Home > Logic > Liars and Knights
| A Fourth Person Problem (Posted on 2006-11-01) |
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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?
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Submitted by K Sengupta
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Rating: 3.1667 (6 votes)
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Solution:
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(Hide)
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A is the Liar; B is the Knight; C is the Knave and the fourth person is a Knave.
EXPLANATION:
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.
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An alternative methodology by Old Original Oskar is provided in this location.
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