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A sequence of sorts

  1. Aug 4, 2005 #1
    1
    2
    1 2
    4
    1 1 3
    6
    1 2 4
    ???

    What comes next?
     
  2. jcsd
  3. Aug 4, 2005 #2
    Answer (in white):
    8 (a partition of 8, but the even numbers are partitioned into a single partition). I haven't figured out how the odd numbers are partitioned, but it seems that the entry for 2^n - 1 is 1 2 4 ... 2^(n-1)
     
  4. Aug 4, 2005 #3
    Nope, that's not it. But that's an interesting observation about the partitions! I hadn't noticed that.
     
  5. Aug 8, 2005 #4
    8, i am not sure what the real pattern is but looking from the most left number in each line, 1,2,1,4,1,6,1,... one could easily guess 8
     
  6. Aug 8, 2005 #5
    Worth a shot.
    [Answer in white]

    Answer: 16

    It increases the first number by one then multiply it with the rest.
    ie:
    1 2 4
    (1+1) * 2 * 4 = 16
     
  7. Aug 8, 2005 #6
    Spoiler warning:

    The answer is 16. Or so I think, if my way is allowed.

    1
    2
    1 2
    4
    1 1 3
    6
    1 2 4
    ???

    seperate the lines into groups just to understand it better:

    1
    2
    --------
    1 2
    4
    --------
    1 1 3
    6
    ------
    1 2 4
    ???

    Multiply the top lines digits by themselves and then by two:
    (a*b)*2

    so the first line:
    (1)*2=2

    and the second & third:
    (1*2)*2=4

    (1*1*3)*2=6


    So for the bottom line you get:
    (1*2*4)*2=16



    Is that a logical answer?
     
  8. Aug 9, 2005 #7
    so you are saying that the top line in each group generated by random ?
     
  9. Aug 15, 2005 #8
    Nope, none of the answers so far are correct. Jimmysnyder was the closest with his comment about the partitions.

    Maybe there isn't quite enough information.

    Here's the pattern a bit longer:

    1
    2
    1 2
    4
    1 1 3
    6
    1 2 4
    2 6
    1 3 5
    10
    ???

    What comes next?
     
  10. Aug 23, 2005 #9
    Moo, how about more clues, or an answer?
     
  11. Aug 23, 2005 #10
    Sure. Here's quite a bit more of the sequence:

    1
    2
    1 2
    4
    1 1 3
    6
    1 2 4
    2 6
    1 3 5
    10
    1 1 1 2 6
    12
    1 5 7
    ???

    Still want a clue? Partitions are correct. But think of the sequence as starting from 2 rather than 1...
     
  12. Aug 24, 2005 #11
    a 16 year olds guess....lol



    4 10
    1 2 4 8
    16


    ??
     
    Last edited: Aug 24, 2005
  13. Aug 25, 2005 #12
    Close. The second two are correct, but 4 10 is not. Care to explain your answer?
     
  14. Aug 25, 2005 #13
    ummm lol nope - im not good at explain them

    ok its sumthin like 4 10...but the numbers add up to 14? i spent about 20 mins workin it out lol ill get it when i get time
     
  15. Aug 25, 2005 #14
    Yeah, the numbers add up to 14 but they're not 4 10.
     
  16. Aug 25, 2005 #15
    is it 2 12?
     
  17. Aug 25, 2005 #16
    and *this is gna seem really stupid* but whats partition?
     
  18. Aug 25, 2005 #17
    A partition is simply a representation of a positive integer as a sum of other positive integers. For instance 12 = 2 + 10 or 12 = 4 + 8, or 12 = 1 + 2 + 9 or in the degenerate case, 12 = 12. The sequence that Moo has presented us with can be viewed as a sequence of partitions. Here is a list of all the possible partitions of 5:

    5 = 1 + 1 + 1 + 1 + 1
    5 = 1 + 1 + 1 + 2
    5 = 1 + 1 + 3
    5 = 1 + 4
    5 = 1 + 2 + 2
    5 = 2 + 3

    I hope I didn't miss any. By the way, I didn't know what a partition was until I was about 21, so now you are 5 years ahead of me.
     
  19. Aug 25, 2005 #18
    Nope. First number is 2, though.
     
  20. Aug 26, 2005 #19
    the only reasonable guess i can think off is 2 6 6
     
  21. Aug 26, 2005 #20
    Now you're just firing blindly :P

    Nope, not 2 6 6.
     
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