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?

If Timothy tells his friend that the two answers were same, i.e. Timothy's answer is Yes, then his friend has three viable scenarios and therefore cannot be sure. These are:
1. That the answers were Y,Y and that A is a Knight and B is a Liar.
2. That the answers were N,N and that they are both Knights.
3. That the answers were N,N and that they are both Liars.

However, if Tomothy tells his friend that the two answers were not same, i.e. Timothy's answer is No, then his friend has only one viable scenario and therefore can be sure. This is:
1. That the answers were Y,N and that A is a Liar and B is a Knight.

Since upon hearing Timothy's answer his friend has enough information to solve what A and B are, Timothy must have answered No.

Hence,
A is a Liar
B is a Knight

Posted by Sanjay on 2003-05-13 12:27:45