|Saturday, October 27, 2001||
THE middle of the 10th century BC: "Here she comes, the wisest and the most beautiful," the arrival of the Queen of Sheba is announced in the court of King Solomon of Israel. "The reason why she has come here is not trade, but you," Solomon's friend whispers in his ear as the Queen enters. Sheba is in what is now called Ethiopia and the reason for its prosperity is the Queen who judges by her brain those who live by the heart.
"The Queen, my
lord, wants to know the reason for the invitation and Israel's interest
in Sheba," says her servant to Solomon." The King says,
"O' beautiful queen, can you not drop your suspicion and consider
me a friend." "Considering the considerable difference of
intelligence between us, a friendship can still be considered, but how
considerably considerate a friend anyone is, that you should consider
only after a lot of consideration, if you consider what I mean,"
says the Queen, with considerable confidence.
"How can I prove myself to be worthy of you," says the King. "Worthy of the Queen of Sheba?" says the Queen. "Her friendship, I mean." The King replies. "For that, you shall have to answer my question," the Queen throws a challenge, "Do you know what's my question?" "No, but I have heard that no one in the world has been able to answer it?" "That's true. One day, my pet rabbit waited, as I left the door, to see which way I should go, and when I started, he raced along to the end of the road, immediately returning to me; again racing to the end of the road and again returning. He did this four times, at a uniform speed, and then ran at my side the remaining distance, which according to my paces measured 27 yards. Afterwards, I measured the distance from my door to the end of the road and found it to be 625 feet. If I walk 4 miles per hour, what is the speed of my rabbit when racing up an down?"
"The distance remaining to be walked side by side with the rabbit was 81 feet, the fourth power of 3 (because the dog returned four times), and the distance to the end of the road was 625 feet, the fourth power of 5. Then, the difference between the speeds (in miles per hour) of the Queen and her rabbit (that is, 12) and the sum of their speeds (20) must be in the same ratio (3 to 5). The rabbit's speed, thus, was 16 miles per hour."
"You are worthy," she says.
"Of your friendship, you mean." "Nay, me," says the
Queen. The Queen returned to Sheba and her marriage to Solomon remained
a secret. That's the story, friends, and now, it's time to go, which
reminds me that my watch shows both date and time in the format HH:MM:SS
Mo/yy. For example, 14:15:56 09/03 is a possible display. It is a
24-hour watch (times run from 00:00:00 to 23:59:59) and leading zeros
are allowed. If all ten digits (0 to 9) appear on the display, what is
the earliest and the latest date and time in the year this could happen?