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Posers and Puzzles

Posers and Puzzles

  1. 13 Dec '03 21:20 / 1 edit
    take any four digit number where all the digits are not the same. rearrange them to make the largest # possible. Rearrange them again to make the smallest # possible. Subtract the smaller # from the larger #. Take the result and do it all over again. repeat this process until you hit 6714, you should get stuck there. if you ever get a result less than four digits put a zero in front of it. (999 would be 0999).



    Ex. 2372

    7322 - 2237 = 5085

    8500 - 5058 = 3442

    4432 - 2344 = 2088

    8802 - 2088 = 6714

    Why is this?
  2. Standard member TheMaster37
    Kupikupopo!
    14 Dec '03 10:58
    Originally posted by palomine
    take any four digit number where all the digits are not the same. rearrange them to make the largest # possible. Rearrange them again to make the smallest # possible. Subtract the smaller # from the larger #. Take the result and do it all over again. repeat this process until you hit 6714, you should get stuck there. if you ever get a result less than fo ...[text shortened]... - 2237 = 5085

    8500 - 5058 = 3442

    4432 - 2344 = 2088

    8802 - 2088 = 6714

    Why is this?
    A guess i haven't proved yet; because of these calculations you cycle through all numbers there are. As soon as you have the 1467 you end up in a cycle;

    7641-1467=6174
  3. Standard member Fiathahel
    Artist in Drawing
    15 Dec '03 15:24
    I don't why it is true, but it is easy to prove that all numbers you get are divisible by 9. This is cause the sum of the digits modulo 9 equals the number itslef modulo 9. And the first are the same for both numbers so the difference always equas 0 modulo 9.
    Perhaps this might help a bit.

    Steffin