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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?

  Submitted by K Sengupta    
Rating: 3.1667 (6 votes)
Solution: (Hide)
A is the Liar; B is the Knight; C is the Knave and the fourth person is a Knave.


Assume that C's first statement is false. If so, the Knight must be either A or B. If A is the Knight, that means that A's third statement must be true and C ia a Liar, which means that C's second statement must be false, which means that A cannot be the Knight, so it must be B. This is however not feasible, because if C were the Liar and B were the Knight; A must be the Knave; but A's first statement would be false and hence A must be the Liar.

Therefore, C's first statement must be true.This means that the fourth individual is a Knave, as only a Knave can claim to be a Liar. It follows that B's first statement is true, and B is either the Knave or the Knight. C's second statement must be false, otherwise both A and C would be Knights. Hence, C is the Knave, B is the Knight and A is the Liar. Consequently, the fourth person must be the Knave.

An alternative methodology by Old Original Oskar is provided in this location.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolAndre2010-05-28 18:30:31
first postRachel2006-12-22 14:08:58
SolutionSolutionMark2006-11-21 20:27:37
Solutionfirst post..neelia2006-11-12 05:21:59
SolutionApproach 2nikki2006-11-08 12:38:41
re: SolutionDej Mar2006-11-08 01:07:36
SolutionSolutionnikki2006-11-07 18:07:57
re(2): Confused...Dej Mar2006-11-03 21:08:19
re: SolutionEric2006-11-03 15:52:44
SolutionDemplez2006-11-03 10:31:38
re(3): Confused...JLo2006-11-02 13:30:32
re(2): Confused...Penny2006-11-02 05:50:19
re: Confused...Penny2006-11-01 13:39:32
QuestionConfused...JLo2006-11-01 12:42:42
SolutionSwift Simple SolutionOld Original Oskar!2006-11-01 10:52:25
SolutionSolutionPenny2006-11-01 09:44:23
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