Home > Logic > Liars and Knights
| Three people (Posted on 2011-02-14) |
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You meet three people, A, B, and C. Each one is either a knight or a liar. A and B make these statements.
A:We are all of the same type.
B:A and C are of different types.
What are A, B, and C?
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Submitted by Math Man
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Solution:
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Suppose A is a knight. Then, they are all of the same type, so they are all knights. Then, B would be lying about A and C being of different types. That is impossible, so A is a liar. Therefore, they are not all of the same type, so either B or C is a knight. If B is a liar, then A and C are of the same type, so C is a liar and they are all liars. However, either B or C is a knight. Therefore, B is a knight. Since B is a knight, A and C are of different types, so C is a knight.
A:liar
B:knight
C:knight
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Subject |
Author |
Date |
 | Solution | Mike Jones | 2011-02-15 04:35:07 |
 | spoiler | Ady TZIDON | 2011-02-14 13:32:25 |
| Solution | hoodat | 2011-02-14 13:12:12 |
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