There is a land where every inhabitant is either a day-knight or a night-knight. Day-knights tell the truth in the day and lie at night. Night-knights lie in the day and tell the truth at night.

Three inhabitants A, B and C are currently engaged in a conversation. A visitor approaches the three inhabitants and ask each of them their types. They say:

A: If asked, B would claim it is morning.
B: If asked, C would claim it is morning.
C: If asked, A would claim it is night.

Is it day or night? What is the type of each of the inhabitants?

I will assume that day equals morning. Suppose it is day. If A is a day-knight, then B would claim that it is day. Then, B is a day-knight, so C would claim that it is day. Then, C is a day-knight, so A would claim that it is night. Then, A would be lying, which is a contradiction. If A is a night-knight, then B would claim that it is night. Then, B is a night-knight, so C would claim that it is night. Then, C is a night-knight, so A would claim that it is day. That would also be a contradiction. Therefore, it is night. If A is a day-knight, then B would claim that it is night. Then, B is a night-knight, so C would claim that it is day. Then, C is a day-knight, so A would claim that it is day. That is possible. If A is a night-knight, then B would claim that it is day. Then, B is a day-knight, so C would claim that it is night. Then, C is a night-knight, so A would claim that it is night. That is also possible. Therefore, B is different from A and C.

Posted by Math Man on 2013-08-14 22:09:05