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A Fourth Person Problem (Posted on 2006-11-01) Difficulty: 2 of 5
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.)
Solution first post.. | Comment 13 of 16 |

seems a suitlabe title given the day and the fact that I've just registered

 

Taking C's statements the two are mutually exclusive  and they are independant of C. Each statement is either true or false. One must be tru and one must be false. Therefore C must be a knave.

Therefore C cannot be less truthful than both A and B and there fore A's third statement is false and so A cannot be a knight and as C has been established as a knave, A must be a Liar, leaving B as the knight.

B tells us that the fourth person is a knave and as B is a knight, the fourth person must indeed be a knave

 


  Posted by neelia on 2006-11-12 05:21:59
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