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Four people (Posted on 2011-11-28) Difficulty: 2 of 5
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?

  Submitted by Math Man    
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Solution: (Hide)
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.


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  Subject Author Date
SolutionNobody answered this yet???Charlie2011-11-29 00:09:26
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