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 A Fourth Person Problem (Posted on 2006-11-01)
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?

 See The Solution Submitted by K Sengupta Rating: 3.1667 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Confused... | Comment 3 of 16 |
When A says that C is less truthful than B or A, I would read that as "(C is less truthful than A) or (C is less truthful than B)". If Penny's and 3O's solution would hold, this would be a true statement because the second part of it is true. But then A cannot be a liar, so the solution is invalid after all. As far as I see there is no solution. Is this another one of my blunders or am I having trouble to understand A's third statement?
 Posted by JLo on 2006-11-01 12:42:42

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