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Somewhat Simple Pattern

  1. May 23, 2005 #1
    1, 4, 9, 6, 5, 6, 9, 4, 1, 0, 1, 4, _, _, _

    What are the three blanks? And why?
     
  2. jcsd
  3. May 23, 2005 #2
    The numbers are the last digits of the squares. The next squares are 169, 196, 225, so the next numbers are 9, 6, 5
     
  4. May 23, 2005 #3
    Next three are 9, 6, 5. Differences between two are antisymmetrical

    3, 5, -3, -1, | 1, 3, -5, -3, -1 | 1, 3, _ _ _

    If you flip marked section, and invert the signs, you get 1, 3 (already there) and then 5, -3, -1.

    Last number was 4 so
    4
    +5 = 9
    -3 = 6
    -1 = 5
     
  5. May 23, 2005 #4
    LOL... that's pretty funny... I didn't even notice that. :biggrin:
    The answer I was looking for was given by BicycleTree.
     
  6. May 23, 2005 #5
    I was pretty surprised that this one had two answers. But probably a number theorist wouldn't be. And I'll leave it to one to prove the answers are equivalent ;)
     
  7. May 24, 2005 #6
    do atrus's answer match with bicycletree answer, for the next 5 sets?
     
  8. May 24, 2005 #7
    Yes they do! :) Sequence of differences is 1 3 5 -3 -1 (first number in line being 0), then you flip it and change signs to get 1 3 -5 -3 -1. And then you do it again, so initial sequence appears. As you can see, only the middle number's sign (+-5) is changed. And it fits quite nicely to series of squares... next five numbers would be 6 9 4 1 0, according to both explanations :) It has been some time that I've taken discrete mathematics course, so I'm a bit rusty in number theory to prove the equivalence. Still, the challenge stands :)
     
  9. May 25, 2005 #8
    what a great co incidence ^^
     
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