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B Dividing the jewel maker's diamonds -Riddle (Easy)

  1. Jun 18, 2016 #1
    After the even greater success of the previous riddle (it didn't even receive a post, but it's known that the sequels aren't often as successful as the original), it's time to bother you yet again with the 3rd installment of the franchise, which will hope to do better than the 2nd one! How will it do it? By employing another Hollywood tactic- ripping off someone who made successful riddles! Yes, this one isn't original, it comes from Malba Tahan's (real name: Júlio César de Mello e Souza) book "The Man Who Counted", which is a great collection of math and logic puzzles. This one wasn't originally intended to be a puzzle, but I modified it a bit. Still, you have to know that the solution isn't exactly mathematically/logically rigorous, it's just very surprising and fun. Many thanks to micromass for inspiring this series!

    The story
    After beating the dice players in their own game (refer to "A whole bunch of dices"), and winning 2 chalices, lots of gold coins, and 1 precious diamond made by the kingdom's finest jewell maker and recently deceased Phidias Bedeer, Theseus lost his riches yet again, playing other, less conventional games. All that he's left with is the diamond he won. He decides to sell the diamond in the jewelry market for money. What he finds there is Bedeer's 3 notoriously naive sons arguing about their father's last will. Apparently, they and their lawyer can't figure out how to divide the 35 diamonds their father left them according to their father's last will. Theseus asks one of the sons to explain what the problem is.

    The problem
    According to Bedeer's last will (who was infamously bad at math), 1/2 of his 35 diamonds are to be given to the oldest one of his sons, 1/3 to the second oldest, and 1/9 to the youngest son. The problem is that neither 1/2, 1/3 and 1/9 of 35 are integer numbers, and they don't want to cut the precious diamonds in half or anything. After thinking about it, Theseus decides to give them his own diamond to add them to the 35.

    The Question
    Was Theseus (known for his greed) just in a good mood when he gifted that diamond, or did he have something in the back of his mind that would benefit him? What's the solution he will propose?

    Alright, it's not much of a puzzle, but it's got a fun solution. Here it is for anyone who wants to see it:

    Now with the added diamond, it's 36 diamonds that have to be divided instead. 1/2 of 36 is 18, 1/3 is 12, and 1/9 is 4. That makes us 18+12+4=34 diamonds, leaving 2 extra diamonds. That's fair. Theseus says that one of them belongs to him, since he gave it before, and the other one also belongs to him, as a reward for solving the puzzle. The naive sons of the jewell maker are thrilled by the solution, and they gladly give him the diamonds. It's only after they talk to their lawyer that they realize it's an illegitimate solution, and the imposter who took their 2 diamonds is arrested.
     
  2. jcsd
  3. Jun 20, 2016 #2

    Simon Bridge

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    1/2 + 1/3 + 1/9 does not add up to 1 ... probably to 1/36th part less than 1. (Oh look, it's 2/36ths short)
    That was Theseus can loan them his diamond, do the maths, divide the diamonds, and end up with the diamonds left over.
    Then he claimes the extra diamond as his interest on the loan.

    You can also compare Theseus' solution with how much each would end up with if they just agreed to round off the numbers.

    This sort of problem seems silly until you read the inheritance rules in the Quran.
     
  4. Jun 21, 2016 #3
    Yeah, that's it. The book I took it from took place in Arabia, so it was probably inspired by those inheritance rules!
     
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