Way to make my head hurt!!!!!!!! [:D]
The Riddle :
Inspector Craig Visits Transylvania
Inspector Craig of Scotland Yard was called to Transylvania to solve some cases of vampirism. Arriving there, he found the country inhabited both by vampires and humans. Vampires always lie and humans always tell the truth. However, half the inhabitants, both human and vampire, are insane and totally deluded in their beliefs: all true propositions they believe false, and all false propositions they believe true. The other half of the inhabitants are completely sane: all true statements they know to be true, and all false statements they know to be false. Thus sane humans and insane vampires make only true statements; insane humans and sane vampires make only false statements. Inspector Craig met two sisters, Lucy and Minna. He knew that one was a vampire and one was a human, but knew nothing about the sanity of either. Here is the interview :
Craig (to Lucy) : Tell me about yourselves?
Lucy : We are both insane.
Craig (to Minna) : Is that true?
Minna : Of course not !
From this interview alone, Craig was able to prove which of the sisters was the vampire. Who was it?
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The Solution:
There are only two possible cases that could occur given the statements of the girls:
Case 1: They are both insane, which would mean that Lucy must be telling the truth. Since the only insane creature that can tell the truth is the vampire, this makes Minna a human, and since she must be lying by saying that Lucy's statement is false, this makes her an insane human.
Case 2: They are both sane. This could occur if Lucy's statement is a lie, which would make her either an insane human or a sane vampire. This would mean that Minna is telling the truth, which would make her either a sane human or an insane vampire. If Minna were an insane vampire, then her statement would be true, meaning that both must be not be insane. In this case, Lucy must be a sane human, which would tell the truth; however since Lucy's statement is that they are both insane, this would be a lie in this case, so we can rule out the possibility that Minna is an insane vampire and that Lucy is a sane human (at the same time). This leaves Minna being a sane human, which makes her statement true, meaning that both are not insane. Lucy would therefore be a vampire (since we know that one is a vampire and one is a human) and since her statement of them both being insane would be false, she must be a sane vampire. Since this condition agrees with the first condition in this argument, then this is the only possibility for this case.
Summary :
The only possible outcomes are as follows :
Lucy is an insane vampire, and Minna is an insane human.
OR
Lucy is a sane vampire, and Minna in a sane human.
Conclusion :
In either of the cases, Lucy must be a vampire, and Minna must be a human.
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