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What's common between the numbers 0 1 8 11 69 88 96 101?

  1. Nov 8, 2007 #1
    Well, this isn't a brain teaser really, but I'll leave what I want to say in #ededed for anyone who might wish to "solve" it themselves.

    What's common between the numbers 0 1 8 11 69 88 96 101? (This is the actual question I saw)

    >
    The answer provided was that they all remain the same even if you looked at them upside down. (Okay, it may not be true in a particular font, but you get the gist.) This isn't the interesting part; what's interesting is that every number apart from the first 0 is formed by the sum of the differences between the previous pairs of numbers, including the pair formed by the current number and the one preceeding it.

    1 = 1-0
    8 = (8-1) + (1-0)
    11 = (11-8) + (8-1) + (1-0)
    ...
    ...

    Just a curiosity [on the way "invertible" integers are arranged] I thought I would share with other geeks. :D
    <
     
  2. jcsd
  3. Nov 8, 2007 #2
    All sequences of numbers that begin with zero have that second property. Just list out some numbers at random and see. Or better yet, consider the following rearrangement:


    11 = (11-8) + (8-1) + (1-0)
    11 = 11 (- 8 + 8) (- 1 + 1) - 0

    eom
     
    Last edited: Nov 8, 2007
  4. Nov 8, 2007 #3
    True. I knew I was missing something really simple there. :)
     
  5. Nov 8, 2007 #4
    They're such that : (self-adjoint)
    [tex] A = A^\dagger [/tex]
     
  6. Nov 15, 2007 #5
    They Are All Symetrical!
     
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