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. An inhabitant says, "Either I am a day-knight or it is day." Is the inhabitant a day-knight or a night-knight, and is it day or night?

There are four choices. Either inhabitant is:

1) A day-knight at day (tells truth).
2) A day-knight at night (tells lie).
3) A night-knight at day (tells lie).
4) A night-knight at night (tells truth).

If the "either __ or __" statement's "or" is exclusive, it works the following way:

Either T or T = F
Either T or F = T
Either F or T = T
Either F or F = F

1) Cannot be the answer since as a day-knight (T) at day (T), statement is false (but day-knight should be truthful).
2) Cannot be the answer since as a day-knight (T) at night (F), statement is true (but day-knight should be lying).
3) Cannot be the answer since as night-knight (F) at day (T), statement is true (but night-knight should be lying).
4) Cannot be the answer since as a night-knight (F) at night (F), statement is false (but night-knight should be truthful).

Given that none can be the answer, we have to assume the "or" is inclusive, so:

Either T or T = T

So, 1) is the solution. Day-knight in the day.

Posted by Monika on 2012-08-11 20:00:50