The inhabitants of the planet Realmazure are Knights, Pretenders, Prevaricators or Liars. All the statements 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 E, F, G and H of Realmazure were busy in a conversation, when a visitor from a neighboring planet stopped by and asked each of them their identity. They said:

Inhabitant E

1. I am a Pretender
2. G’s second statement is false.
3. F is not a Prevaricator.

Inhabitant F

1. H is a Liar.
2. G’s second statement is true.
3. E’s second statement is true.

Inhabitant G

1. F’s second statement is true.
2. E’s first statement is false.
3. F is a Prevaricator.

Inhabitant H

1. I am a Knight.
2. E is a Pretender.
3. F’s third statement is true.

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

let e1,e2,e3,f1,f2,f3,g1,g2,g3,h1,h2,h3 be the 12 statements.

e2 implies not g2 which in turn implies e1, thus if e2 if true then so is e1, but then e would then have 2 true statements contradicting e1 being true.  Thus e2 is false which in turn makes g2 true.  From these we can get f2 true, f3 false, g1 true, and h3 false.  Now if e1 is true then so is h2, thus h is not a liar and f1 is false, which makes f a prevaricator which makes e3 true which contradicts e1 being true.  Thus e1 is false which makes h2 false and thus h is a liar.  That makes f1 true and f is a pervaricator which makes g3 true and e3 false.  Thus make e a liar and g a knight.

Thus in recap E is a lair, F is a prevaricator, G is a knight, and H is a liar.

Posted by Daniel on 2009-08-02 13:50:53