Timothy once visited a land of knights and liars,and met two inhabitants,A and B. He had the following conversation.

Timothy:A,is B a liar?
Timothy hears A's answer,but he will not tell you what it was.
Timothy:B,are you both liars?
Timothy hears B's answer,but he will not tell you what it was.
At this point,I will not tell you whether or not he knew what they were.

He once told his friend what questions he asked,but not what answers he got. The friend did not have enough information,so the following dialogue occurred.

Friend:Were your answers the same?
Timothy's friend hears his answer,and finally the friend has enough information to solve what A and B are.
What are they?

The following table shows what the answers would be to questions 1 and 2 depending on the identities of the two inhabitants:

A B 1 2
Kt L Y Y
Kt Kt N N
L L N N
L Kt Y N

There are three situations in which the two answers are the same, and only one in which they are different. So the friend must have made his conclusion based on the answers being different, and A is a liar and B a knight.

Posted by Charlie on 2003-05-13 04:21:29