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.

Members of the Smith family are day-knights and, members of the Jones family are night-knights.

Four inhabitants Art, Barry, Cole and Dan approach a visitor to the island. It is known that precisely two of them are members of the Jones family and the remaining two are members of the Smith family.

They say:

Art: Barry’s last name is Smith.
Barry: Cole belongs to the Jones family.
Cole: Art and Dan are from different families.
Dan: Art and Barry are from the same family.

What are the surnames of the three inhabitants? Is it day or night?

Cole can't be lying, because then Art and Dan would both be telling the truth, which contradicts Dan's statement.

So Cole is telling the truth.  This means Barry is lying, and thus Cole is a Smith and Barry is a Jones.

This contradicts Art's statement, which means Art is also lying.

Thus we have:

Art and Barry are Joneses.

Cole and Dan are Smiths.

It is day. 

Posted by tomarken on 2014-03-03 11:32:34