A problem with vampires
Sherlock Holmes went to Transilvania to solve some cases of vampirism. Getting in the village where he had to inspect the case he found it populated by vampires and humans alike.
Vampires always lie and humans always tell the truth. Moreover half of the citizens are insane (mentally that is anyway) both vampires and humans while the other part is sane.
Crazy people consider true all false statements and false all true statements , while the sane citizens do exactly the contrary considering true true statements and false the other. Therefore sane humans and crazy vampires say just true statements and crazy humans and sane vampries make just false statements.
At a moment of his investigation Sherlock meets 2 sisters out of which by his unsurpassed deductive skills of course he immediately found that one is a human and the other is a vampire but since all human mental capacities are limited and anyway even if they wouldn't they would still be limited in deductive capacities he didn't knew how sane are them anyway.
Therefore Sherlock asks A about them and A replies "We are both crazy!" , then asks B about what A said and receives from B the reply : "Of course not!!" anyway.
From this discussion Sherlock , with his completely flawless logic and reasoning found out who is a vampire and who isn't anyway.
Question who is a vampire anyway ?
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We will show, that B can't be a vampire.
If we presume, that B is a vampire, then:
1.) A has to be a human.
2.) B cannot be crazy, because crazy vampires always tell the truth, which means that her statement is true and both sisters are crazy.
Therefore, A has to be a crazy human. However, this is impossible, as crazy humans always give false statements and she wouldn't be able to say that they are both crazy. (contradiction)
3.) B cannot be a sane vampire, either, because that would mean, that A was not correct (has to be a crazy human), but then B is telling the truth (what sane vampires wouldn't do). (contradiction again)
For the reasons above, the vampire is A .
(And now it is easy to find out, that they are either both sane or both crazy: either a crazy vampire is telling the truth, when stating that both are crazy and a crazy human denies it incorrectly; or a sane vampire claims that falsely and a sane human denies it correctly).