Home > Logic > Liars and Knights
| Four people (Posted on 2011-11-28) |
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You meet four people. Their names are Gladys, Kate, Tom, and Tim. Each one is either a knight or a liar. They say the following statements.
Gladys:Kate and Tom are both liars.
Kate:Tim is a knight.
Tom:Gladys is a knight and Tim is a liar.
What are Gladys, Kate, Tom, and Tim?
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Submitted by Math Man
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Rating: 4.0000 (1 votes)
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Solution:
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Suppose Tom is a knight. Then, Gladys is a knight and Tim is a liar. Since Gladys is a knight, Kate and Tom are both liars. However, Tom is a knight, so that is a contradiction. Therefore, Tom is a liar.
Suppose Kate is a liar. Then, Kate and Tom are both liars. That is what Gladys said, so she is a knight. Also, Kate is lying, so Tim is a liar. Then, Tom's statement is true, so he is a knight. However, we know that Tom is a liar, so Kate is a knight.
Since Kate is a knight, her statement is true, so Tim is also a knight. Also, Kate and Tom are not both liars, so Gladys is a liar.
Gladys:liar
Kate:knight
Tom:liar
Tim:knight
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