth. Then $A$ is a knave, in which case he is lying, contradiction. If he is lying, then $A$ cannot be a knight since otherwise he would be telling the truth. Thus he tells the truth about himself but lies about $B$. Thus both of them are knaves.
Regarding your further question, if $B$ tells that he is a knave, then all cases are eliminated. This is basically the self-refuting paradox (this might be incorrect terminology): "This sentence is false."