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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 Solution | Comment 10 of 16 |

C cannot be a knight. If he were a knight, then the fourth person would have to be a knight by C2. But knights can never claim to be a liar, so C1 must be false, which means C cannot be a knight.

C cannot be a knight. If he were a knight, then the fourth person would have to be a knight by C2. But knights can never claim to be a liar, so C1 must be false, which means C cannot be a knight.

C cannot be a liar. If he were a liar, then the fourth person would be a knave by C1. If the fourth person is a knave, then A1 is false and A3 is true (since C is assumed to be a liar and liars are truthful 0% of the time). Neither a Liar, nor a Knight, nor a Knave can have their first and third statements be true/false or false/true, which means C cannot be a liar.

Therefore C is a knave.

A cannot be a knight. If he were a knight, then C would have to be a liar by A3 (since a Liar is truthful 0% of the time, a knave 50% and a knight 100%, saying C is less truthful than the other two means C must be a liar). But C is a knave, so A cannot be a knight.

Therefore A is a liar.

Therefore B is a knight.

Therefore the fourth person is a knave.

Edited on November 7, 2006, 6:14 pm
  Posted by nikki on 2006-11-07 18:07:57

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