Vampire Holiday


THE PROBLEM:

The eve of St. George (April 23) is a night of terror in Romania. It is said to be the night when evil beings, such as vampires, witches and demons, wander the earth looking for victims.

Last St. George's Eve, seven vampires (Alexandru, Bogdan, Mircea,Petru, Radu, Stefan, and Vlad) all left their resting places in the cemeteries of several small villages in Moldavia and met with each other at a secret spot in the Carpathian Mountains. Each belongs to one of the four types of Romanian vampires: the Strigoii, who always tell the truth; the Nosferatu, who never do; the Moroii, who alternate between true and false statements, always beginning with a true one; and the Pricolici, who also alternate, but always beginning with a false one.

The seven (whose surnames in life were Amzulescu, Florescu, Grigorescu, Otescu, Pavelescu, Radulescu and Vulpescu) made the following statements. Can you find each vampire's full name and vampire type?

Amzulescu said:
  1. I'm either a Strigoi or a Pricolici.
  2. Otescu is the only vampire of his type here tonight.
Florescu said:
  1. Mircea isn't Nosferatu.
  2. Petru and Vulpescu are the same type of vampire.
  3. I'm a Nosferatu.
Grigorescu said:
  1. Amzulescu's first name is Radu.
  2. Alexandru and Radulescu are different types of vampires.
  3. I'm a Pricolici.
Otescu said:
  1. I'm not a Pricolici.
  2. Radulescu is a Strigoi.
Pavelescu said:
  1. Bogdan and Amzulescu are different types of vampires.
  2. Stefan is a Pricolici.
  3. I'm not a Moroi
Radulescu said:
  1. I'm a Moroi.
  2. Vulpescu is a Nosferatu.
Vulpescu said:
  1. Otescu is a Pricolici.


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THE SOLUTION:

Florescu claims to be Nosferatu (5). Nosferatu always lie, so this cannot be a true statement, and Florescu must be a Pricolici. That makes (3) false and (4) true.

Grigorescu claims to be a Pricolici (8). If he is a Pricolici, then (8) would be a false statement, so he is Nosferatu and (6) and (7) are false, too.

Pavelescu claims that he is not a Moroi (13). If this is a false statement, he can be either Nosferatu or a Pricolici, but then he would be telling the truth about not being a Moroi, so (13) must be true. Since he isn't a Moroi, he must be a Strigoi, making (11) and (12) true statements, too.

Otescu claims that Radulescu is a Strigoi (10). If this is true, then Radulescu always tells the truth. But Radulescu says that he's a Moroi, so (10) must be false, and Otescu cannot be a Strigoi. Otescu is either Nosferatu or a Moroi but not a Pricolici, making (9) true. Therefore, Otescu is a Moroi.

Knowing that Otescu is a Moroi, Vulpescu's statement that Otescu is a Pricolici (16) is false. Having made one false statement, Vulpescu cannot be a Strigoi (17), so he is Nosferatu. This makes (15) true, so Radulesco must be either a Strigoi or a Pricolici. But Radulesco claims to be a Moroi (14) which would make (15) false, so (14) is false, and Radulesco is not a Moroi. He is a Pricolici.

Finally, Amzulescu claims to be either a Strigoi or a Pricolici (1). If this statement is true, he is a Strigoi and (2) is also true. If (1) is false, he cannot be Strigoi, Pricolici or Moroi and must be Nosferatu. But that would make (2) also false, which is not possible because Otescu IS the only Moroi there. So Amzulescu is a Strigoi.


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To recap, Amzulescu and Pavelescu are both Strigoii, Florescu and Radulescu are Pricolicis, Grigorescu and Vulpescu are Nosferatu, and Otescu is a Moroi. And their statements are as follows:

Amzulescu said:
  1. I'm either a Strigoi or a Pricolici.  (True)
  2. Otescu is the only vampire of his type here tonight.   (True)
Florescu said:
  1. Mircea isn't Nosferatu.  (False)
  2. Petru and Vulpescu are the same type of vampire.  (True)
  3. I'm a Nosferatu.  (False)
Grigorescu said:
  1. Amzulescu's first name is Radu.  (False)
  2. Alexandru and Radulescu are different types of vampires.  (False)
  3. I'm a Pricolici.   (False)
Otescu said:
  1. I'm not a Pricolici.   (True)
  2. Radulescu is a Strigoi.  (False)
Pavelescu said:
  1. Bogdan and Amzulescu are different types of vampires.   (True)
  2. Stefan is a Pricolici.   (True)
  3. I'm not a Moroi  (True)
Radulescu said:
  1. I'm a Moroi.  (False)
  2. Vulpescu is a Nosferatu.  (True)
Vulpescu said:
  1. Otescu is a Pricolici.   (False)
  2. I'm a Strigoi.  (False)



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Now let's figure out each vampire's first name.

Florescu says truthfully that Vulpescu and Petru are the same type of vampire (4). Vulpescu is Nosferatu, so Grigorescu must be Petru. Grigorescu says falsely that Alexandru and Radulescu are different types of vampires (7). Radulescu is a Pricolici, so the other Pricolici (Florescu) must be Alexandru. Florescu says falsely that Mircea is not Nosferatu (3), so Mircea must be Vulpescu. Pavelescu says truthfully that Stefan is a Pricolici, so Stefan is Radulescu.

By elimination, Amzulescu cannot be Bogdan (11) or Radu (6), so he is Vlad. Pavelescu cannot be Bogdan (11) so he is Radu. Bogdan is Otescu.

THE ANSWERS

Vlad Amzulescu - Strigoi
Radu Pavelescu - Strigoi
Petru Grigorescu - Nosferatu
Mircea Vulpescu - Nosferatu
Alexandru Florescu - Pricolici
Stefan Radulescu - Pricolici
Bogdan Otescu - Moroi