The Missing King
The ancient Arabic mathematician, bin Hassad, was crossing a kingdom at the time of a great crisis. The king had gone missing. When the frazzled high officials heard that the great scholar was passing through, they beseached him: "bin Hassad, revered scholar, great mathematician, holder of an unparalled logical eye, can you please help us? Our king has gone missing.
He has left a document making a demand that he will not return until a solution to a conundrum, that has been haunting him, is posted in the public square. O bin Hassad, famous scholar and true friend of all the Arabs, mightiest brain of all. We beg you, help us!
bin Hassad said "Let me see the document. I will help if I can. You are most gracious to let me travel through your lands. It is the least I can do."
bin Hassad looked closely at the king's document. After a short time, he placed a cross on one part of it and said "Copy this drawing and put it in the main square as demanded by the king"
The officials were wide-eyed in amazement at the scholar's confidence and speed. They did what he said. Soon afterwards, the king returned to the palace! He declared a week-long holiday and bestowed great gifts on everyone. He declared to his close friends that this solution enabled him to be free of a personal fear.
Indeed, though he did not elaborate, he was obviously a happier man for the next 20 years of his reign.
Essentially, the problem is a chess position with a missing king which can be thought to have fallen off the board. The question that needs answering is which square must it have been on to give a legal position. The black king is on d1, black bishop on d5, black rook on b5 and white bishop on a4.