EXPLAIN EXTENDED

Here is a riddle I read a long time ago in Nauka i Zhizn, a popular Russian science magazine.

The Sultan's Riddle

Once upon a time there was a Sultan who was looking for a vizier to help him rule his country. It became known to him that among the multitudes of his loyal subjects that populated his glorious empire, two were regarded as the most wise and sharp in mind. Their names were Ali-ibn-Wali and Wali-ibn-Ali. The Sultan summoned the men to his palace and ordered them to stand in front of him.

"It has come to my attention that you, Ali, and you, Wali, are the smartest men of all the people of Faith. Is that right?", asked the Sultan, sipping his sharbat. "We do know a thing or two of the beasts of the land and the fish of the sea and stars of the sky, indeed, but your sheer wisdom, o Great Sultan, outshines whatever puny bits of knowledge we might have and makes words coming from our mouths sound like child's babbling", said the wise men, kneeling before the Sultan (as they were truly wise and knew how to talk to a man of high power).

"Good, good," said the Sultan with a sneer, "I see you are good with words but are you as good with numbers? Let me test your knowledge."

"A diviner once came to my palace and revealed two numbers to me," continued the Sultan, "one being my lucky number, and another one being my unlucky number. Each of these numbers is more than one and less than a hundred. I never tell these numbers to anyone as this could put the fate of my empire in enemy's hands. But I am going to multiply those numbers and secretly tell their product to you, Ali, and then I am going to add those numbers and secretly tell their sum to you, Wali. If you are as wise as they say, you will have no problem figuring out those numbers."

And then he ordered the men to approach him and kneel before him, and he whispered the numbers to their ears.

Once Ali raised from his knees, he stood there for a moment, silently moving his lips, and then said: "Unfortunately, о the Brightest One, I cannot tell you those numbers."

"This is true," confirmed Wali, stroking his beard.

"Thank you, most esteemed Wali," said Ali, his face brightening with joy. "Now I can tell those numbers."

"Thank you too, most esteemed Ali," answered Wali. "Now I can tell them too."

And they whispered the numbers to the ear of the astonished Sultan, and they turned out right. And they both were appointed viziers.

Can you tell those numbers?

At first glance, this riddle seems impossible to solve. However, if we carefully read and parse what did Ali and Wali say, we can easily solve this riddle too. And to make things even more fun, we'll do that in SQL.

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