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BGonline.org Forums
Counterfeit Checker
Posted By: Nack Ballard
Date: Thursday, 14 February 2019, at 10:36 p.m.
King Shahryar, who rules over India and China, has a fondness not only for his own power and riches, but also for... backgammon.
Upon discovering that one of his subjects -- Aladdin -- shared his ancient passion, the king invited him to his palace to play.
A happy but poor man, Aladdin could not afford to play for money. However, he enjoyed the fine trappings of the castle, the exquisite food and wines, and the royal treatment. And the two of them were a good match at the board.
Perhaps what impressed the visitor most was the luster and texture of the thick gold and silver coins that were used for checkers in their backgammon games. Aladdin's manifest interest in these shiny checkers did not escape his leige's attention.
One afternoon, when Aladdin showed up at the usual time, there were six gold checkers/coins placed in his home board, one on each of the six points.
Seeing that his layout had been noticed, the man with the crowned head exclaimed, "I have a proposition for you!" Aladdin raised his eyebrows politely, encouraging his majesty to elaborate.
"These six checkers all weigh exactly the same, except for one, which is a counterfeit and has a slightly different weight. It is either lighter or heavier and I'm not telling you which. You cannot tell the difference with your human senses, but I have a sensitive enough balance scale that you can use. The catch is that you are allowed only TWO weighs to identify the counterfeit."
"And if I do?" queried Aladdin.
"Then you get to keep all six coins." The emperor gestured grandly.
"And if I don't? Or if I guess wrong?" "Or if I do one weigh and change my mind?" The younger man ventured, his head spinning with possibilities.
"I will claim your lovely wife as my own bride." Unable to contain his excitement, the monarch's voice trailed off into an involuntary squeak.
This would be a fate worse than death to Aladdin. "Can I decline the proposition?"
"Yes, in which case we'll forget the whole thing." The sovereign was clearly disappointed at the prospect, but he always kept his word.
The peasant had been absent-mindedly fondling the checkers. "I see now that one of them is marked with an "X" on the underside. What does that mean?"
"Ah yes, I forgot," the supreme ruler rejoined. That coin is NOT the counterfeit; it weighs the same as the others. You may use it in either or both weighs, or not, as you wish. The other conditions still stand.
Should Aladdin accept his lordship's high-stakes proposition?
Nack
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