Raymond Smullyan's Knights and Knaves
Raymond Smullyan, my favorite mathematician, posed a large number of questions involving the Isle of Knights and Knaves. Inhabitants are either knights, who always tell the truth, or knaves, who always tell falsehoods.
One of the best Knight and Knave problems is Og and Bog from Smullyan’s book Logical Labyrinths
Og and Bog are brothers living on the Isle of Knights and Knaves, and one of them is the chief.
- Og says: Bog is the chief and he is a knave!
- Bog says: Og is not the chief, but he is a knight.
Which one is the chief?