We know that Liars always lie about everything, Knights always tell the truth. and Knaves strictly alternate between lying and telling the truth. All the inhabitants of Island T are Knights, Knaves or Liars.

A visiting tourist was busy in conversation with A, B and C who are inhabitants of Island T, when a fourth inhabitant passed them by. It is known that one of A, B, and C is a Knight; the other is a Knave while the remaining one is a Liar. Nothing definite is known about the fourth inhabitant. A, B, and C, say:

A's statements:
1. The fourth person is a Knight like me.
2. Both B and C have been known to speak falsely.
3. C is less truthful than B or myself.

B's statements:
1. The fourth person is a Knave.
2. He (the fourth person) is not like me.

C's statements:
1. If you were to ask the fourth person, he could claim to be a Liar.
2. The fourth person is a Knight.

Out of the first three, who is the Knight, who is the Liar, and who is the Knave? And what is the fourth person?

If A is the Knight,<o:p></o:p>

Then according to (A1) D is a Knight.<o:p></o:p>

According to (A2) & (A3), B is the Knave and C is the Liar<o:p></o:p>

But C tells a truth in (C2)<o:p></o:p>

Therefore A cannot be the Knight.<o:p></o:p>

<o:p> </o:p>

If C is the Knight,<o:p></o:p>

Then according to (C1) D is a Knave<o:p></o:p>

But C then tells a lie in (C2)<o:p></o:p>

Therefore C cannot be the Knight.<o:p></o:p>

<o:p> </o:p>

Since one of A, B or C must be the Knight, it must be B<o:p></o:p>

According to (B1) D is the Knave.<o:p></o:p>

<o:p> </o:p>

(C1) is true and (C2) is false,<o:p></o:p>

Therefore C is Knave.<o:p></o:p>

<o:p> </o:p>

Since one of A, B or C must be the Liar, it must be A.<o:p></o:p>

<o:p> </o:p>

i.e. A is the Liar, B is the Knight, C is the Knave, and D is a Knave.

Posted by Mark on 2006-11-21 20:27:37