Knights and Knaves, both accuse each other of being Knaves. I'm having a bit of an issue with figuring this one out. I ended up saying one has to be a knave, but I feel like it doesn't have a concrete solution, from the contradiction.
Knights always tell the truth, and knaves always lie.    
E says: F is a Knave.
F says: E is a knave.
How many knaves are there?

My thinking is if you assume E is a knight, So what E said must be true. So, F is a knave. Then assume F is a knight, so what F says is true. This gives a contradicition, so E is not a knight and must be a knave. Thus what F says must be true, and F is a knight.  But, it feels like this question could fall into the liar's paradox making what ever solution is found both false and true.
So, what's the logical answer for this one?  
 A: If both were knaves, both would be telling the truth => contradiction.
If both were knights, both would be lying => contradiction.
Therefore, one of them is a knight and the other a knave, which it turns out does not lead to a contradiction: The knight tells the truth about the other being a knave, and the knave lies about the other being a knight, thus both claim the other to be a knave.
A: You were on the right track at the beginning but wandered off it. If $E$ is a knight, then he’s telling the truth, so $F$ is a knave. Is that consistent with $F$’s statement? Yes: when $F$ says that $E$ is a knave, he’s lying (since we assumed that $E$ is a knight), which is what he must do as a knave. Thus, if $E$ is a knight, exactly one of them is a knave, namely, $F$.
Now suppose that $E$ is a knave. Then he’s lying, so $F$ is a knight. And that’s also fine, because $F$’s statement that $E$ is a knave is in fact true, as it should be if he’s a knight. Again we find that exactly one of them is a knave, but this time it’s $E$.
These are the only two possibilities, since $E$ must be either a knight or a knave. Thus, we can be sure that exactly one of the two is a knight and the other a knave, even though we have no way to tell which is which.
