[Guest]

The inhabitants of an island are Truthtellers, Pretenders, Prevaricators or Liars.

All the statements by a Truthteller 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 P, Q, R and S of that island were busy in a conversation, when a visitor stopped by and asked each of them their identity. They said:

Inhabitant P:

1. I am a Pretender.

2. R’s second statement is false..

3. Q is not a Prevaricator.

Inhabitant Q:

1. S is a Liar.

2. R’s second statement is true.

3. P’s second statement is true.

Inhabitant R:

1. Q’s second statement is true.

2. P’s first statement is false.

3. Q is a Prevaricator.

Inhabitant S:

1. I am a Truthteller.

2. P is a Pretender.

3. Q’s third statement is true.

Determine the type of each of the four inhabitants on the basis of the above statements.

[Guest]

I enjoyed this one

P = Liar, Q = Prevaricator, R = Truthteller, S = Liar

OK, starting from the top:

If P1 is true, then P2 is false, and so R2 is true = P1 is false --> Broken, so P1 is FALSE. This means P is a Prevaricator or Liar.

If P2 is true, then R2 is false, and so P1 would be true --> Wrong, so P2 is FALSE. This only leaves the possibility of P being a Liar, so P3 is also False.

Since P3 is false, Q is a Prevaricator. Let's find the one false statement. We know Q3 is FALSE because P is a Liar. So, Q1 and Q2 are True.

Since Q1 is true, S is a Liar. S1, S2 and S3 are False.

Thus we know that P = FFF and Q = TTF. This means R = TTT, so R is a Truthteller.

P = FFF, Q = TTF, R = TTT, S = FFF

[preflop]

see spoiler

methinks you have a problem

Your logic does not work - lets look at it

P cant be the truth teller - if so his first statement is a lie.

cant be a pretender - if so his first statement is the truth and his second is the truth and he is allowed only one true statement

cant be a Prevaricator - if so his first is a lie, and the other two must be the truth, but this cant happen because if his second statement is true he must be a pretender.

P must be a liar

Q if P is a liar Q must be a Prevaricator

S if P is a liar S can't be a truth teller so that makes him the pretender

leaving R as the truth teller.

But wait .....

Q cannot be a Prevaricator because he has only 1 truthful statement in this scenario

Q statement 1 is false (P is the liar not S)

Q statement 2 is true (R is a truth teller so this statement must be true)

Q statement 3 is false (stating P's 2nd statement is the truth, but that statement calls R(the truth teller) a liar)

It looks to me like you have a mistake in the puzzle somewhere.

[Guest]

see spoiler

methinks you have a problem

Your logic does not work - lets look at it

P cant be the truth teller - if so his first statement is a lie.

cant be a pretender - if so his first statement is the truth and his second is the truth and he is allowed only one true statement

cant be a Prevaricator - if so his first is a lie, and the other two must be the truth, but this cant happen because if his second statement is true he must be a pretender.

P must be a liar

Q if P is a liar Q must be a Prevaricator

S if P is a liar S can't be a truth teller so that makes him the pretender

leaving R as the truth teller.

But wait .....

Q cannot be a Prevaricator because he has only 1 truthful statement in this scenario

Q statement 1 is false (P is the liar not S)

Q statement 2 is true (R is a truth teller so this statement must be true)

Q statement 3 is false (stating P's 2nd statement is the truth, but that statement calls R(the truth teller) a liar)

It looks to me like you have a mistake in the puzzle somewhere.

The OP never said that each group had to be represented exactly once.

[CaptainEd]

see spoiler

methinks you have a problem

Your logic does not work - lets look at it

P cant be the truth teller - if so his first statement is a lie.

cant be a pretender - if so his first statement is the truth and his second is the truth and he is allowed only one true statement

cant be a Prevaricator - if so his first is a lie, and the other two must be the truth, but this cant happen because if his second statement is true he must be a pretender.

P must be a liar

Q if P is a liar Q must be a Prevaricator

S if P is a liar S can't be a truth teller so that makes him the pretender

leaving R as the truth teller.

But wait .....

Q cannot be a Prevaricator because he has only 1 truthful statement in this scenario

Q statement 1 is false (P is the liar not S)

Q statement 2 is true (R is a truth teller so this statement must be true)

Q statement 3 is false (stating P's 2nd statement is the truth, but that statement calls R(the truth teller) a liar)

It looks to me like you have a mistake in the puzzle somewhere.

Well, preflop, your analysis sounds like you think that all four types of inhabitants have to be present. I don't see that requirement in the OP.

(((Oops, everything I was going to say, JB already said--good job, jb_riddler!)))

Edited March 17, 2009 by CaptainEd

[Guest]

I have

Q = Truth

R = Prev (Third statement is false)

P= Pretender (First and Third are false)

S = Liar

[Guest]

Wait - my last answer was wrong

[Guest]

P is a Prev... (1 F, 2 and 3 T)

Q is a pretender (only #3 is T)

R is a liar

S is a pretender (only #3 is T)

[Guest]

P is a Prev... (1 F, 2 and 3 T)

Q is a pretender (only #3 is T)

R is a liar

S is a pretender (only #3 is T)

jbk, you are on the right track with your assumption, but...

If P2 is true, then R2 would be false. If R2 is false, then P1 must be true. But you already said P1 was false.

[Guest]

P & S are both liars

Q is a Prev

R is "The Truth"

[Guest]

I found it easier to start the puzzle by removing the references from the statements and changing them into definitive statements.

P:

1) I am a Pretender

2) I am a Pretender

3) Q is not a Prevaricator

Q:

1) S is a liar

2) P is not a Pretender

3) P is a Pretender

R:

1) P is not a Pretender

2) P is not a Pretender

3) Q is a Prevaricator

S:

1) I am a Truthteller

2) P is a Pretender

3) P is a Pretender

From there it's easy to follow the solutions already posted.

[Guest]

Inhabitant P:(liar)

1. I am a Pretender. (false)

2. R’s second statement is false.. (false)

3. Q is not a Prevaricator. (false)

Inhabitant Q:(prevaricator)

1. S is a Liar. (true)

2. R’s second statement is true. (true)

3. P’s second statement is true. (false)

Inhabitant R: (truthteller)

1. Q’s second statement is true.(true)

2. P’s first statement is false. (true)

3. Q is a Prevaricator.(true)

Inhabitant S: (liar)

1. I am a Truthteller. (false)

2. P is a Pretender. (False)

3. Q’s third statement is true. (false)

Edited March 17, 2009 by Leza

[Guest]

Thank you so much for the tip. I'll have to remember it for future puzzles.

I found it easier to start the puzzle by removing the references from the statements and changing them into definitive statements.

P:

1) I am a Pretender

2) I am a Pretender

3) Q is not a Prevaricator

Q:

1) S is a liar

2) P is not a Pretender

3) P is a Pretender

R:

1) P is not a Pretender

2) P is not a Pretender

3) Q is a Prevaricator

S:

1) I am a Truthteller

2) P is a Pretender

3) P is a Pretender

From there it's easy to follow the solutions already posted.

[Guest]

P = Prev

Q = Pret

R = Truth

S = Liar

[Guest]

P = Liar, Q = Prevaricator, R = Truthteller, S = Liar

For detailed explanation, refer to jb_riddler’s methodology in the comments. As jb_riddler has rightly explained, it is not required in terms of the problem text that all four types of inhabitants have to be present.

I thank the members for their considered views on the puzzle.