The inhabitants of planet Realmazure are Knights, Pretenders, Prevaricators or Liars. All the statements made by a Knight are true, a Pretender will tell precisely one true statement, a Prevaricator will tell precisely two true statements, and all the statements made by a Liar will be false.

Four inhabitants N, O, P and Q of Realmazure are busy in a conversation, when a visitor from a neighboring planet stops by and asks each of them their identity. They say:

Inhabitant N

1. I am a Knight.
2. P is a Knight.
3. P’s second statement is true.

Inhabitant O

1. Q’s second statement is true.
2. N’s first statement is true.
3. P is a Knight.

Inhabitant P

1. N is a Pretender.
2. O’s third statement is false.
3. O is a Pretender.

Inhabitant Q

1. P is a Prevaricator.
2. O’s third statement is true.
3. O is a Pretender.

Determine the type of each of the four inhabitants in terms of the above statements.

Inhabitant N is a Pretender [F,F,T].

1. N is NOT a Knight.
2. P is NOT a Knight.
3. P's second statement is true, (i.e., P is not a Knight).

Inhabitant O is a Liar [F,F,F]

1. Q's second statement is NOT true, (i.e., P is not a Knight).
2. N's first statement is NOT true, (i.e., N is not a Knight).
3. P is NOT a Knight.

Inhabitant P is a Prevaricator [T,T,F].

1. N is a Pretender.
2. O's third statement is false, (i.e., P is not a Knight).
3. O is NOT a Pretender.

Inhabitant Q is a Pretender [T,F,F].

1. P is a Prevaricator.
2. O's third statement is NOT true, (i.e., P is not a Knight).
3. O is NOT a Pretender.

Posted by Dej Mar on 2010-01-17 15:29:05