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?
(In reply to
Puzzle Answer by K Sengupta)
Assume that Gladys is a knight. Then Kate's false statement implies that Tim is a liar. Thus, Tom's statement is true in both the parts, so that he must be a knight. This contradicts Gladys' statement that Tom is a liar. Therefore, it follows that Galdys is a liar so that, precisely one of Kate and Tom is a liar and the other is a knight. .......(i)
Also, Galdys is a liar. So at least one part of Tom's statement is false. Therefore, Tom is also a liar.
Then, from (i), it immediately follows that Kate is a knight, and her true statement implies that Tim is also a knight.
Summarizing, we have:
Gladys -> Liar
Kate -> Knight
Tom -> Liar
Tim -> Knight
Explanation for Puzzle Answer
