Monday, September 08, 2008

Three sequences

Here are three finite sequences. There is no next element, I give you the complete sequence. What rule did I use to form these sequences?
  1. 8,5,4,9,1,7,6,3,2
  2. 8,5,1,4,9,2,7,6,3
  3. a,i,s,e,t,d,m,c,o,l,p,n,x,v,b,w,y,f,r,u,k,g,z,h,j,q

8 comments:

  1. Sequence 1 seems to be the the numbers 1-9 in English alphabetical order. It is even listed as such in Sloane's, but I already knew this `riddle' from highschool. (Though in Holland it is 8 3 1 9 2 4 5 6 7, for ``acht drie een negen twee vier vijf zes zeven'')
    Second one doesn't show up in Sloane.

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  2. Only 1 and 2 moved...

    8th,5th,1st,4th,9th,2nd,7th,6th,3rd.

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  3. Second sequence is ordinals alphabetized, just as first sequence is cardinals alphabetized.

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  4. Third sequence looks vaguely like letter frequencies, although if it is, either the source text is really odd or the language isn't English... possibly Esperanto?

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  5. Since these are finite sequences, I can always fit a polynomial and there is nothing more significant than that.

    So, no matter what rule you chose to generate them I can interpret that rule as a polynomial function and nothing more.

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  6. First sequence is indeed
    the numbers in alph order.
    Second sequence is indeed
    the ordinals in alph order.
    The third sequence is
    sortof freq-- I typed
    a, b, c, ... into google
    and this is the number of
    hits in order.

    YES, any finite sequence
    has some poly that generates it. I was looking
    for the ``best explanation''. Not sure
    that can be rigorously defined, perhaps with
    Kolg theory.

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  7. The 3rd is pretty close to the count of results from Google. It is worth noting that since that's a moving target it doesn't make a great question. Right now, Google is reporting more results for o then c and more for b then v, and I only checked half the letters.

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  8. What I'm curious about is this: say you type numbers at random and ask people to "explain" the sequence. What kind of answers would people come up with?

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