The last shall be first
bin Hassad, the famous ancient Arabic mathematician was visiting the Sultan of Ben Gazzi when the Sultan came to him with a request.
"O bin Hassad, Famed mathematician! Holder of the Logical Eye! I have a problem which I can trust you to help me with"
"In any way I can, Greatest of all Sultans!", declared bin Hassad
"Well", said the Sultan, "The King of El Gabara has offered me a number of his beautiful daughters. All his girls are one of ten types and so have been named after one of the ten digits, 0-9. The king tells me that he once lined up a certain number of these girls in such a way that when a daughter called 8 was moved from the last position to the first position, the number represented by the line-up exactly doubled. Are you with me bin Hassad?
"Of course, I hope they are all beautiful and please your eye Sultan", said bin Hassad, "this is simply about a number which ends in 8 but which doubles when the 8 is taken off and put as the first digit!"
The King went on, "Well, you must be right! Also there is no doubt, from trusted reports, about their beauty. The thing is, when I visit, I can have these girls only if I can line them up in the way the king did. Now, I'm no mathematician, O bin Hassad. But I rule my people with fairness and they have a good life, and so I have other saving graces. Can you help me?
"Why, of course I can, your Excellancy. You are too modest. Your qualities are of a far higher order than the merely mathematical. I take it that all the daughters will wear their names on them so you can clearly see them ...
What line-up did bin Hassad suggest?