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 J, K, L and M of Realmazure were busy in a conversation, when another visitor from a neighboring planet stopped by and asked each of them their identity. They said:

Inhabitant J

1. M is a Pretender.
2. K’s first statement is true.
3. M’s third statement is true.

Inhabitant K

1. J is a not a Knight.
2. J’s first statement is true.
3. M is a Prevaricator.

Inhabitant L

1. J is a Prevaricator.
2. M is a Liar.
3. K’s second statement is false.

Inhabitant M

1. L’s third statement is true.
2. I am a Pretender.
3. J is a Knight.

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

to start with we have that if J3 is true then M3 is true which implies J is a knight, but then J2 must be true and thus J is not a knight. Thus J3 must be false. If J3 is false then M3 is false and since J is not a then K1 is true and thus J2 is true.

next if M1 is true then L3 is true and thus K2 is false thus J1 is false thus M is not a pretender thus M2 is false, but then M has told only 1 true statement and thus is a Pretender thus contradicting M2 being false.  Thus M1 is false, L3 is false, then K2 is true and J1 is true.  Then M is a Pretender and M2 is true.

Since M is a Pretender then L2 is false and since J is a Prevaricator then L1 is true which makes L a Pretender, and finally since M is a Pretender then K3 is false and thus K is a Pretender.

So in summary J is a Prevaricator, K is a Prevaricator, L is a Pretender, and M is a Pretender.

**edited to correct error Charlie pointed out**

Edited on September 23, 2009, 2:01 pm

Posted by Daniel on 2009-09-23 11:50:29